This is ../../info/calc, produced by makeinfo version 4.11 from calc.texi. This file documents Calc, the GNU Emacs calculator. Copyright (C) 1990, 1991, 2001, 2002, 2003, 2004, 2005, 2006, 2007, 2008, 2009, 2010 Free Software Foundation, Inc. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with the Invariant Sections being just "GNU GENERAL PUBLIC LICENSE", with the Front-Cover texts being "A GNU Manual," and with the Back-Cover Texts as in (a) below. A copy of the license is included in the section entitled "GNU Free Documentation License." (a) The FSF's Back-Cover Text is: "You have the freedom to copy and modify this GNU manual. Buying copies from the FSF supports it in developing GNU and promoting software freedom." INFO-DIR-SECTION Emacs START-INFO-DIR-ENTRY * Calc: (calc). Advanced desk calculator and mathematical tool. END-INFO-DIR-ENTRY  File: calc, Node: Interactive Lisp Functions, Next: Stack Lisp Functions, Prev: Data Type Formats, Up: Internals 19.5.7.2 Interactive Functions .............................. The functions described here are used in implementing interactive Calc commands. Note that this list is not exhaustive! If there is an existing command that behaves similarly to the one you want to define, you may find helpful tricks by checking the source code for that command. -- Function: calc-set-command-flag flag Set the command flag FLAG. This is generally a Lisp symbol, but may in fact be anything. The effect is to add FLAG to the list stored in the variable `calc-command-flags', unless it is already there. *Note Defining Simple Commands::. -- Function: calc-clear-command-flag flag If FLAG appears among the list of currently-set command flags, remove it from that list. -- Function: calc-record-undo rec Add the "undo record" REC to the list of steps to take if the current operation should need to be undone. Stack push and pop functions automatically call `calc-record-undo', so the kinds of undo records you might need to create take the form `(set SYM VALUE)', which says that the Lisp variable SYM was changed and had previously contained VALUE; `(store VAR VALUE)' which says that the Calc variable VAR (a string which is the name of the symbol that contains the variable's value) was stored and its previous value was VALUE (either a Calc data object, or `nil' if the variable was previously void); or `(eval UNDO REDO ARGS ...)', which means that to undo requires calling the function `(UNDO ARGS ...)' and, if the undo is later redone, calling `(REDO ARGS ...)'. -- Function: calc-record-why msg args Record the error or warning message MSG, which is normally a string. This message will be replayed if the user types `w' (`calc-why'); if the message string begins with a `*', it is considered important enough to display even if the user doesn't type `w'. If one or more ARGS are present, the displayed message will be of the form, `MSG: ARG1, ARG2, ...', where the arguments are formatted on the assumption that they are either strings or Calc objects of some sort. If MSG is a symbol, it is the name of a Calc predicate (such as `integerp' or `numvecp') which the arguments did not satisfy; it is expanded to a suitable string such as "Expected an integer." The `reject-arg' function calls `calc-record-why' automatically; *note Predicates::. -- Function: calc-is-inverse This predicate returns true if the current command is inverse, i.e., if the Inverse (`I' key) flag was set. -- Function: calc-is-hyperbolic This predicate is the analogous function for the `H' key.  File: calc, Node: Stack Lisp Functions, Next: Predicates, Prev: Interactive Lisp Functions, Up: Internals 19.5.7.3 Stack-Oriented Functions ................................. The functions described here perform various operations on the Calc stack and trail. They are to be used in interactive Calc commands. -- Function: calc-push-list vals n Push the Calc objects in list VALS onto the stack at stack level N. If N is omitted it defaults to 1, so that the elements are pushed at the top of the stack. If N is greater than 1, the elements will be inserted into the stack so that the last element will end up at level N, the next-to-last at level N+1, etc. The elements of VALS are assumed to be valid Calc objects, and are not evaluated, rounded, or renormalized in any way. If VALS is an empty list, nothing happens. The stack elements are pushed without any sub-formula selections. You can give an optional third argument to this function, which must be a list the same size as VALS of selections. Each selection must be `eq' to some sub-formula of the corresponding formula in VALS, or `nil' if that formula should have no selection. -- Function: calc-top-list n m Return a list of the N objects starting at level M of the stack. If M is omitted it defaults to 1, so that the elements are taken from the top of the stack. If N is omitted, it also defaults to 1, so that the top stack element (in the form of a one-element list) is returned. If M is greater than 1, the Mth stack element will be at the end of the list, the M+1st element will be next-to-last, etc. If N or M are out of range, the command is aborted with a suitable error message. If N is zero, the function returns an empty list. The stack elements are not evaluated, rounded, or renormalized. If any stack elements contain selections, and selections have not been disabled by the `j e' (`calc-enable-selections') command, this function returns the selected portions rather than the entire stack elements. It can be given a third "selection-mode" argument which selects other behaviors. If it is the symbol `t', then a selection in any of the requested stack elements produces an "invalid operation on selections" error. If it is the symbol `full', the whole stack entry is always returned regardless of selections. If it is the symbol `sel', the selected portion is always returned, or `nil' if there is no selection. (This mode ignores the `j e' command.) If the symbol is `entry', the complete stack entry in list form is returned; the first element of this list will be the whole formula, and the third element will be the selection (or `nil'). -- Function: calc-pop-stack n m Remove the specified elements from the stack. The parameters N and M are defined the same as for `calc-top-list'. The return value of `calc-pop-stack' is uninteresting. If there are any selected sub-formulas among the popped elements, and `j e' has not been used to disable selections, this produces an error without changing the stack. If you supply an optional third argument of `t', the stack elements are popped even if they contain selections. -- Function: calc-record-list vals tag This function records one or more results in the trail. The VALS are a list of strings or Calc objects. The TAG is the four-character tag string to identify the values. If TAG is omitted, a blank tag will be used. -- Function: calc-normalize n This function takes a Calc object and "normalizes" it. At the very least this involves re-rounding floating-point values according to the current precision and other similar jobs. Also, unless the user has selected No-Simplify mode (*note Simplification Modes::), this involves actually evaluating a formula object by executing the function calls it contains, and possibly also doing algebraic simplification, etc. -- Function: calc-top-list-n n m This function is identical to `calc-top-list', except that it calls `calc-normalize' on the values that it takes from the stack. They are also passed through `check-complete', so that incomplete objects will be rejected with an error message. All computational commands should use this in preference to `calc-top-list'; the only standard Calc commands that operate on the stack without normalizing are stack management commands like `calc-enter' and `calc-roll-up'. This function accepts the same optional selection-mode argument as `calc-top-list'. -- Function: calc-top-n m This function is a convenient form of `calc-top-list-n' in which only a single element of the stack is taken and returned, rather than a list of elements. This also accepts an optional selection-mode argument. -- Function: calc-enter-result n tag vals This function is a convenient interface to most of the above functions. The VALS argument should be either a single Calc object, or a list of Calc objects; the object or objects are normalized, and the top N stack entries are replaced by the normalized objects. If TAG is non-`nil', the normalized objects are also recorded in the trail. A typical stack-based computational command would take the form, (calc-enter-result N TAG (cons 'calcFunc-FUNC (calc-top-list-n N))) If any of the N stack elements replaced contain sub-formula selections, and selections have not been disabled by `j e', this function takes one of two courses of action. If N is equal to the number of elements in VALS, then each element of VALS is spliced into the corresponding selection; this is what happens when you use the key, or when you use a unary arithmetic operation like `sqrt'. If VALS has only one element but N is greater than one, there must be only one selection among the top N stack elements; the element from VALS is spliced into that selection. This is what happens when you use a binary arithmetic operation like `+'. Any other combination of N and VALS is an error when selections are present. -- Function: calc-unary-op tag func arg This function implements a unary operator that allows a numeric prefix argument to apply the operator over many stack entries. If the prefix argument ARG is `nil', this uses `calc-enter-result' as outlined above. Otherwise, it maps the function over several stack elements; *note Prefix Arguments::. For example, (defun calc-zeta (arg) (interactive "P") (calc-unary-op "zeta" 'calcFunc-zeta arg)) -- Function: calc-binary-op tag func arg ident unary This function implements a binary operator, analogously to `calc-unary-op'. The optional IDENT and UNARY arguments specify the behavior when the prefix argument is zero or one, respectively. If the prefix is zero, the value IDENT is pushed onto the stack, if specified, otherwise an error message is displayed. If the prefix is one, the unary function UNARY is applied to the top stack element, or, if UNARY is not specified, nothing happens. When the argument is two or more, the binary function FUNC is reduced across the top ARG stack elements; when the argument is negative, the function is mapped between the next-to-top -ARG stack elements and the top element. -- Function: calc-stack-size Return the number of elements on the stack as an integer. This count does not include elements that have been temporarily hidden by stack truncation; *note Truncating the Stack::. -- Function: calc-cursor-stack-index n Move the point to the Nth stack entry. If N is zero, this will be the `.' line. If N is from 1 to the current stack size, this will be the beginning of the first line of that stack entry's display. If line numbers are enabled, this will move to the first character of the line number, not the stack entry itself. -- Function: calc-substack-height n Return the number of lines between the beginning of the Nth stack entry and the bottom of the buffer. If N is zero, this will be one (assuming no stack truncation). If all stack entries are one line long (i.e., no matrices are displayed), the return value will be equal N+1 as long as N is in range. (Note that in Big mode, the return value includes the blank lines that separate stack entries.) -- Function: calc-refresh Erase the `*Calculator*' buffer and reformat its contents from memory. This must be called after changing any parameter, such as the current display radix, which might change the appearance of existing stack entries. (During a keyboard macro invoked by the `X' key, refreshing is suppressed, but a flag is set so that the entire stack will be refreshed rather than just the top few elements when the macro finishes.)  File: calc, Node: Predicates, Next: Computational Lisp Functions, Prev: Stack Lisp Functions, Up: Internals 19.5.7.4 Predicates ................... The functions described here are predicates, that is, they return a true/false value where `nil' means false and anything else means true. These predicates are expanded by `defmath', for example, from `zerop' to `math-zerop'. In many cases they correspond to native Lisp functions by the same name, but are extended to cover the full range of Calc data types. -- Function: zerop x Returns true if X is numerically zero, in any of the Calc data types. (Note that for some types, such as error forms and intervals, it never makes sense to return true.) In `defmath', the expression `(= x 0)' will automatically be converted to `(math-zerop x)', and `(/= x 0)' will be converted to `(not (math-zerop x))'. -- Function: negp x Returns true if X is negative. This accepts negative real numbers of various types, negative HMS and date forms, and intervals in which all included values are negative. In `defmath', the expression `(< x 0)' will automatically be converted to `(math-negp x)', and `(>= x 0)' will be converted to `(not (math-negp x))'. -- Function: posp x Returns true if X is positive (and non-zero). For complex numbers, none of these three predicates will return true. -- Function: looks-negp x Returns true if X is "negative-looking." This returns true if X is a negative number, or a formula with a leading minus sign such as `-a/b'. In other words, this is an object which can be made simpler by calling `(- X)'. -- Function: integerp x Returns true if X is an integer of any size. -- Function: fixnump x Returns true if X is a native Lisp integer. -- Function: natnump x Returns true if X is a nonnegative integer of any size. -- Function: fixnatnump x Returns true if X is a nonnegative Lisp integer. -- Function: num-integerp x Returns true if X is numerically an integer, i.e., either a true integer or a float with no significant digits to the right of the decimal point. -- Function: messy-integerp x Returns true if X is numerically, but not literally, an integer. A value is `num-integerp' if it is `integerp' or `messy-integerp' (but it is never both at once). -- Function: num-natnump x Returns true if X is numerically a nonnegative integer. -- Function: evenp x Returns true if X is an even integer. -- Function: looks-evenp x Returns true if X is an even integer, or a formula with a leading multiplicative coefficient which is an even integer. -- Function: oddp x Returns true if X is an odd integer. -- Function: ratp x Returns true if X is a rational number, i.e., an integer or a fraction. -- Function: realp x Returns true if X is a real number, i.e., an integer, fraction, or floating-point number. -- Function: anglep x Returns true if X is a real number or HMS form. -- Function: floatp x Returns true if X is a float, or a complex number, error form, interval, date form, or modulo form in which at least one component is a float. -- Function: complexp x Returns true if X is a rectangular or polar complex number (but not a real number). -- Function: rect-complexp x Returns true if X is a rectangular complex number. -- Function: polar-complexp x Returns true if X is a polar complex number. -- Function: numberp x Returns true if X is a real number or a complex number. -- Function: scalarp x Returns true if X is a real or complex number or an HMS form. -- Function: vectorp x Returns true if X is a vector (this simply checks if its argument is a list whose first element is the symbol `vec'). -- Function: numvecp x Returns true if X is a number or vector. -- Function: matrixp x Returns true if X is a matrix, i.e., a vector of one or more vectors, all of the same size. -- Function: square-matrixp x Returns true if X is a square matrix. -- Function: objectp x Returns true if X is any numeric Calc object, including real and complex numbers, HMS forms, date forms, error forms, intervals, and modulo forms. (Note that error forms and intervals may include formulas as their components; see `constp' below.) -- Function: objvecp x Returns true if X is an object or a vector. This also accepts incomplete objects, but it rejects variables and formulas (except as mentioned above for `objectp'). -- Function: primp x Returns true if X is a "primitive" or "atomic" Calc object, i.e., one whose components cannot be regarded as sub-formulas. This includes variables, and all `objectp' types except error forms and intervals. -- Function: constp x Returns true if X is constant, i.e., a real or complex number, HMS form, date form, or error form, interval, or vector all of whose components are `constp'. -- Function: lessp x y Returns true if X is numerically less than Y. Returns false if X is greater than or equal to Y, or if the order is undefined or cannot be determined. Generally speaking, this works by checking whether `X - Y' is `negp'. In `defmath', the expression `(< x y)' will automatically be converted to `(lessp x y)'; expressions involving `>', `<=', and `>=' are similarly converted in terms of `lessp'. -- Function: beforep x y Returns true if X comes before Y in a canonical ordering of Calc objects. If X and Y are both real numbers, this will be the same as `lessp'. But whereas `lessp' considers other types of objects to be unordered, `beforep' puts any two objects into a definite, consistent order. The `beforep' function is used by the `V S' vector-sorting command, and also by `a s' to put the terms of a product into canonical order: This allows `x y + y x' to be simplified easily to `2 x y'. -- Function: equal x y This is the standard Lisp `equal' predicate; it returns true if X and Y are structurally identical. This is the usual way to compare numbers for equality, but note that `equal' will treat 0 and 0.0 as different. -- Function: math-equal x y Returns true if X and Y are numerically equal, either because they are `equal', or because their difference is `zerop'. In `defmath', the expression `(= x y)' will automatically be converted to `(math-equal x y)'. -- Function: equal-int x n Returns true if X and N are numerically equal, where N is a fixnum which is not a multiple of 10. This will automatically be used by `defmath' in place of the more general `math-equal' whenever possible. -- Function: nearly-equal x y Returns true if X and Y, as floating-point numbers, are equal except possibly in the last decimal place. For example, 314.159 and 314.166 are considered nearly equal if the current precision is 6 (since they differ by 7 units), but not if the current precision is 7 (since they differ by 70 units). Most functions which use series expansions use `with-extra-prec' to evaluate the series with 2 extra digits of precision, then use `nearly-equal' to decide when the series has converged; this guards against cumulative error in the series evaluation without doing extra work which would be lost when the result is rounded back down to the current precision. In `defmath', this can be written `(~= X Y)'. The X and Y can be numbers of any kind, including complex. -- Function: nearly-zerop x y Returns true if X is nearly zero, compared to Y. This checks whether X plus Y would by be `nearly-equal' to Y itself, to within the current precision, in other words, if adding X to Y would have a negligible effect on Y due to roundoff error. X may be a real or complex number, but Y must be real. -- Function: is-true x Return true if the formula X represents a true value in Calc, not Lisp, terms. It tests if X is a non-zero number or a provably non-zero formula. -- Function: reject-arg val pred Abort the current function evaluation due to unacceptable argument values. This calls `(calc-record-why PRED VAL)', then signals a Lisp error which `normalize' will trap. The net effect is that the function call which led here will be left in symbolic form. -- Function: inexact-value If Symbolic mode is enabled, this will signal an error that causes `normalize' to leave the formula in symbolic form, with the message "Inexact result." (This function has no effect when not in Symbolic mode.) Note that if your function calls `(sin 5)' in Symbolic mode, the `sin' function will call `inexact-value', which will cause your function to be left unsimplified. You may instead wish to call `(normalize (list 'calcFunc-sin 5))', which in Symbolic mode will return the formula `sin(5)' to your function. -- Function: overflow This signals an error that will be reported as a floating-point overflow. -- Function: underflow This signals a floating-point underflow.  File: calc, Node: Computational Lisp Functions, Next: Vector Lisp Functions, Prev: Predicates, Up: Internals 19.5.7.5 Computational Functions ................................ The functions described here do the actual computational work of the Calculator. In addition to these, note that any function described in the main body of this manual may be called from Lisp; for example, if the documentation refers to the `calc-sqrt' [`sqrt'] command, this means `calc-sqrt' is an interactive stack-based square-root command and `sqrt' (which `defmath' expands to `calcFunc-sqrt') is the actual Lisp function for taking square roots. The functions `math-add', `math-sub', `math-mul', `math-div', `math-mod', and `math-neg' are not included in this list, since `defmath' allows you to write native Lisp `+', `-', `*', `/', `%', and unary `-', respectively, instead. -- Function: normalize val (Full form: `math-normalize'.) Reduce the value VAL to standard form. For example, if VAL is a fixnum, it will be converted to a bignum if it is too large, and if VAL is a bignum it will be normalized by clipping off trailing (i.e., most-significant) zero digits and converting to a fixnum if it is small. All the various data types are similarly converted to their standard forms. Variables are left alone, but function calls are actually evaluated in formulas. For example, normalizing `(+ 2 (calcFunc-abs -4))' will return 6. If a function call fails, because the function is void or has the wrong number of parameters, or because it returns `nil' or calls `reject-arg' or `inexact-result', `normalize' returns the formula still in symbolic form. If the current simplification mode is "none" or "numeric arguments only," `normalize' will act appropriately. However, the more powerful simplification modes (like Algebraic Simplification) are not handled by `normalize'. They are handled by `calc-normalize', which calls `normalize' and possibly some other routines, such as `simplify' or `simplify-units'. Programs generally will never call `calc-normalize' except when popping or pushing values on the stack. -- Function: evaluate-expr expr Replace all variables in EXPR that have values with their values, then use `normalize' to simplify the result. This is what happens when you press the `=' key interactively. -- Macro: with-extra-prec n body Evaluate the Lisp forms in BODY with precision increased by N digits. This is a macro which expands to (math-normalize (let ((calc-internal-prec (+ calc-internal-prec N))) BODY)) The surrounding call to `math-normalize' causes a floating-point result to be rounded down to the original precision afterwards. This is important because some arithmetic operations assume a number's mantissa contains no more digits than the current precision allows. -- Function: make-frac n d Build a fraction `N:D'. This is equivalent to calling `(normalize (list 'frac N D))', but more efficient. -- Function: make-float mant exp Build a floating-point value out of MANT and EXP, both of which are arbitrary integers. This function will return a properly normalized float value, or signal an overflow or underflow if EXP is out of range. -- Function: make-sdev x sigma Build an error form out of X and the absolute value of SIGMA. If SIGMA is zero, the result is the number X directly. If SIGMA is negative or complex, its absolute value is used. If X or SIGMA is not a valid type of object for use in error forms, this calls `reject-arg'. -- Function: make-intv mask lo hi Build an interval form out of MASK (which is assumed to be an integer from 0 to 3), and the limits LO and HI. If LO is greater than HI, an empty interval form is returned. This calls `reject-arg' if LO or HI is unsuitable. -- Function: sort-intv mask lo hi Build an interval form, similar to `make-intv', except that if LO is less than HI they are simply exchanged, and the bits of MASK are swapped accordingly. -- Function: make-mod n m Build a modulo form out of N and the modulus M. Since modulo forms do not allow formulas as their components, if N or M is not a real number or HMS form the result will be a formula which is a call to `makemod', the algebraic version of this function. -- Function: float x Convert X to floating-point form. Integers and fractions are converted to numerically equivalent floats; components of complex numbers, vectors, HMS forms, date forms, error forms, intervals, and modulo forms are recursively floated. If the argument is a variable or formula, this calls `reject-arg'. -- Function: compare x y Compare the numbers X and Y, and return -1 if `(lessp X Y)', 1 if `(lessp Y X)', 0 if `(math-equal X Y)', or 2 if the order is undefined or cannot be determined. -- Function: numdigs n Return the number of digits of integer N, effectively `ceil(log10(N))', but much more efficient. Zero is considered to have zero digits. -- Function: scale-int x n Shift integer X left N decimal digits, or right -N digits with truncation toward zero. -- Function: scale-rounding x n Like `scale-int', except that a right shift rounds to the nearest integer rather than truncating. -- Function: fixnum n Return the integer N as a fixnum, i.e., a native Lisp integer. If N is outside the permissible range for Lisp integers (usually 24 binary bits) the result is undefined. -- Function: sqr x Compute the square of X; short for `(* X X)'. -- Function: quotient x y Divide integer X by integer Y; return an integer quotient and discard the remainder. If X or Y is negative, the direction of rounding is undefined. -- Function: idiv x y Perform an integer division; if X and Y are both nonnegative integers, this uses the `quotient' function, otherwise it computes `floor(X/Y)'. Thus the result is well-defined but slower than for `quotient'. -- Function: imod x y Divide integer X by integer Y; return the integer remainder and discard the quotient. Like `quotient', this works only for integer arguments and is not well-defined for negative arguments. For a more well-defined result, use `(% X Y)'. -- Function: idivmod x y Divide integer X by integer Y; return a cons cell whose `car' is `(quotient X Y)' and whose `cdr' is `(imod X Y)'. -- Function: pow x y Compute X to the power Y. In `defmath' code, this can also be written `(^ X Y)' or `(expt X Y)'. -- Function: abs-approx x Compute a fast approximation to the absolute value of X. For example, for a rectangular complex number the result is the sum of the absolute values of the components. -- Function: pi The function `(pi)' computes `pi' to the current precision. Other related constant-generating functions are `two-pi', `pi-over-2', `pi-over-4', `pi-over-180', `sqrt-two-pi', `e', `sqrt-e', `ln-2', `ln-10', `phi' and `gamma-const'. Each function returns a floating-point value in the current precision, and each uses caching so that all calls after the first are essentially free. -- Macro: math-defcache FUNC INITIAL FORM This macro, usually used as a top-level call like `defun' or `defvar', defines a new cached constant analogous to `pi', etc. It defines a function `func' which returns the requested value; if INITIAL is non-`nil' it must be a `(float ...)' form which serves as an initial value for the cache. If FUNC is called when the cache is empty or does not have enough digits to satisfy the current precision, the Lisp expression FORM is evaluated with the current precision increased by four, and the result minus its two least significant digits is stored in the cache. For example, calling `(pi)' with a precision of 30 computes `pi' to 34 digits, rounds it down to 32 digits for future use, then rounds it again to 30 digits for use in the present request. -- Function: full-circle symb If the current angular mode is Degrees or HMS, this function returns the integer 360. In Radians mode, this function returns either the corresponding value in radians to the current precision, or the formula `2*pi', depending on the Symbolic mode. There are also similar function `half-circle' and `quarter-circle'. -- Function: power-of-2 n Compute two to the integer power N, as a (potentially very large) integer. Powers of two are cached, so only the first call for a particular N is expensive. -- Function: integer-log2 n Compute the base-2 logarithm of N, which must be an integer which is a power of two. If N is not a power of two, this function will return `nil'. -- Function: div-mod a b m Divide A by B, modulo M. This returns `nil' if there is no solution, or if any of the arguments are not integers. -- Function: pow-mod a b m Compute A to the power B, modulo M. If A, B, and M are integers, this uses an especially efficient algorithm. Otherwise, it simply computes `(% (^ a b) m)'. -- Function: isqrt n Compute the integer square root of N. This is the square root of N rounded down toward zero, i.e., `floor(sqrt(N))'. If N is itself an integer, the computation is especially efficient. -- Function: to-hms a ang Convert the argument A into an HMS form. If ANG is specified, it is the angular mode in which to interpret A, either `deg' or `rad'. Otherwise, the current angular mode is used. If A is already an HMS form it is returned as-is. -- Function: from-hms a ang Convert the HMS form A into a real number. If ANG is specified, it is the angular mode in which to express the result, otherwise the current angular mode is used. If A is already a real number, it is returned as-is. -- Function: to-radians a Convert the number or HMS form A to radians from the current angular mode. -- Function: from-radians a Convert the number A from radians to the current angular mode. If A is a formula, this returns the formula `deg(A)'. -- Function: to-radians-2 a Like `to-radians', except that in Symbolic mode a degrees to radians conversion yields a formula like `A*pi/180'. -- Function: from-radians-2 a Like `from-radians', except that in Symbolic mode a radians to degrees conversion yields a formula like `A*180/pi'. -- Function: random-digit Produce a random base-1000 digit in the range 0 to 999. -- Function: random-digits n Produce a random N-digit integer; this will be an integer in the interval `[0, 10^N)'. -- Function: random-float Produce a random float in the interval `[0, 1)'. -- Function: prime-test n iters Determine whether the integer N is prime. Return a list which has one of these forms: `(nil F)' means the number is non-prime because it was found to be divisible by F; `(nil)' means it was found to be non-prime by table look-up (so no factors are known); `(nil unknown)' means it is definitely non-prime but no factors are known because N was large enough that Fermat's probabilistic test had to be used; `(t)' means the number is definitely prime; and `(maybe I P)' means that Fermat's test, after I iterations, is P percent sure that the number is prime. The ITERS parameter is the number of Fermat iterations to use, in the case that this is necessary. If `prime-test' returns "maybe," you can call it again with the same N to get a greater certainty; `prime-test' remembers where it left off. -- Function: to-simple-fraction f If F is a floating-point number which can be represented exactly as a small rational number. return that number, else return F. For example, 0.75 would be converted to 3:4. This function is very fast. -- Function: to-fraction f tol Find a rational approximation to floating-point number F to within a specified tolerance TOL; this corresponds to the algebraic function `frac', and can be rather slow. -- Function: quarter-integer n If N is an integer or integer-valued float, this function returns zero. If N is a half-integer (i.e., an integer plus 1:2 or 0.5), it returns 2. If N is a quarter-integer, it returns 1 or 3. If N is anything else, this function returns `nil'.  File: calc, Node: Vector Lisp Functions, Next: Symbolic Lisp Functions, Prev: Computational Lisp Functions, Up: Internals 19.5.7.6 Vector Functions ......................... The functions described here perform various operations on vectors and matrices. -- Function: math-concat x y Do a vector concatenation; this operation is written `X | Y' in a symbolic formula. *Note Building Vectors::. -- Function: vec-length v Return the length of vector V. If V is not a vector, the result is zero. If V is a matrix, this returns the number of rows in the matrix. -- Function: mat-dimens m Determine the dimensions of vector or matrix M. If M is not a vector, the result is an empty list. If M is a plain vector but not a matrix, the result is a one-element list containing the length of the vector. If M is a matrix with R rows and C columns, the result is the list `(R C)'. Higher-order tensors produce lists of more than two dimensions. Note that the object `[[1, 2, 3], [4, 5]]' is a vector of vectors not all the same size, and is treated by this and other Calc routines as a plain vector of two elements. -- Function: dimension-error Abort the current function with a message of "Dimension error." The Calculator will leave the function being evaluated in symbolic form; this is really just a special case of `reject-arg'. -- Function: build-vector args Return a Calc vector with ARGS as elements. For example, `(build-vector 1 2 3)' returns the Calc vector `[1, 2, 3]', stored internally as the list `(vec 1 2 3)'. -- Function: make-vec obj dims Return a Calc vector or matrix all of whose elements are equal to OBJ. For example, `(make-vec 27 3 4)' returns a 3x4 matrix filled with 27's. -- Function: row-matrix v If V is a plain vector, convert it into a row matrix, i.e., a matrix whose single row is V. If V is already a matrix, leave it alone. -- Function: col-matrix v If V is a plain vector, convert it into a column matrix, i.e., a matrix with each element of V as a separate row. If V is already a matrix, leave it alone. -- Function: map-vec f v Map the Lisp function F over the Calc vector V. For example, `(map-vec 'math-floor v)' returns a vector of the floored components of vector V. -- Function: map-vec-2 f a b Map the Lisp function F over the two vectors A and B. If A and B are vectors of equal length, the result is a vector of the results of calling `(F AI BI)' for each pair of elements AI and BI. If either A or B is a scalar, it is matched with each value of the other vector. For example, `(map-vec-2 'math-add v 1)' returns the vector V with each element increased by one. Note that using `'+' would not work here, since `defmath' does not expand function names everywhere, just where they are in the function position of a Lisp expression. -- Function: reduce-vec f v Reduce the function F over the vector V. For example, if V is `[10, 20, 30, 40]', this calls `(f (f (f 10 20) 30) 40)'. If V is a matrix, this reduces over the rows of V. -- Function: reduce-cols f m Reduce the function F over the columns of matrix M. For example, if M is `[[1, 2], [3, 4], [5, 6]]', the result is a vector of the two elements `(f (f 1 3) 5)' and `(f (f 2 4) 6)'. -- Function: mat-row m n Return the Nth row of matrix M. This is equivalent to `(elt m n)'. For a slower but safer version, use `mrow'. (*Note Extracting Elements::.) -- Function: mat-col m n Return the Nth column of matrix M, in the form of a vector. The arguments are not checked for correctness. -- Function: mat-less-row m n Return a copy of matrix M with its Nth row deleted. The number N must be in range from 1 to the number of rows in M. -- Function: mat-less-col m n Return a copy of matrix M with its Nth column deleted. -- Function: transpose m Return the transpose of matrix M. -- Function: flatten-vector v Flatten nested vector V into a vector of scalars. For example, if V is `[[1, 2, 3], [4, 5]]' the result is `[1, 2, 3, 4, 5]'. -- Function: copy-matrix m If M is a matrix, return a copy of M. This maps `copy-sequence' over the rows of M; in Lisp terms, each element of the result matrix will be `eq' to the corresponding element of M, but none of the `cons' cells that make up the structure of the matrix will be `eq'. If M is a plain vector, this is the same as `copy-sequence'. -- Function: swap-rows m r1 r2 Exchange rows R1 and R2 of matrix M in-place. In other words, unlike most of the other functions described here, this function changes M itself rather than building up a new result matrix. The return value is M, i.e., `(eq (swap-rows m 1 2) m)' is true, with the side effect of exchanging the first two rows of M.  File: calc, Node: Symbolic Lisp Functions, Next: Formatting Lisp Functions, Prev: Vector Lisp Functions, Up: Internals 19.5.7.7 Symbolic Functions ........................... The functions described here operate on symbolic formulas in the Calculator. -- Function: calc-prepare-selection num Prepare a stack entry for selection operations. If NUM is omitted, the stack entry containing the cursor is used; otherwise, it is the number of the stack entry to use. This function stores useful information about the current stack entry into a set of variables. `calc-selection-cache-num' contains the number of the stack entry involved (equal to NUM if you specified it); `calc-selection-cache-entry' contains the stack entry as a list (such as `calc-top-list' would return with `entry' as the selection mode); and `calc-selection-cache-comp' contains a special "tagged" composition (*note Formatting Lisp Functions::) which allows Calc to relate cursor positions in the buffer with their corresponding sub-formulas. A slight complication arises in the selection mechanism because formulas may contain small integers. For example, in the vector `[1, 2, 1]' the first and last elements are `eq' to each other; selections are recorded as the actual Lisp object that appears somewhere in the tree of the whole formula, but storing `1' would falsely select both `1''s in the vector. So `calc-prepare-selection' also checks the stack entry and replaces any plain integers with "complex number" lists of the form `(cplx N 0)'. This list will be displayed the same as a plain N and the change will be completely invisible to the user, but it will guarantee that no two sub-formulas of the stack entry will be `eq' to each other. Next time the stack entry is involved in a computation, `calc-normalize' will replace these lists with plain numbers again, again invisibly to the user. -- Function: calc-encase-atoms x This modifies the formula X to ensure that each part of the formula is a unique atom, using the `(cplx N 0)' trick described above. This function may use `setcar' to modify the formula in-place. -- Function: calc-find-selected-part Find the smallest sub-formula of the current formula that contains the cursor. This assumes `calc-prepare-selection' has been called already. If the cursor is not actually on any part of the formula, this returns `nil'. -- Function: calc-change-current-selection selection Change the currently prepared stack element's selection to SELECTION, which should be `eq' to some sub-formula of the stack element, or `nil' to unselect the formula. The stack element's appearance in the Calc buffer is adjusted to reflect the new selection. -- Function: calc-find-nth-part expr n Return the Nth sub-formula of EXPR. This function is used by the selection commands, and (unless `j b' has been used) treats sums and products as flat many-element formulas. Thus if EXPR is `((a + b) - c) + d', calling `calc-find-nth-part' with N equal to four will return `d'. -- Function: calc-find-parent-formula expr part Return the sub-formula of EXPR which immediately contains PART. If EXPR is `a*b + (c+1)*d' and PART is `eq' to the `c+1' term of EXPR, then this function will return `(c+1)*d'. If PART turns out not to be a sub-formula of EXPR, the function returns `nil'. If PART is `eq' to EXPR, the function returns `t'. This function does not take associativity into account. -- Function: calc-find-assoc-parent-formula expr part This is the same as `calc-find-parent-formula', except that (unless `j b' has been used) it continues widening the selection to contain a complete level of the formula. Given `a' from `((a + b) - c) + d', `calc-find-parent-formula' will return `a + b' but `calc-find-assoc-parent-formula' will return the whole expression. -- Function: calc-grow-assoc-formula expr part This expands sub-formula PART of EXPR to encompass a complete level of the formula. If PART and its immediate parent are not compatible associative operators, or if `j b' has been used, this simply returns PART. -- Function: calc-find-sub-formula expr part This finds the immediate sub-formula of EXPR which contains PART. It returns an index N such that `(calc-find-nth-part EXPR N)' would return PART. If PART is not a sub-formula of EXPR, it returns `nil'. If PART is `eq' to EXPR, it returns `t'. This function does not take associativity into account. -- Function: calc-replace-sub-formula expr old new This function returns a copy of formula EXPR, with the sub-formula that is `eq' to OLD replaced by NEW. -- Function: simplify expr Simplify the expression EXPR by applying various algebraic rules. This is what the `a s' (`calc-simplify') command uses. This always returns a copy of the expression; the structure EXPR points to remains unchanged in memory. More precisely, here is what `simplify' does: The expression is first normalized and evaluated by calling `normalize'. If any `AlgSimpRules' have been defined, they are then applied. Then the expression is traversed in a depth-first, bottom-up fashion; at each level, any simplifications that can be made are made until no further changes are possible. Once the entire formula has been traversed in this way, it is compared with the original formula (from before the call to `normalize') and, if it has changed, the entire procedure is repeated (starting with `normalize') until no further changes occur. Usually only two iterations are needed: one to simplify the formula, and another to verify that no further simplifications were possible. -- Function: simplify-extended expr Simplify the expression EXPR, with additional rules enabled that help do a more thorough job, while not being entirely "safe" in all circumstances. (For example, this mode will simplify `sqrt(x^2)' to `x', which is only valid when X is positive.) This is implemented by temporarily binding the variable `math-living-dangerously' to `t' (using a `let' form) and calling `simplify'. Dangerous simplification rules are written to check this variable before taking any action. -- Function: simplify-units expr Simplify the expression EXPR, treating variable names as units whenever possible. This works by binding the variable `math-simplifying-units' to `t' while calling `simplify'. -- Macro: math-defsimplify funcs body Register a new simplification rule; this is normally called as a top-level form, like `defun' or `defmath'. If FUNCS is a symbol (like `+' or `calcFunc-sqrt'), this simplification rule is applied to the formulas which are calls to the specified function. Or, FUNCS can be a list of such symbols; the rule applies to all functions on the list. The BODY is written like the body of a function with a single argument called `expr'. The body will be executed with `expr' bound to a formula which is a call to one of the functions FUNCS. If the function body returns `nil', or if it returns a result `equal' to the original `expr', it is ignored and Calc goes on to try the next simplification rule that applies. If the function body returns something different, that new formula is substituted for EXPR in the original formula. At each point in the formula, rules are tried in the order of the original calls to `math-defsimplify'; the search stops after the first rule that makes a change. Thus later rules for that same function will not have a chance to trigger until the next iteration of the main `simplify' loop. Note that, since `defmath' is not being used here, BODY must be written in true Lisp code without the conveniences that `defmath' provides. If you prefer, you can have BODY simply call another function (defined with `defmath') which does the real work. The arguments of a function call will already have been simplified before any rules for the call itself are invoked. Since a new argument list is consed up when this happens, this means that the rule's body is allowed to rearrange the function's arguments destructively if that is convenient. Here is a typical example of a simplification rule: (math-defsimplify calcFunc-arcsinh (or (and (math-looks-negp (nth 1 expr)) (math-neg (list 'calcFunc-arcsinh (math-neg (nth 1 expr))))) (and (eq (car-safe (nth 1 expr)) 'calcFunc-sinh) (or math-living-dangerously (math-known-realp (nth 1 (nth 1 expr)))) (nth 1 (nth 1 expr))))) This is really a pair of rules written with one `math-defsimplify' for convenience; the first replaces `arcsinh(-x)' with `-arcsinh(x)', and the second, which is safe only for real `x', replaces `arcsinh(sinh(x))' with `x'. -- Function: common-constant-factor expr Check EXPR to see if it is a sum of terms all multiplied by the same rational value. If so, return this value. If not, return `nil'. For example, if called on `6x + 9y + 12z', it would return 3, since 3 is a common factor of all the terms. -- Function: cancel-common-factor expr factor Assuming EXPR is a sum with FACTOR as a common factor, divide each term of the sum by FACTOR. This is done by destructively modifying parts of EXPR, on the assumption that it is being used by a simplification rule (where such things are allowed; see above). For example, consider this built-in rule for square roots: (math-defsimplify calcFunc-sqrt (let ((fac (math-common-constant-factor (nth 1 expr)))) (and fac (not (eq fac 1)) (math-mul (math-normalize (list 'calcFunc-sqrt fac)) (math-normalize (list 'calcFunc-sqrt (math-cancel-common-factor (nth 1 expr) fac))))))) -- Function: frac-gcd a b Compute a "rational GCD" of A and B, which must both be rational numbers. This is the fraction composed of the GCD of the numerators of A and B, over the GCD of the denominators. It is used by `common-constant-factor'. Note that the standard `gcd' function uses the LCM to combine the denominators. -- Function: map-tree func expr many Try applying Lisp function FUNC to various sub-expressions of EXPR. Initially, call FUNC with EXPR itself as an argument. If this returns an expression which is not `equal' to EXPR, apply FUNC again until eventually it does return EXPR with no changes. Then, if EXPR is a function call, recursively apply FUNC to each of the arguments. This keeps going until no changes occur anywhere in the expression; this final expression is returned by `map-tree'. Note that, unlike simplification rules, FUNC functions may _not_ make destructive changes to EXPR. If a third argument MANY is provided, it is an integer which says how many times FUNC may be applied; the default, as described above, is infinitely many times. -- Function: compile-rewrites rules Compile the rewrite rule set specified by RULES, which should be a formula that is either a vector or a variable name. If the latter, the compiled rules are saved so that later `compile-rules' calls for that same variable can return immediately. If there are problems with the rules, this function calls `error' with a suitable message. -- Function: apply-rewrites expr crules heads Apply the compiled rewrite rule set CRULES to the expression EXPR. This will make only one rewrite and only checks at the top level of the expression. The result `nil' if no rules matched, or if the only rules that matched did not actually change the expression. The HEADS argument is optional; if is given, it should be a list of all function names that (may) appear in EXPR. The rewrite compiler tags each rule with the rarest-looking function name in the rule; if you specify HEADS, `apply-rewrites' can use this information to narrow its search down to just a few rules in the rule set. -- Function: rewrite-heads expr Compute a HEADS list for EXPR suitable for use with `apply-rewrites', as discussed above. -- Function: rewrite expr rules many This is an all-in-one rewrite function. It compiles the rule set specified by RULES, then uses `map-tree' to apply the rules throughout EXPR up to MANY (default infinity) times. -- Function: match-patterns pat vec not-flag Given a Calc vector VEC and an uncompiled pattern set or pattern set variable PAT, this function returns a new vector of all elements of VEC which do (or don't, if NOT-FLAG is non-`nil') match any of the patterns in PAT. -- Function: deriv expr var value symb Compute the derivative of EXPR with respect to variable VAR (which may actually be any sub-expression). If VALUE is specified, the derivative is evaluated at the value of VAR; otherwise, the derivative is left in terms of VAR. If the expression contains functions for which no derivative formula is known, new derivative functions are invented by adding primes to the names; *note Calculus::. However, if SYMB is non-`nil', the presence of undifferentiable functions in EXPR instead cancels the whole differentiation, and `deriv' returns `nil' instead. Derivatives of an N-argument function can be defined by adding a `math-derivative-N' property to the property list of the symbol for the function's derivative, which will be the function name followed by an apostrophe. The value of the property should be a Lisp function; it is called with the same arguments as the original function call that is being differentiated. It should return a formula for the derivative. For example, the derivative of `ln' is defined by (put 'calcFunc-ln\' 'math-derivative-1 (function (lambda (u) (math-div 1 u)))) The two-argument `log' function has two derivatives, (put 'calcFunc-log\' 'math-derivative-2 ; d(log(x,b)) / dx (function (lambda (x b) ... ))) (put 'calcFunc-log\'2 'math-derivative-2 ; d(log(x,b)) / db (function (lambda (x b) ... ))) -- Function: tderiv expr var value symb Compute the total derivative of EXPR. This is the same as `deriv', except that variables other than VAR are not assumed to be constant with respect to VAR. -- Function: integ expr var low high Compute the integral of EXPR with respect to VAR. *Note Calculus::, for further details. -- Macro: math-defintegral funcs body Define a rule for integrating a function or functions of one argument; this macro is very similar in format to `math-defsimplify'. The main difference is that here BODY is the body of a function with a single argument `u' which is bound to the argument to the function being integrated, not the function call itself. Also, the variable of integration is available as `math-integ-var'. If evaluation of the integral requires doing further integrals, the body should call `(math-integral X)' to find the integral of X with respect to `math-integ-var'; this function returns `nil' if the integral could not be done. Some examples: (math-defintegral calcFunc-conj (let ((int (math-integral u))) (and int (list 'calcFunc-conj int)))) (math-defintegral calcFunc-cos (and (equal u math-integ-var) (math-from-radians-2 (list 'calcFunc-sin u)))) In the `cos' example, we define only the integral of `cos(x) dx', relying on the general integration-by-substitution facility to handle cosines of more complicated arguments. An integration rule should return `nil' if it can't do the integral; if several rules are defined for the same function, they are tried in order until one returns a non-`nil' result. -- Macro: math-defintegral-2 funcs body Define a rule for integrating a function or functions of two arguments. This is exactly analogous to `math-defintegral', except that BODY is written as the body of a function with two arguments, U and V. -- Function: solve-for lhs rhs var full Attempt to solve the equation `LHS = RHS' by isolating the variable VAR on the lefthand side; return the resulting righthand side, or `nil' if the equation cannot be solved. The variable VAR must appear at least once in LHS or RHS. Note that the return value is a formula which does not contain VAR; this is different from the user-level `solve' and `finv' functions, which return a rearranged equation or a functional inverse, respectively. If FULL is non-`nil', a full solution including dummy signs and dummy integers will be produced. User-defined inverses are provided as properties in a manner similar to derivatives: (put 'calcFunc-ln 'math-inverse (function (lambda (x) (list 'calcFunc-exp x)))) This function can call `(math-solve-get-sign X)' to create a new arbitrary sign variable, returning X times that sign, and `(math-solve-get-int X)' to create a new arbitrary integer variable multiplied by X. These functions simply return X if the caller requested a non-"full" solution. -- Function: solve-eqn expr var full This version of `solve-for' takes an expression which will typically be an equation or inequality. (If it is not, it will be interpreted as the equation `EXPR = 0'.) It returns an equation or inequality, or `nil' if no solution could be found. -- Function: solve-system exprs vars full This function solves a system of equations. Generally, EXPRS and VARS will be vectors of equal length. *Note Solving Systems of Equations::, for other options. -- Function: expr-contains expr var Returns a non-`nil' value if VAR occurs as a subexpression of EXPR. This function might seem at first to be identical to `calc-find-sub-formula'. The key difference is that `expr-contains' uses `equal' to test for matches, whereas `calc-find-sub-formula' uses `eq'. In the formula `f(a, a)', the two `a's will be `equal' but not `eq' to each other. -- Function: expr-contains-count expr var Returns the number of occurrences of VAR as a subexpression of EXPR, or `nil' if there are no occurrences. -- Function: expr-depends expr var Returns true if EXPR refers to any variable the occurs in VAR. In other words, it checks if EXPR and VAR have any variables in common. -- Function: expr-contains-vars expr Return true if EXPR contains any variables, or `nil' if EXPR contains only constants and functions with constant arguments. -- Function: expr-subst expr old new Returns a copy of EXPR, with all occurrences of OLD replaced by NEW. This treats `lambda' forms specially with respect to the dummy argument variables, so that the effect is always to return EXPR evaluated at OLD = NEW. -- Function: multi-subst expr old new This is like `expr-subst', except that OLD and NEW are lists of expressions to be substituted simultaneously. If one list is shorter than the other, trailing elements of the longer list are ignored. -- Function: expr-weight expr Returns the "weight" of EXPR, basically a count of the total number of objects and function calls that appear in EXPR. For "primitive" objects, this will be one. -- Function: expr-height expr Returns the "height" of EXPR, which is the deepest level to which function calls are nested. (Note that `A + B' counts as a function call.) For primitive objects, this returns zero. -- Function: polynomial-p expr var Check if EXPR is a polynomial in variable (or sub-expression) VAR. If so, return the degree of the polynomial, that is, the highest power of VAR that appears in EXPR. For example, for `(x^2 + 3)^3 + 4' this would return 6. This function returns `nil' unless EXPR, when expanded out by `a x' (`calc-expand'), would consist of a sum of terms in which VAR appears only raised to nonnegative integer powers. Note that if VAR does not occur in EXPR, then EXPR is considered a polynomial of degree 0. -- Function: is-polynomial expr var degree loose Check if EXPR is a polynomial in variable or sub-expression VAR, and, if so, return a list representation of the polynomial where the elements of the list are coefficients of successive powers of VAR: `A + B x + C x^3' would produce the list `(A B 0 C)', and `(x + 1)^2' would produce the list `(1 2 1)'. The highest element of the list will be non-zero, with the special exception that if EXPR is the constant zero, the returned value will be `(0)'. Return `nil' if EXPR is not a polynomial in VAR. If DEGREE is specified, this will not consider polynomials of degree higher than that value. This is a good precaution because otherwise an input of `(x+1)^1000' will cause a huge coefficient list to be built. If LOOSE is non-`nil', then a looser definition of a polynomial is used in which coefficients are no longer required not to depend on VAR, but are only required not to take the form of polynomials themselves. For example, `sin(x) x^2 + cos(x)' is a loose polynomial with coefficients `((calcFunc-cos x) 0 (calcFunc-sin x))'. The result will never be `nil' in loose mode, since any expression can be interpreted as a "constant" loose polynomial. -- Function: polynomial-base expr pred Check if EXPR is a polynomial in any variable that occurs in it; if so, return that variable. (If EXPR is a multivariate polynomial, this chooses one variable arbitrarily.) If PRED is specified, it should be a Lisp function which is called as `(PRED SUBEXPR)', and which should return true if `mpb-top-expr' (a global name for the original EXPR) is a suitable polynomial in SUBEXPR. The default predicate uses `(polynomial-p mpb-top-expr SUBEXPR)'; you can use PRED to specify additional conditions. Or, you could have PRED build up a list of every suitable SUBEXPR that is found. -- Function: poly-simplify poly Simplify polynomial coefficient list POLY by (destructively) clipping off trailing zeros. -- Function: poly-mix a ac b bc Mix two polynomial lists A and B (in the form returned by `is-polynomial') in a linear combination with coefficient expressions AC and BC. The result is a (not necessarily simplified) polynomial list representing `AC A + BC B'. -- Function: poly-mul a b Multiply two polynomial coefficient lists A and B. The result will be in simplified form if the inputs were simplified. -- Function: build-polynomial-expr poly var Construct a Calc formula which represents the polynomial coefficient list POLY applied to variable VAR. The `a c' (`calc-collect') command uses `is-polynomial' to turn an expression into a coefficient list, then `build-polynomial-expr' to turn the list back into an expression in regular form. -- Function: check-unit-name var Check if VAR is a variable which can be interpreted as a unit name. If so, return the units table entry for that unit. This will be a list whose first element is the unit name (not counting prefix characters) as a symbol and whose second element is the Calc expression which defines the unit. (Refer to the Calc sources for details on the remaining elements of this list.) If VAR is not a variable or is not a unit name, return `nil'. -- Function: units-in-expr-p expr sub-exprs Return true if EXPR contains any variables which can be interpreted as units. If SUB-EXPRS is `t', the entire expression is searched. If SUB-EXPRS is `nil', this checks whether EXPR is directly a units expression. -- Function: single-units-in-expr-p expr Check whether EXPR contains exactly one units variable. If so, return the units table entry for the variable. If EXPR does not contain any units, return `nil'. If EXPR contains two or more units, return the symbol `wrong'. -- Function: to-standard-units expr which Convert units expression EXPR to base units. If WHICH is `nil', use Calc's native base units. Otherwise, WHICH can specify a units system, which is a list of two-element lists, where the first element is a Calc base symbol name and the second is an expression to substitute for it. -- Function: remove-units expr Return a copy of EXPR with all units variables replaced by ones. This expression is generally normalized before use. -- Function: extract-units expr Return a copy of EXPR with everything but units variables replaced by ones.  File: calc, Node: Formatting Lisp Functions, Next: Hooks, Prev: Symbolic Lisp Functions, Up: Internals 19.5.7.8 I/O and Formatting Functions ..................................... The functions described here are responsible for parsing and formatting Calc numbers and formulas. -- Function: calc-eval str sep arg1 arg2 ... This is the simplest interface to the Calculator from another Lisp program. *Note Calling Calc from Your Programs::. -- Function: read-number str If string STR contains a valid Calc number, either integer, fraction, float, or HMS form, this function parses and returns that number. Otherwise, it returns `nil'. -- Function: read-expr str Read an algebraic expression from string STR. If STR does not have the form of a valid expression, return a list of the form `(error POS MSG)' where POS is an integer index into STR of the general location of the error, and MSG is a string describing the problem. -- Function: read-exprs str Read a list of expressions separated by commas, and return it as a Lisp list. If an error occurs in any expressions, an error list as shown above is returned instead. -- Function: calc-do-alg-entry initial prompt no-norm Read an algebraic formula or formulas using the minibuffer. All conventions of regular algebraic entry are observed. The return value is a list of Calc formulas; there will be more than one if the user entered a list of values separated by commas. The result is `nil' if the user presses Return with a blank line. If INITIAL is given, it is a string which the minibuffer will initially contain. If PROMPT is given, it is the prompt string to use; the default is "Algebraic:". If NO-NORM is `t', the formulas will be returned exactly as parsed; otherwise, they will be passed through `calc-normalize' first. To support the use of `$' characters in the algebraic entry, use `let' to bind `calc-dollar-values' to a list of the values to be substituted for `$', `$$', and so on, and bind `calc-dollar-used' to 0. Upon return, `calc-dollar-used' will have been changed to the highest number of consecutive `$'s that actually appeared in the input. -- Function: format-number a Convert the real or complex number or HMS form A to string form. -- Function: format-flat-expr a prec Convert the arbitrary Calc number or formula A to string form, in the style used by the trail buffer and the `calc-edit' command. This is a simple format designed mostly to guarantee the string is of a form that can be re-parsed by `read-expr'. Most formatting modes, such as digit grouping, complex number format, and point character, are ignored to ensure the result will be re-readable. The PREC parameter is normally 0; if you pass a large integer like 1000 instead, the expression will be surrounded by parentheses unless it is a plain number or variable name. -- Function: format-nice-expr a width This is like `format-flat-expr' (with PREC equal to 0), except that newlines will be inserted to keep lines down to the specified WIDTH, and vectors that look like matrices or rewrite rules are written in a pseudo-matrix format. The `calc-edit' command uses this when only one stack entry is being edited. -- Function: format-value a width Convert the Calc number or formula A to string form, using the format seen in the stack buffer. Beware the string returned may not be re-readable by `read-expr', for example, because of digit grouping. Multi-line objects like matrices produce strings that contain newline characters to separate the lines. The W parameter, if given, is the target window size for which to format the expressions. If W is omitted, the width of the Calculator window is used. -- Function: compose-expr a prec Format the Calc number or formula A according to the current language mode, returning a "composition." To learn about the structure of compositions, see the comments in the Calc source code. You can specify the format of a given type of function call by putting a `math-compose-LANG' property on the function's symbol, whose value is a Lisp function that takes A and PREC as arguments and returns a composition. Here LANG is a language mode name, one of `normal', `big', `c', `pascal', `fortran', `tex', `eqn', `math', or `maple'. In Big mode, Calc actually tries `math-compose-big' first, then tries `math-compose-normal'. If this property does not exist, or if the function returns `nil', the function is written in the normal function-call notation for that language. -- Function: composition-to-string c w Convert a composition structure returned by `compose-expr' into a string. Multi-line compositions convert to strings containing newline characters. The target window size is given by W. The `format-value' function basically calls `compose-expr' followed by `composition-to-string'. -- Function: comp-width c Compute the width in characters of composition C. -- Function: comp-height c Compute the height in lines of composition C. -- Function: comp-ascent c Compute the portion of the height of composition C which is on or above the baseline. For a one-line composition, this will be one. -- Function: comp-descent c Compute the portion of the height of composition C which is below the baseline. For a one-line composition, this will be zero. -- Function: comp-first-char c If composition C is a "flat" composition, return the first (leftmost) character of the composition as an integer. Otherwise, return `nil'. -- Function: comp-last-char c If composition C is a "flat" composition, return the last (rightmost) character, otherwise return `nil'.  File: calc, Node: Hooks, Prev: Formatting Lisp Functions, Up: Internals 19.5.7.9 Hooks .............. Hooks are variables which contain Lisp functions (or lists of functions) which are called at various times. Calc defines a number of hooks that help you to customize it in various ways. Calc uses the Lisp function `run-hooks' to invoke the hooks shown below. Several other customization-related variables are also described here. -- Variable: calc-load-hook This hook is called at the end of `calc.el', after the file has been loaded, before any functions in it have been called, but after `calc-mode-map' and similar variables have been set up. -- Variable: calc-ext-load-hook This hook is called at the end of `calc-ext.el'. -- Variable: calc-start-hook This hook is called as the last step in a `M-x calc' command. At this point, the Calc buffer has been created and initialized if necessary, the Calc window and trail window have been created, and the "Welcome to Calc" message has been displayed. -- Variable: calc-mode-hook This hook is called when the Calc buffer is being created. Usually this will only happen once per Emacs session. The hook is called after Emacs has switched to the new buffer, the mode-settings file has been read if necessary, and all other buffer-local variables have been set up. After this hook returns, Calc will perform a `calc-refresh' operation, set up the mode line display, then evaluate any deferred `calc-define' properties that have not been evaluated yet. -- Variable: calc-trail-mode-hook This hook is called when the Calc Trail buffer is being created. It is called as the very last step of setting up the Trail buffer. Like `calc-mode-hook', this will normally happen only once per Emacs session. -- Variable: calc-end-hook This hook is called by `calc-quit', generally because the user presses `q' or `C-x * c' while in Calc. The Calc buffer will be the current buffer. The hook is called as the very first step, before the Calc window is destroyed. -- Variable: calc-window-hook If this hook is non-`nil', it is called to create the Calc window. Upon return, this new Calc window should be the current window. (The Calc buffer will already be the current buffer when the hook is called.) If the hook is not defined, Calc will generally use `split-window', `set-window-buffer', and `select-window' to create the Calc window. -- Variable: calc-trail-window-hook If this hook is non-`nil', it is called to create the Calc Trail window. The variable `calc-trail-buffer' will contain the buffer which the window should use. Unlike `calc-window-hook', this hook must _not_ switch into the new window. -- Variable: calc-embedded-mode-hook This hook is called the first time that Embedded mode is entered. -- Variable: calc-embedded-new-buffer-hook This hook is called each time that Embedded mode is entered in a new buffer. -- Variable: calc-embedded-new-formula-hook This hook is called each time that Embedded mode is enabled for a new formula. -- Variable: calc-edit-mode-hook This hook is called by `calc-edit' (and the other "edit" commands) when the temporary editing buffer is being created. The buffer will have been selected and set up to be in `calc-edit-mode', but will not yet have been filled with text. (In fact it may still have leftover text from a previous `calc-edit' command.) -- Variable: calc-mode-save-hook This hook is called by the `calc-save-modes' command, after Calc's own mode features have been inserted into the Calc init file and just before the "End of mode settings" message is inserted. -- Variable: calc-reset-hook This hook is called after `C-x * 0' (`calc-reset') has reset all modes. The Calc buffer will be the current buffer. -- Variable: calc-other-modes This variable contains a list of strings. The strings are concatenated at the end of the modes portion of the Calc mode line (after standard modes such as "Deg", "Inv" and "Hyp"). Each string should be a short, single word followed by a space. The variable is `nil' by default. -- Variable: calc-mode-map This is the keymap that is used by Calc mode. The best time to adjust it is probably in a `calc-mode-hook'. If the Calc extensions package (`calc-ext.el') has not yet been loaded, many of these keys will be bound to `calc-missing-key', which is a command that loads the extensions package and "retypes" the key. If your `calc-mode-hook' rebinds one of these keys, it will probably be overridden when the extensions are loaded. -- Variable: calc-digit-map This is the keymap that is used during numeric entry. Numeric entry uses the minibuffer, but this map binds every non-numeric key to `calcDigit-nondigit' which generally calls `exit-minibuffer' and "retypes" the key. -- Variable: calc-alg-ent-map This is the keymap that is used during algebraic entry. This is mostly a copy of `minibuffer-local-map'. -- Variable: calc-store-var-map This is the keymap that is used during entry of variable names for commands like `calc-store' and `calc-recall'. This is mostly a copy of `minibuffer-local-completion-map'. -- Variable: calc-edit-mode-map This is the (sparse) keymap used by `calc-edit' and other temporary editing commands. It binds , , and `C-c C-c' to `calc-edit-finish'. -- Variable: calc-mode-var-list This is a list of variables which are saved by `calc-save-modes'. Each entry is a list of two items, the variable (as a Lisp symbol) and its default value. When modes are being saved, each variable is compared with its default value (using `equal') and any non-default variables are written out. -- Variable: calc-local-var-list This is a list of variables which should be buffer-local to the Calc buffer. Each entry is a variable name (as a Lisp symbol). These variables also have their default values manipulated by the `calc' and `calc-quit' commands; *note Multiple Calculators::. Since `calc-mode-hook' is called after this list has been used the first time, your hook should add a variable to the list and also call `make-local-variable' itself.  File: calc, Node: Copying, Next: GNU Free Documentation License, Prev: Programming, Up: Top Appendix A GNU GENERAL PUBLIC LICENSE ************************************* Version 3, 29 June 2007 Copyright (C) 2007 Free Software Foundation, Inc. `http://fsf.org/' Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. Preamble ======== The GNU General Public License is a free, copyleft license for software and other kinds of works. The licenses for most software and other practical works are designed to take away your freedom to share and change the works. By contrast, the GNU General Public License is intended to guarantee your freedom to share and change all versions of a program--to make sure it remains free software for all its users. We, the Free Software Foundation, use the GNU General Public License for most of our software; it applies also to any other work released this way by its authors. You can apply it to your programs, too. When we speak of free software, we are referring to freedom, not price. Our General Public Licenses are designed to make sure that you have the freedom to distribute copies of free software (and charge for them if you wish), that you receive source code or can get it if you want it, that you can change the software or use pieces of it in new free programs, and that you know you can do these things. To protect your rights, we need to prevent others from denying you these rights or asking you to surrender the rights. Therefore, you have certain responsibilities if you distribute copies of the software, or if you modify it: responsibilities to respect the freedom of others. For example, if you distribute copies of such a program, whether gratis or for a fee, you must pass on to the recipients the same freedoms that you received. You must make sure that they, too, receive or can get the source code. And you must show them these terms so they know their rights. Developers that use the GNU GPL protect your rights with two steps: (1) assert copyright on the software, and (2) offer you this License giving you legal permission to copy, distribute and/or modify it. For the developers' and authors' protection, the GPL clearly explains that there is no warranty for this free software. For both users' and authors' sake, the GPL requires that modified versions be marked as changed, so that their problems will not be attributed erroneously to authors of previous versions. Some devices are designed to deny users access to install or run modified versions of the software inside them, although the manufacturer can do so. This is fundamentally incompatible with the aim of protecting users' freedom to change the software. The systematic pattern of such abuse occurs in the area of products for individuals to use, which is precisely where it is most unacceptable. Therefore, we have designed this version of the GPL to prohibit the practice for those products. If such problems arise substantially in other domains, we stand ready to extend this provision to those domains in future versions of the GPL, as needed to protect the freedom of users. Finally, every program is threatened constantly by software patents. States should not allow patents to restrict development and use of software on general-purpose computers, but in those that do, we wish to avoid the special danger that patents applied to a free program could make it effectively proprietary. To prevent this, the GPL assures that patents cannot be used to render the program non-free. The precise terms and conditions for copying, distribution and modification follow. TERMS AND CONDITIONS ==================== 0. Definitions. "This License" refers to version 3 of the GNU General Public License. "Copyright" also means copyright-like laws that apply to other kinds of works, such as semiconductor masks. "The Program" refers to any copyrightable work licensed under this License. Each licensee is addressed as "you". "Licensees" and "recipients" may be individuals or organizations. To "modify" a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a "modified version" of the earlier work or a work "based on" the earlier work. A "covered work" means either the unmodified Program or a work based on the Program. To "propagate" a work means to do anything with it that, without permission, would make you directly or secondarily liable for infringement under applicable copyright law, except executing it on a computer or modifying a private copy. Propagation includes copying, distribution (with or without modification), making available to the public, and in some countries other activities as well. To "convey" a work means any kind of propagation that enables other parties to make or receive copies. Mere interaction with a user through a computer network, with no transfer of a copy, is not conveying. An interactive user interface displays "Appropriate Legal Notices" to the extent that it includes a convenient and prominently visible feature that (1) displays an appropriate copyright notice, and (2) tells the user that there is no warranty for the work (except to the extent that warranties are provided), that licensees may convey the work under this License, and how to view a copy of this License. If the interface presents a list of user commands or options, such as a menu, a prominent item in the list meets this criterion. 1. Source Code. The "source code" for a work means the preferred form of the work for making modifications to it. "Object code" means any non-source form of a work. A "Standard Interface" means an interface that either is an official standard defined by a recognized standards body, or, in the case of interfaces specified for a particular programming language, one that is widely used among developers working in that language. The "System Libraries" of an executable work include anything, other than the work as a whole, that (a) is included in the normal form of packaging a Major Component, but which is not part of that Major Component, and (b) serves only to enable use of the work with that Major Component, or to implement a Standard Interface for which an implementation is available to the public in source code form. A "Major Component", in this context, means a major essential component (kernel, window system, and so on) of the specific operating system (if any) on which the executable work runs, or a compiler used to produce the work, or an object code interpreter used to run it. The "Corresponding Source" for a work in object code form means all the source code needed to generate, install, and (for an executable work) run the object code and to modify the work, including scripts to control those activities. However, it does not include the work's System Libraries, or general-purpose tools or generally available free programs which are used unmodified in performing those activities but which are not part of the work. For example, Corresponding Source includes interface definition files associated with source files for the work, and the source code for shared libraries and dynamically linked subprograms that the work is specifically designed to require, such as by intimate data communication or control flow between those subprograms and other parts of the work. The Corresponding Source need not include anything that users can regenerate automatically from other parts of the Corresponding Source. The Corresponding Source for a work in source code form is that same work. 2. Basic Permissions. All rights granted under this License are granted for the term of copyright on the Program, and are irrevocable provided the stated conditions are met. This License explicitly affirms your unlimited permission to run the unmodified Program. The output from running a covered work is covered by this License only if the output, given its content, constitutes a covered work. This License acknowledges your rights of fair use or other equivalent, as provided by copyright law. You may make, run and propagate covered works that you do not convey, without conditions so long as your license otherwise remains in force. You may convey covered works to others for the sole purpose of having them make modifications exclusively for you, or provide you with facilities for running those works, provided that you comply with the terms of this License in conveying all material for which you do not control copyright. Those thus making or running the covered works for you must do so exclusively on your behalf, under your direction and control, on terms that prohibit them from making any copies of your copyrighted material outside their relationship with you. Conveying under any other circumstances is permitted solely under the conditions stated below. Sublicensing is not allowed; section 10 makes it unnecessary. 3. Protecting Users' Legal Rights From Anti-Circumvention Law. No covered work shall be deemed part of an effective technological measure under any applicable law fulfilling obligations under article 11 of the WIPO copyright treaty adopted on 20 December 1996, or similar laws prohibiting or restricting circumvention of such measures. When you convey a covered work, you waive any legal power to forbid circumvention of technological measures to the extent such circumvention is effected by exercising rights under this License with respect to the covered work, and you disclaim any intention to limit operation or modification of the work as a means of enforcing, against the work's users, your or third parties' legal rights to forbid circumvention of technological measures. 4. Conveying Verbatim Copies. You may convey verbatim copies of the Program's source code as you receive it, in any medium, provided that you conspicuously and appropriately publish on each copy an appropriate copyright notice; keep intact all notices stating that this License and any non-permissive terms added in accord with section 7 apply to the code; keep intact all notices of the absence of any warranty; and give all recipients a copy of this License along with the Program. You may charge any price or no price for each copy that you convey, and you may offer support or warranty protection for a fee. 5. Conveying Modified Source Versions. You may convey a work based on the Program, or the modifications to produce it from the Program, in the form of source code under the terms of section 4, provided that you also meet all of these conditions: a. The work must carry prominent notices stating that you modified it, and giving a relevant date. b. The work must carry prominent notices stating that it is released under this License and any conditions added under section 7. This requirement modifies the requirement in section 4 to "keep intact all notices". c. You must license the entire work, as a whole, under this License to anyone who comes into possession of a copy. This License will therefore apply, along with any applicable section 7 additional terms, to the whole of the work, and all its parts, regardless of how they are packaged. This License gives no permission to license the work in any other way, but it does not invalidate such permission if you have separately received it. d. If the work has interactive user interfaces, each must display Appropriate Legal Notices; however, if the Program has interactive interfaces that do not display Appropriate Legal Notices, your work need not make them do so. A compilation of a covered work with other separate and independent works, which are not by their nature extensions of the covered work, and which are not combined with it such as to form a larger program, in or on a volume of a storage or distribution medium, is called an "aggregate" if the compilation and its resulting copyright are not used to limit the access or legal rights of the compilation's users beyond what the individual works permit. Inclusion of a covered work in an aggregate does not cause this License to apply to the other parts of the aggregate. 6. Conveying Non-Source Forms. You may convey a covered work in object code form under the terms of sections 4 and 5, provided that you also convey the machine-readable Corresponding Source under the terms of this License, in one of these ways: a. Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by the Corresponding Source fixed on a durable physical medium customarily used for software interchange. b. Convey the object code in, or embodied in, a physical product (including a physical distribution medium), accompanied by a written offer, valid for at least three years and valid for as long as you offer spare parts or customer support for that product model, to give anyone who possesses the object code either (1) a copy of the Corresponding Source for all the software in the product that is covered by this License, on a durable physical medium customarily used for software interchange, for a price no more than your reasonable cost of physically performing this conveying of source, or (2) access to copy the Corresponding Source from a network server at no charge. c. Convey individual copies of the object code with a copy of the written offer to provide the Corresponding Source. This alternative is allowed only occasionally and noncommercially, and only if you received the object code with such an offer, in accord with subsection 6b. d. Convey the object code by offering access from a designated place (gratis or for a charge), and offer equivalent access to the Corresponding Source in the same way through the same place at no further charge. You need not require recipients to copy the Corresponding Source along with the object code. If the place to copy the object code is a network server, the Corresponding Source may be on a different server (operated by you or a third party) that supports equivalent copying facilities, provided you maintain clear directions next to the object code saying where to find the Corresponding Source. Regardless of what server hosts the Corresponding Source, you remain obligated to ensure that it is available for as long as needed to satisfy these requirements. e. Convey the object code using peer-to-peer transmission, provided you inform other peers where the object code and Corresponding Source of the work are being offered to the general public at no charge under subsection 6d. A separable portion of the object code, whose source code is excluded from the Corresponding Source as a System Library, need not be included in conveying the object code work. A "User Product" is either (1) a "consumer product", which means any tangible personal property which is normally used for personal, family, or household purposes, or (2) anything designed or sold for incorporation into a dwelling. In determining whether a product is a consumer product, doubtful cases shall be resolved in favor of coverage. For a particular product received by a particular user, "normally used" refers to a typical or common use of that class of product, regardless of the status of the particular user or of the way in which the particular user actually uses, or expects or is expected to use, the product. A product is a consumer product regardless of whether the product has substantial commercial, industrial or non-consumer uses, unless such uses represent the only significant mode of use of the product. "Installation Information" for a User Product means any methods, procedures, authorization keys, or other information required to install and execute modified versions of a covered work in that User Product from a modified version of its Corresponding Source. The information must suffice to ensure that the continued functioning of the modified object code is in no case prevented or interfered with solely because modification has been made. If you convey an object code work under this section in, or with, or specifically for use in, a User Product, and the conveying occurs as part of a transaction in which the right of possession and use of the User Product is transferred to the recipient in perpetuity or for a fixed term (regardless of how the transaction is characterized), the Corresponding Source conveyed under this section must be accompanied by the Installation Information. But this requirement does not apply if neither you nor any third party retains the ability to install modified object code on the User Product (for example, the work has been installed in ROM). The requirement to provide Installation Information does not include a requirement to continue to provide support service, warranty, or updates for a work that has been modified or installed by the recipient, or for the User Product in which it has been modified or installed. Access to a network may be denied when the modification itself materially and adversely affects the operation of the network or violates the rules and protocols for communication across the network. Corresponding Source conveyed, and Installation Information provided, in accord with this section must be in a format that is publicly documented (and with an implementation available to the public in source code form), and must require no special password or key for unpacking, reading or copying. 7. Additional Terms. "Additional permissions" are terms that supplement the terms of this License by making exceptions from one or more of its conditions. Additional permissions that are applicable to the entire Program shall be treated as though they were included in this License, to the extent that they are valid under applicable law. If additional permissions apply only to part of the Program, that part may be used separately under those permissions, but the entire Program remains governed by this License without regard to the additional permissions. When you convey a copy of a covered work, you may at your option remove any additional permissions from that copy, or from any part of it. (Additional permissions may be written to require their own removal in certain cases when you modify the work.) You may place additional permissions on material, added by you to a covered work, for which you have or can give appropriate copyright permission. Notwithstanding any other provision of this License, for material you add to a covered work, you may (if authorized by the copyright holders of that material) supplement the terms of this License with terms: a. Disclaiming warranty or limiting liability differently from the terms of sections 15 and 16 of this License; or b. Requiring preservation of specified reasonable legal notices or author attributions in that material or in the Appropriate Legal Notices displayed by works containing it; or c. Prohibiting misrepresentation of the origin of that material, or requiring that modified versions of such material be marked in reasonable ways as different from the original version; or d. Limiting the use for publicity purposes of names of licensors or authors of the material; or e. Declining to grant rights under trademark law for use of some trade names, trademarks, or service marks; or f. Requiring indemnification of licensors and authors of that material by anyone who conveys the material (or modified versions of it) with contractual assumptions of liability to the recipient, for any liability that these contractual assumptions directly impose on those licensors and authors. All other non-permissive additional terms are considered "further restrictions" within the meaning of section 10. If the Program as you received it, or any part of it, contains a notice stating that it is governed by this License along with a term that is a further restriction, you may remove that term. If a license document contains a further restriction but permits relicensing or conveying under this License, you may add to a covered work material governed by the terms of that license document, provided that the further restriction does not survive such relicensing or conveying. If you add terms to a covered work in accord with this section, you must place, in the relevant source files, a statement of the additional terms that apply to those files, or a notice indicating where to find the applicable terms. Additional terms, permissive or non-permissive, may be stated in the form of a separately written license, or stated as exceptions; the above requirements apply either way. 8. Termination. You may not propagate or modify a covered work except as expressly provided under this License. Any attempt otherwise to propagate or modify it is void, and will automatically terminate your rights under this License (including any patent licenses granted under the third paragraph of section 11). However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, you do not qualify to receive new licenses for the same material under section 10. 9. Acceptance Not Required for Having Copies. You are not required to accept this License in order to receive or run a copy of the Program. Ancillary propagation of a covered work occurring solely as a consequence of using peer-to-peer transmission to receive a copy likewise does not require acceptance. However, nothing other than this License grants you permission to propagate or modify any covered work. These actions infringe copyright if you do not accept this License. Therefore, by modifying or propagating a covered work, you indicate your acceptance of this License to do so. 10. Automatic Licensing of Downstream Recipients. Each time you convey a covered work, the recipient automatically receives a license from the original licensors, to run, modify and propagate that work, subject to this License. You are not responsible for enforcing compliance by third parties with this License. An "entity transaction" is a transaction transferring control of an organization, or substantially all assets of one, or subdividing an organization, or merging organizations. If propagation of a covered work results from an entity transaction, each party to that transaction who receives a copy of the work also receives whatever licenses to the work the party's predecessor in interest had or could give under the previous paragraph, plus a right to possession of the Corresponding Source of the work from the predecessor in interest, if the predecessor has it or can get it with reasonable efforts. You may not impose any further restrictions on the exercise of the rights granted or affirmed under this License. For example, you may not impose a license fee, royalty, or other charge for exercise of rights granted under this License, and you may not initiate litigation (including a cross-claim or counterclaim in a lawsuit) alleging that any patent claim is infringed by making, using, selling, offering for sale, or importing the Program or any portion of it. 11. Patents. A "contributor" is a copyright holder who authorizes use under this License of the Program or a work on which the Program is based. The work thus licensed is called the contributor's "contributor version". A contributor's "essential patent claims" are all patent claims owned or controlled by the contributor, whether already acquired or hereafter acquired, that would be infringed by some manner, permitted by this License, of making, using, or selling its contributor version, but do not include claims that would be infringed only as a consequence of further modification of the contributor version. For purposes of this definition, "control" includes the right to grant patent sublicenses in a manner consistent with the requirements of this License. Each contributor grants you a non-exclusive, worldwide, royalty-free patent license under the contributor's essential patent claims, to make, use, sell, offer for sale, import and otherwise run, modify and propagate the contents of its contributor version. In the following three paragraphs, a "patent license" is any express agreement or commitment, however denominated, not to enforce a patent (such as an express permission to practice a patent or covenant not to sue for patent infringement). To "grant" such a patent license to a party means to make such an agreement or commitment not to enforce a patent against the party. If you convey a covered work, knowingly relying on a patent license, and the Corresponding Source of the work is not available for anyone to copy, free of charge and under the terms of this License, through a publicly available network server or other readily accessible means, then you must either (1) cause the Corresponding Source to be so available, or (2) arrange to deprive yourself of the benefit of the patent license for this particular work, or (3) arrange, in a manner consistent with the requirements of this License, to extend the patent license to downstream recipients. "Knowingly relying" means you have actual knowledge that, but for the patent license, your conveying the covered work in a country, or your recipient's use of the covered work in a country, would infringe one or more identifiable patents in that country that you have reason to believe are valid. If, pursuant to or in connection with a single transaction or arrangement, you convey, or propagate by procuring conveyance of, a covered work, and grant a patent license to some of the parties receiving the covered work authorizing them to use, propagate, modify or convey a specific copy of the covered work, then the patent license you grant is automatically extended to all recipients of the covered work and works based on it. A patent license is "discriminatory" if it does not include within the scope of its coverage, prohibits the exercise of, or is conditioned on the non-exercise of one or more of the rights that are specifically granted under this License. You may not convey a covered work if you are a party to an arrangement with a third party that is in the business of distributing software, under which you make payment to the third party based on the extent of your activity of conveying the work, and under which the third party grants, to any of the parties who would receive the covered work from you, a discriminatory patent license (a) in connection with copies of the covered work conveyed by you (or copies made from those copies), or (b) primarily for and in connection with specific products or compilations that contain the covered work, unless you entered into that arrangement, or that patent license was granted, prior to 28 March 2007. Nothing in this License shall be construed as excluding or limiting any implied license or other defenses to infringement that may otherwise be available to you under applicable patent law. 12. No Surrender of Others' Freedom. If conditions are imposed on you (whether by court order, agreement or otherwise) that contradict the conditions of this License, they do not excuse you from the conditions of this License. If you cannot convey a covered work so as to satisfy simultaneously your obligations under this License and any other pertinent obligations, then as a consequence you may not convey it at all. For example, if you agree to terms that obligate you to collect a royalty for further conveying from those to whom you convey the Program, the only way you could satisfy both those terms and this License would be to refrain entirely from conveying the Program. 13. Use with the GNU Affero General Public License. Notwithstanding any other provision of this License, you have permission to link or combine any covered work with a work licensed under version 3 of the GNU Affero General Public License into a single combined work, and to convey the resulting work. The terms of this License will continue to apply to the part which is the covered work, but the special requirements of the GNU Affero General Public License, section 13, concerning interaction through a network will apply to the combination as such. 14. Revised Versions of this License. The Free Software Foundation may publish revised and/or new versions of the GNU General Public License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. Each version is given a distinguishing version number. If the Program specifies that a certain numbered version of the GNU General Public License "or any later version" applies to it, you have the option of following the terms and conditions either of that numbered version or of any later version published by the Free Software Foundation. If the Program does not specify a version number of the GNU General Public License, you may choose any version ever published by the Free Software Foundation. If the Program specifies that a proxy can decide which future versions of the GNU General Public License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Program. Later license versions may give you additional or different permissions. However, no additional obligations are imposed on any author or copyright holder as a result of your choosing to follow a later version. 15. Disclaimer of Warranty. THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF ALL NECESSARY SERVICING, REPAIR OR CORRECTION. 16. Limitation of Liability. IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. 17. Interpretation of Sections 15 and 16. If the disclaimer of warranty and limitation of liability provided above cannot be given local legal effect according to their terms, reviewing courts shall apply local law that most closely approximates an absolute waiver of all civil liability in connection with the Program, unless a warranty or assumption of liability accompanies a copy of the Program in return for a fee. END OF TERMS AND CONDITIONS =========================== How to Apply These Terms to Your New Programs ============================================= If you develop a new program, and you want it to be of the greatest possible use to the public, the best way to achieve this is to make it free software which everyone can redistribute and change under these terms. To do so, attach the following notices to the program. It is safest to attach them to the start of each source file to most effectively state the exclusion of warranty; and each file should have at least the "copyright" line and a pointer to where the full notice is found. ONE LINE TO GIVE THE PROGRAM'S NAME AND A BRIEF IDEA OF WHAT IT DOES. Copyright (C) YEAR NAME OF AUTHOR This program is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details. You should have received a copy of the GNU General Public License along with this program. If not, see `http://www.gnu.org/licenses/'. Also add information on how to contact you by electronic and paper mail. If the program does terminal interaction, make it output a short notice like this when it starts in an interactive mode: PROGRAM Copyright (C) YEAR NAME OF AUTHOR This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. This is free software, and you are welcome to redistribute it under certain conditions; type `show c' for details. The hypothetical commands `show w' and `show c' should show the appropriate parts of the General Public License. Of course, your program's commands might be different; for a GUI interface, you would use an "about box". You should also get your employer (if you work as a programmer) or school, if any, to sign a "copyright disclaimer" for the program, if necessary. For more information on this, and how to apply and follow the GNU GPL, see `http://www.gnu.org/licenses/'. The GNU General Public License does not permit incorporating your program into proprietary programs. If your program is a subroutine library, you may consider it more useful to permit linking proprietary applications with the library. If this is what you want to do, use the GNU Lesser General Public License instead of this License. But first, please read `http://www.gnu.org/philosophy/why-not-lgpl.html'.  File: calc, Node: GNU Free Documentation License, Next: Customizing Calc, Prev: Copying, Up: Top Appendix B GNU Free Documentation License ***************************************** Version 1.3, 3 November 2008 Copyright (C) 2000, 2001, 2002, 2007, 2008, 2009 Free Software Foundation, Inc. `http://fsf.org/' Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed. 0. PREAMBLE The purpose of this License is to make a manual, textbook, or other functional and useful document "free" in the sense of freedom: to assure everyone the effective freedom to copy and redistribute it, with or without modifying it, either commercially or noncommercially. Secondarily, this License preserves for the author and publisher a way to get credit for their work, while not being considered responsible for modifications made by others. This License is a kind of "copyleft", which means that derivative works of the document must themselves be free in the same sense. It complements the GNU General Public License, which is a copyleft license designed for free software. We have designed this License in order to use it for manuals for free software, because free software needs free documentation: a free program should come with manuals providing the same freedoms that the software does. But this License is not limited to software manuals; it can be used for any textual work, regardless of subject matter or whether it is published as a printed book. We recommend this License principally for works whose purpose is instruction or reference. 1. APPLICABILITY AND DEFINITIONS This License applies to any manual or other work, in any medium, that contains a notice placed by the copyright holder saying it can be distributed under the terms of this License. Such a notice grants a world-wide, royalty-free license, unlimited in duration, to use that work under the conditions stated herein. The "Document", below, refers to any such manual or work. Any member of the public is a licensee, and is addressed as "you". You accept the license if you copy, modify or distribute the work in a way requiring permission under copyright law. A "Modified Version" of the Document means any work containing the Document or a portion of it, either copied verbatim, or with modifications and/or translated into another language. A "Secondary Section" is a named appendix or a front-matter section of the Document that deals exclusively with the relationship of the publishers or authors of the Document to the Document's overall subject (or to related matters) and contains nothing that could fall directly within that overall subject. (Thus, if the Document is in part a textbook of mathematics, a Secondary Section may not explain any mathematics.) The relationship could be a matter of historical connection with the subject or with related matters, or of legal, commercial, philosophical, ethical or political position regarding them. The "Invariant Sections" are certain Secondary Sections whose titles are designated, as being those of Invariant Sections, in the notice that says that the Document is released under this License. If a section does not fit the above definition of Secondary then it is not allowed to be designated as Invariant. The Document may contain zero Invariant Sections. If the Document does not identify any Invariant Sections then there are none. The "Cover Texts" are certain short passages of text that are listed, as Front-Cover Texts or Back-Cover Texts, in the notice that says that the Document is released under this License. A Front-Cover Text may be at most 5 words, and a Back-Cover Text may be at most 25 words. A "Transparent" copy of the Document means a machine-readable copy, represented in a format whose specification is available to the general public, that is suitable for revising the document straightforwardly with generic text editors or (for images composed of pixels) generic paint programs or (for drawings) some widely available drawing editor, and that is suitable for input to text formatters or for automatic translation to a variety of formats suitable for input to text formatters. A copy made in an otherwise Transparent file format whose markup, or absence of markup, has been arranged to thwart or discourage subsequent modification by readers is not Transparent. An image format is not Transparent if used for any substantial amount of text. A copy that is not "Transparent" is called "Opaque". Examples of suitable formats for Transparent copies include plain ASCII without markup, Texinfo input format, LaTeX input format, SGML or XML using a publicly available DTD, and standard-conforming simple HTML, PostScript or PDF designed for human modification. Examples of transparent image formats include PNG, XCF and JPG. Opaque formats include proprietary formats that can be read and edited only by proprietary word processors, SGML or XML for which the DTD and/or processing tools are not generally available, and the machine-generated HTML, PostScript or PDF produced by some word processors for output purposes only. The "Title Page" means, for a printed book, the title page itself, plus such following pages as are needed to hold, legibly, the material this License requires to appear in the title page. For works in formats which do not have any title page as such, "Title Page" means the text near the most prominent appearance of the work's title, preceding the beginning of the body of the text. The "publisher" means any person or entity that distributes copies of the Document to the public. A section "Entitled XYZ" means a named subunit of the Document whose title either is precisely XYZ or contains XYZ in parentheses following text that translates XYZ in another language. (Here XYZ stands for a specific section name mentioned below, such as "Acknowledgements", "Dedications", "Endorsements", or "History".) To "Preserve the Title" of such a section when you modify the Document means that it remains a section "Entitled XYZ" according to this definition. The Document may include Warranty Disclaimers next to the notice which states that this License applies to the Document. These Warranty Disclaimers are considered to be included by reference in this License, but only as regards disclaiming warranties: any other implication that these Warranty Disclaimers may have is void and has no effect on the meaning of this License. 2. VERBATIM COPYING You may copy and distribute the Document in any medium, either commercially or noncommercially, provided that this License, the copyright notices, and the license notice saying this License applies to the Document are reproduced in all copies, and that you add no other conditions whatsoever to those of this License. You may not use technical measures to obstruct or control the reading or further copying of the copies you make or distribute. However, you may accept compensation in exchange for copies. If you distribute a large enough number of copies you must also follow the conditions in section 3. You may also lend copies, under the same conditions stated above, and you may publicly display copies. 3. COPYING IN QUANTITY If you publish printed copies (or copies in media that commonly have printed covers) of the Document, numbering more than 100, and the Document's license notice requires Cover Texts, you must enclose the copies in covers that carry, clearly and legibly, all these Cover Texts: Front-Cover Texts on the front cover, and Back-Cover Texts on the back cover. Both covers must also clearly and legibly identify you as the publisher of these copies. The front cover must present the full title with all words of the title equally prominent and visible. You may add other material on the covers in addition. Copying with changes limited to the covers, as long as they preserve the title of the Document and satisfy these conditions, can be treated as verbatim copying in other respects. If the required texts for either cover are too voluminous to fit legibly, you should put the first ones listed (as many as fit reasonably) on the actual cover, and continue the rest onto adjacent pages. If you publish or distribute Opaque copies of the Document numbering more than 100, you must either include a machine-readable Transparent copy along with each Opaque copy, or state in or with each Opaque copy a computer-network location from which the general network-using public has access to download using public-standard network protocols a complete Transparent copy of the Document, free of added material. If you use the latter option, you must take reasonably prudent steps, when you begin distribution of Opaque copies in quantity, to ensure that this Transparent copy will remain thus accessible at the stated location until at least one year after the last time you distribute an Opaque copy (directly or through your agents or retailers) of that edition to the public. It is requested, but not required, that you contact the authors of the Document well before redistributing any large number of copies, to give them a chance to provide you with an updated version of the Document. 4. MODIFICATIONS You may copy and distribute a Modified Version of the Document under the conditions of sections 2 and 3 above, provided that you release the Modified Version under precisely this License, with the Modified Version filling the role of the Document, thus licensing distribution and modification of the Modified Version to whoever possesses a copy of it. In addition, you must do these things in the Modified Version: A. Use in the Title Page (and on the covers, if any) a title distinct from that of the Document, and from those of previous versions (which should, if there were any, be listed in the History section of the Document). You may use the same title as a previous version if the original publisher of that version gives permission. B. List on the Title Page, as authors, one or more persons or entities responsible for authorship of the modifications in the Modified Version, together with at least five of the principal authors of the Document (all of its principal authors, if it has fewer than five), unless they release you from this requirement. C. State on the Title page the name of the publisher of the Modified Version, as the publisher. D. Preserve all the copyright notices of the Document. E. Add an appropriate copyright notice for your modifications adjacent to the other copyright notices. F. Include, immediately after the copyright notices, a license notice giving the public permission to use the Modified Version under the terms of this License, in the form shown in the Addendum below. G. Preserve in that license notice the full lists of Invariant Sections and required Cover Texts given in the Document's license notice. H. Include an unaltered copy of this License. I. Preserve the section Entitled "History", Preserve its Title, and add to it an item stating at least the title, year, new authors, and publisher of the Modified Version as given on the Title Page. If there is no section Entitled "History" in the Document, create one stating the title, year, authors, and publisher of the Document as given on its Title Page, then add an item describing the Modified Version as stated in the previous sentence. J. Preserve the network location, if any, given in the Document for public access to a Transparent copy of the Document, and likewise the network locations given in the Document for previous versions it was based on. These may be placed in the "History" section. You may omit a network location for a work that was published at least four years before the Document itself, or if the original publisher of the version it refers to gives permission. K. For any section Entitled "Acknowledgements" or "Dedications", Preserve the Title of the section, and preserve in the section all the substance and tone of each of the contributor acknowledgements and/or dedications given therein. L. Preserve all the Invariant Sections of the Document, unaltered in their text and in their titles. Section numbers or the equivalent are not considered part of the section titles. M. Delete any section Entitled "Endorsements". Such a section may not be included in the Modified Version. N. Do not retitle any existing section to be Entitled "Endorsements" or to conflict in title with any Invariant Section. O. Preserve any Warranty Disclaimers. If the Modified Version includes new front-matter sections or appendices that qualify as Secondary Sections and contain no material copied from the Document, you may at your option designate some or all of these sections as invariant. To do this, add their titles to the list of Invariant Sections in the Modified Version's license notice. These titles must be distinct from any other section titles. You may add a section Entitled "Endorsements", provided it contains nothing but endorsements of your Modified Version by various parties--for example, statements of peer review or that the text has been approved by an organization as the authoritative definition of a standard. You may add a passage of up to five words as a Front-Cover Text, and a passage of up to 25 words as a Back-Cover Text, to the end of the list of Cover Texts in the Modified Version. Only one passage of Front-Cover Text and one of Back-Cover Text may be added by (or through arrangements made by) any one entity. If the Document already includes a cover text for the same cover, previously added by you or by arrangement made by the same entity you are acting on behalf of, you may not add another; but you may replace the old one, on explicit permission from the previous publisher that added the old one. The author(s) and publisher(s) of the Document do not by this License give permission to use their names for publicity for or to assert or imply endorsement of any Modified Version. 5. COMBINING DOCUMENTS You may combine the Document with other documents released under this License, under the terms defined in section 4 above for modified versions, provided that you include in the combination all of the Invariant Sections of all of the original documents, unmodified, and list them all as Invariant Sections of your combined work in its license notice, and that you preserve all their Warranty Disclaimers. The combined work need only contain one copy of this License, and multiple identical Invariant Sections may be replaced with a single copy. If there are multiple Invariant Sections with the same name but different contents, make the title of each such section unique by adding at the end of it, in parentheses, the name of the original author or publisher of that section if known, or else a unique number. Make the same adjustment to the section titles in the list of Invariant Sections in the license notice of the combined work. In the combination, you must combine any sections Entitled "History" in the various original documents, forming one section Entitled "History"; likewise combine any sections Entitled "Acknowledgements", and any sections Entitled "Dedications". You must delete all sections Entitled "Endorsements." 6. COLLECTIONS OF DOCUMENTS You may make a collection consisting of the Document and other documents released under this License, and replace the individual copies of this License in the various documents with a single copy that is included in the collection, provided that you follow the rules of this License for verbatim copying of each of the documents in all other respects. You may extract a single document from such a collection, and distribute it individually under this License, provided you insert a copy of this License into the extracted document, and follow this License in all other respects regarding verbatim copying of that document. 7. AGGREGATION WITH INDEPENDENT WORKS A compilation of the Document or its derivatives with other separate and independent documents or works, in or on a volume of a storage or distribution medium, is called an "aggregate" if the copyright resulting from the compilation is not used to limit the legal rights of the compilation's users beyond what the individual works permit. When the Document is included in an aggregate, this License does not apply to the other works in the aggregate which are not themselves derivative works of the Document. If the Cover Text requirement of section 3 is applicable to these copies of the Document, then if the Document is less than one half of the entire aggregate, the Document's Cover Texts may be placed on covers that bracket the Document within the aggregate, or the electronic equivalent of covers if the Document is in electronic form. Otherwise they must appear on printed covers that bracket the whole aggregate. 8. TRANSLATION Translation is considered a kind of modification, so you may distribute translations of the Document under the terms of section 4. Replacing Invariant Sections with translations requires special permission from their copyright holders, but you may include translations of some or all Invariant Sections in addition to the original versions of these Invariant Sections. You may include a translation of this License, and all the license notices in the Document, and any Warranty Disclaimers, provided that you also include the original English version of this License and the original versions of those notices and disclaimers. In case of a disagreement between the translation and the original version of this License or a notice or disclaimer, the original version will prevail. If a section in the Document is Entitled "Acknowledgements", "Dedications", or "History", the requirement (section 4) to Preserve its Title (section 1) will typically require changing the actual title. 9. TERMINATION You may not copy, modify, sublicense, or distribute the Document except as expressly provided under this License. Any attempt otherwise to copy, modify, sublicense, or distribute it is void, and will automatically terminate your rights under this License. However, if you cease all violation of this License, then your license from a particular copyright holder is reinstated (a) provisionally, unless and until the copyright holder explicitly and finally terminates your license, and (b) permanently, if the copyright holder fails to notify you of the violation by some reasonable means prior to 60 days after the cessation. Moreover, your license from a particular copyright holder is reinstated permanently if the copyright holder notifies you of the violation by some reasonable means, this is the first time you have received notice of violation of this License (for any work) from that copyright holder, and you cure the violation prior to 30 days after your receipt of the notice. Termination of your rights under this section does not terminate the licenses of parties who have received copies or rights from you under this License. If your rights have been terminated and not permanently reinstated, receipt of a copy of some or all of the same material does not give you any rights to use it. 10. FUTURE REVISIONS OF THIS LICENSE The Free Software Foundation may publish new, revised versions of the GNU Free Documentation License from time to time. Such new versions will be similar in spirit to the present version, but may differ in detail to address new problems or concerns. See `http://www.gnu.org/copyleft/'. Each version of the License is given a distinguishing version number. If the Document specifies that a particular numbered version of this License "or any later version" applies to it, you have the option of following the terms and conditions either of that specified version or of any later version that has been published (not as a draft) by the Free Software Foundation. If the Document does not specify a version number of this License, you may choose any version ever published (not as a draft) by the Free Software Foundation. If the Document specifies that a proxy can decide which future versions of this License can be used, that proxy's public statement of acceptance of a version permanently authorizes you to choose that version for the Document. 11. RELICENSING "Massive Multiauthor Collaboration Site" (or "MMC Site") means any World Wide Web server that publishes copyrightable works and also provides prominent facilities for anybody to edit those works. A public wiki that anybody can edit is an example of such a server. A "Massive Multiauthor Collaboration" (or "MMC") contained in the site means any set of copyrightable works thus published on the MMC site. "CC-BY-SA" means the Creative Commons Attribution-Share Alike 3.0 license published by Creative Commons Corporation, a not-for-profit corporation with a principal place of business in San Francisco, California, as well as future copyleft versions of that license published by that same organization. "Incorporate" means to publish or republish a Document, in whole or in part, as part of another Document. An MMC is "eligible for relicensing" if it is licensed under this License, and if all works that were first published under this License somewhere other than this MMC, and subsequently incorporated in whole or in part into the MMC, (1) had no cover texts or invariant sections, and (2) were thus incorporated prior to November 1, 2008. The operator of an MMC Site may republish an MMC contained in the site under CC-BY-SA on the same site at any time before August 1, 2009, provided the MMC is eligible for relicensing. ADDENDUM: How to use this License for your documents ==================================================== To use this License in a document you have written, include a copy of the License in the document and put the following copyright and license notices just after the title page: Copyright (C) YEAR YOUR NAME. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.3 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled ``GNU Free Documentation License''. If you have Invariant Sections, Front-Cover Texts and Back-Cover Texts, replace the "with...Texts." line with this: with the Invariant Sections being LIST THEIR TITLES, with the Front-Cover Texts being LIST, and with the Back-Cover Texts being LIST. If you have Invariant Sections without Cover Texts, or some other combination of the three, merge those two alternatives to suit the situation. If your document contains nontrivial examples of program code, we recommend releasing these examples in parallel under your choice of free software license, such as the GNU General Public License, to permit their use in free software.  File: calc, Node: Customizing Calc, Next: Reporting Bugs, Prev: GNU Free Documentation License, Up: Top Appendix C Customizing Calc *************************** The usual prefix for Calc is the key sequence `C-x *'. If you wish to use a different prefix, you can put (global-set-key "NEWPREFIX" 'calc-dispatch) in your .emacs file. (*Note Customizing Key Bindings: (emacs)Key Bindings, for more information on binding keys.) A convenient way to start Calc is with `C-x * *'; to make it equally convenient for users who use a different prefix, the prefix can be followed by `=', `&', `#', `\', `/', `+' or `-' as well as `*' to start Calc, and so in many cases the last character of the prefix can simply be typed twice. Calc is controlled by many variables, most of which can be reset from within Calc. Some variables are less involved with actual calculation, and can be set outside of Calc using Emacs's customization facilities. These variables are listed below. Typing `M-x customize-variable RET VARIABLE-NAME RET' will bring up a buffer in which the variable's value can be redefined. Typing `M-x customize-group RET calc RET' will bring up a buffer which contains all of Calc's customizable variables. (These variables can also be reset by putting the appropriate lines in your .emacs file; *Note Init File: (emacs)Init File.) Some of the customizable variables are regular expressions. A regular expression is basically a pattern that Calc can search for. See *note Regular Expression Search: (emacs)Regexp Search. to see how regular expressions work. -- Variable: calc-settings-file The variable `calc-settings-file' holds the file name in which commands like `m m' and `Z P' store "permanent" definitions. If `calc-settings-file' is not your user init file (typically `~/.emacs') and if the variable `calc-loaded-settings-file' is `nil', then Calc will automatically load your settings file (if it exists) the first time Calc is invoked. The default value for this variable is `"~/.calc.el"'. -- Variable: calc-gnuplot-name See *note Graphics::. The variable `calc-gnuplot-name' should be the name of the GNUPLOT program (a string). If you have GNUPLOT installed on your system but Calc is unable to find it, you may need to set this variable. You may also need to set some Lisp variables to show Calc how to run GNUPLOT on your system, see *note Graphical Devices: Devices . The default value of `calc-gnuplot-name' is `"gnuplot"'. -- Variable: calc-gnuplot-plot-command -- Variable: calc-gnuplot-print-command See *note Graphical Devices: Devices. The variables `calc-gnuplot-plot-command' and `calc-gnuplot-print-command' represent system commands to display and print the output of GNUPLOT, respectively. These may be `nil' if no command is necessary, or strings which can include `%s' to signify the name of the file to be displayed or printed. Or, these variables may contain Lisp expressions which are evaluated to display or print the output. The default value of `calc-gnuplot-plot-command' is `nil', and the default value of `calc-gnuplot-print-command' is `"lp %s"'. -- Variable: calc-language-alist See *note Basic Embedded Mode::. The variable `calc-language-alist' controls the languages that Calc will associate with major modes. When Calc embedded mode is enabled, it will try to use the current major mode to determine what language should be used. (This can be overridden using Calc's mode changing commands, *Note Mode Settings in Embedded Mode::.) The variable `calc-language-alist' consists of a list of pairs of the form `(MAJOR-MODE . LANGUAGE)'; for example, `(latex-mode . latex)' is one such pair. If Calc embedded is activated in a buffer whose major mode is MAJOR-MODE, it will set itself to use the language LANGUAGE. The default value of `calc-language-alist' is ((latex-mode . latex) (tex-mode . tex) (plain-tex-mode . tex) (context-mode . tex) (nroff-mode . eqn) (pascal-mode . pascal) (c-mode . c) (c++-mode . c) (fortran-mode . fortran) (f90-mode . fortran)) -- Variable: calc-embedded-announce-formula -- Variable: calc-embedded-announce-formula-alist See *note Customizing Embedded Mode::. The variable `calc-embedded-announce-formula' helps determine what formulas `C-x * a' will activate in a buffer. It is a regular expression, and when activating embedded formulas with `C-x * a', it will tell Calc that what follows is a formula to be activated. (Calc also uses other patterns to find formulas, such as `=>' and `:='.) The default pattern is `"%Embed\n\\(% .*\n\\)*"', which checks for `%Embed' followed by any number of lines beginning with `%' and a space. The variable `calc-embedded-announce-formula-alist' is used to set `calc-embedded-announce-formula' to different regular expressions depending on the major mode of the editing buffer. It consists of a list of pairs of the form `(MAJOR-MODE . REGEXP)', and its default value is ((c++-mode . "//Embed\n\\(// .*\n\\)*") (c-mode . "/\\*Embed\\*/\n\\(/\\* .*\\*/\n\\)*") (f90-mode . "!Embed\n\\(! .*\n\\)*") (fortran-mode . "C Embed\n\\(C .*\n\\)*") (html-helper-mode . "\n\\(\n\\)*") (html-mode . "\n\\(\n\\)*") (nroff-mode . "\\\\\"Embed\n\\(\\\\\" .*\n\\)*") (pascal-mode . "{Embed}\n\\({.*}\n\\)*") (sgml-mode . "\n\\(\n\\)*") (xml-mode . "\n\\(\n\\)*") (texinfo-mode . "@c Embed\n\\(@c .*\n\\)*")) Any major modes added to `calc-embedded-announce-formula-alist' should also be added to `calc-embedded-open-close-plain-alist' and `calc-embedded-open-close-mode-alist'. -- Variable: calc-embedded-open-formula -- Variable: calc-embedded-close-formula -- Variable: calc-embedded-open-close-formula-alist See *note Customizing Embedded Mode::. The variables `calc-embedded-open-formula' and `calc-embedded-close-formula' control the region that Calc will activate as a formula when Embedded mode is entered with `C-x * e'. They are regular expressions; Calc normally scans backward and forward in the buffer for the nearest text matching these regular expressions to be the "formula delimiters". The simplest delimiters are blank lines. Other delimiters that Embedded mode understands by default are: 1. The TeX and LaTeX math delimiters `$ $', `$$ $$', `\[ \]', and `\( \)'; 2. Lines beginning with `\begin' and `\end' (except matrix delimiters); 3. Lines beginning with `@' (Texinfo delimiters). 4. Lines beginning with `.EQ' and `.EN' ("eqn" delimiters); 5. Lines containing a single `%' or `.\"' symbol and nothing else. The variable `calc-embedded-open-close-formula-alist' is used to set `calc-embedded-open-formula' and `calc-embedded-close-formula' to different regular expressions depending on the major mode of the editing buffer. It consists of a list of lists of the form `(MAJOR-MODE OPEN-FORMULA-REGEXP CLOSE-FORMULA-REGEXP)', and its default value is `nil'. -- Variable: calc-embedded-word-regexp -- Variable: calc-embedded-word-regexp-alist See *note Customizing Embedded Mode::. The variable `calc-embedded-word-regexp' determines the expression that Calc will activate when Embedded mode is entered with `C-x * w'. It is a regular expressions. The default value of `calc-embedded-word-regexp' is `"[-+]?[0-9]+\\(\\.[0-9]+\\)?\\([eE][-+]?[0-9]+\\)?"'. The variable `calc-embedded-word-regexp-alist' is used to set `calc-embedded-word-regexp' to a different regular expression depending on the major mode of the editing buffer. It consists of a list of lists of the form `(MAJOR-MODE WORD-REGEXP)', and its default value is `nil'. -- Variable: calc-embedded-open-plain -- Variable: calc-embedded-close-plain -- Variable: calc-embedded-open-close-plain-alist See *note Customizing Embedded Mode::. The variables `calc-embedded-open-plain' and `calc-embedded-open-plain' are used to delimit "plain" formulas. Note that these are actual strings, not regular expressions, because Calc must be able to write these string into a buffer as well as to recognize them. The default string for `calc-embedded-open-plain' is `"%%% "', note the trailing space. The default string for `calc-embedded-close-plain' is `" %%%\n"', without the trailing newline here, the first line of a Big mode formula that followed might be shifted over with respect to the other lines. The variable `calc-embedded-open-close-plain-alist' is used to set `calc-embedded-open-plain' and `calc-embedded-close-plain' to different strings depending on the major mode of the editing buffer. It consists of a list of lists of the form `(MAJOR-MODE OPEN-PLAIN-STRING CLOSE-PLAIN-STRING)', and its default value is ((c++-mode "// %% " " %%\n") (c-mode "/* %% " " %% */\n") (f90-mode "! %% " " %%\n") (fortran-mode "C %% " " %%\n") (html-helper-mode "\n") (html-mode "\n") (nroff-mode "\\\" %% " " %%\n") (pascal-mode "{%% " " %%}\n") (sgml-mode "\n") (xml-mode "\n") (texinfo-mode "@c %% " " %%\n")) Any major modes added to `calc-embedded-open-close-plain-alist' should also be added to `calc-embedded-announce-formula-alist' and `calc-embedded-open-close-mode-alist'. -- Variable: calc-embedded-open-new-formula -- Variable: calc-embedded-close-new-formula -- Variable: calc-embedded-open-close-new-formula-alist See *note Customizing Embedded Mode::. The variables `calc-embedded-open-new-formula' and `calc-embedded-close-new-formula' are strings which are inserted before and after a new formula when you type `C-x * f'. The default value of `calc-embedded-open-new-formula' is `"\n\n"'. If this string begins with a newline character and the `C-x * f' is typed at the beginning of a line, `C-x * f' will skip this first newline to avoid introducing unnecessary blank lines in the file. The default value of `calc-embedded-close-new-formula' is also `"\n\n"'. The final newline is omitted by `C-x * f' if typed at the end of a line. (It follows that if `C-x * f' is typed on a blank line, both a leading opening newline and a trailing closing newline are omitted.) The variable `calc-embedded-open-close-new-formula-alist' is used to set `calc-embedded-open-new-formula' and `calc-embedded-close-new-formula' to different strings depending on the major mode of the editing buffer. It consists of a list of lists of the form `(MAJOR-MODE OPEN-NEW-FORMULA-STRING CLOSE-NEW-FORMULA-STRING)', and its default value is `nil'. -- Variable: calc-embedded-open-mode -- Variable: calc-embedded-close-mode -- Variable: calc-embedded-open-close-mode-alist See *note Customizing Embedded Mode::. The variables `calc-embedded-open-mode' and `calc-embedded-close-mode' are strings which Calc will place before and after any mode annotations that it inserts. Calc never scans for these strings; Calc always looks for the annotation itself, so it is not necessary to add them to user-written annotations. The default value of `calc-embedded-open-mode' is `"% "' and the default value of `calc-embedded-close-mode' is `"\n"'. If you change the value of `calc-embedded-close-mode', it is a good idea still to end with a newline so that mode annotations will appear on lines by themselves. The variable `calc-embedded-open-close-mode-alist' is used to set `calc-embedded-open-mode' and `calc-embedded-close-mode' to different strings expressions depending on the major mode of the editing buffer. It consists of a list of lists of the form `(MAJOR-MODE OPEN-MODE-STRING CLOSE-MODE-STRING)', and its default value is ((c++-mode "// " "\n") (c-mode "/* " " */\n") (f90-mode "! " "\n") (fortran-mode "C " "\n") (html-helper-mode "\n") (html-mode "\n") (nroff-mode "\\\" " "\n") (pascal-mode "{ " " }\n") (sgml-mode "\n") (xml-mode "\n") (texinfo-mode "@c " "\n")) Any major modes added to `calc-embedded-open-close-mode-alist' should also be added to `calc-embedded-announce-formula-alist' and `calc-embedded-open-close-plain-alist'. -- Variable: calc-multiplication-has-precedence The variable `calc-multiplication-has-precedence' determines whether multiplication has precedence over division in algebraic formulas in normal language modes. If `calc-multiplication-has-precedence' is non-`nil', then multiplication has precedence (and, for certain obscure reasons, is right associative), and so for example `a/b*c' will be interpreted as `a/(b*c)'. If `calc-multiplication-has-precedence' is `nil', then multiplication has the same precedence as division (and, like division, is left associative), and so for example `a/b*c' will be interpreted as `(a/b)*c'. The default value of `calc-multiplication-has-precedence' is `t'. -- Variable: calc-undo-length The variable `calc-undo-length' determines the number of undo steps that Calc will keep track of when `calc-quit' is called. If `calc-undo-length' is a non-negative integer, then this is the number of undo steps that will be preserved; if `calc-undo-length' has any other value, then all undo steps will be preserved. The default value of `calc-undo-length' is `100'.  File: calc, Node: Reporting Bugs, Next: Summary, Prev: Customizing Calc, Up: Top Appendix D Reporting Bugs ************************* If you find a bug in Calc, send e-mail to Jay Belanger, jay.p.belanger@gmail.com There is an automatic command `M-x report-calc-bug' which helps you to report bugs. This command prompts you for a brief subject line, then leaves you in a mail editing buffer. Type `C-c C-c' to send your mail. Make sure your subject line indicates that you are reporting a Calc bug; this command sends mail to the maintainer's regular mailbox. If you have suggestions for additional features for Calc, please send them. Some have dared to suggest that Calc is already top-heavy with features; this obviously cannot be the case, so if you have ideas, send them right in. At the front of the source file, `calc.el', is a list of ideas for future work. If any enthusiastic souls wish to take it upon themselves to work on these, please send a message (using `M-x report-calc-bug') so any efforts can be coordinated. The latest version of Calc is available from Savannah, in the Emacs repository. See `http://savannah.gnu.org/projects/emacs'.  File: calc, Node: Summary, Next: Key Index, Prev: Reporting Bugs, Up: Top Appendix E Calc Summary *********************** This section includes a complete list of Calc keystroke commands. Each line lists the stack entries used by the command (top-of-stack last), the keystrokes themselves, the prompts asked by the command, and the result of the command (also with top-of-stack last). The result is expressed using the equivalent algebraic function. Commands which put no results on the stack show the full `M-x' command name in that position. Numbers preceding the result or command name refer to notes at the end. Algebraic functions and `M-x' commands that don't have corresponding keystrokes are not listed in this summary. *Note Command Index::. *Note Function Index::. C-x * a 33 calc-embedded-activate C-x * b calc-big-or-small C-x * c calc C-x * d calc-embedded-duplicate C-x * e 34 calc-embedded C-x * f formula calc-embedded-new-formula C-x * g 35 calc-grab-region C-x * i calc-info C-x * j calc-embedded-select C-x * k calc-keypad C-x * l calc-load-everything C-x * m read-kbd-macro C-x * n 4 calc-embedded-next C-x * o calc-other-window C-x * p 4 calc-embedded-previous C-x * q formula quick-calc C-x * r 36 calc-grab-rectangle C-x * s calc-info-summary C-x * t calc-tutorial C-x * u calc-embedded-update-formula C-x * w calc-embedded-word C-x * x calc-quit C-x * y 1,28,49 calc-copy-to-buffer C-x * z calc-user-invocation C-x * : 36 calc-grab-sum-down C-x * _ 36 calc-grab-sum-across C-x * ` editing 30 calc-embedded-edit C-x * 0 (zero) calc-reset 0-9 number number . number 0.number _ number -number e number 1e number # number current-radix#number P (in number) +/- M (in number) mod @ ' " (in number) HMS form h m s (in number) HMS form ' formula 37,46 formula $ formula 37,46 $formula " string 37,46 string a b + 2 add(a,b) a+b a b - 2 sub(a,b) a-b a b * 2 mul(a,b) a b, a*b a b / 2 div(a,b) a/b a b ^ 2 pow(a,b) a^b a b I ^ 2 nroot(a,b) a^(1/b) a b % 2 mod(a,b) a%b a b \ 2 idiv(a,b) a\b a b : 2 fdiv(a,b) a b | 2 vconcat(a,b) a|b a b I | vconcat(b,a) b|a a b H | 2 append(a,b) a b I H | append(b,a) a & 1 inv(a) 1/a a ! 1 fact(a) a! a = 1 evalv(a) a M-% percent(a) a% ... a RET 1 ... a a ... a SPC 1 ... a a ... a b TAB 3 ... b a . a b c M-TAB 3 ... b c a ... a b LFD 1 ... a b a ... a DEL 1 ... ... a b M-DEL 1 ... b M-RET 4 calc-last-args a ` editing 1,30 calc-edit ... a C-d 1 ... C-k 27 calc-kill C-w 27 calc-kill-region C-y calc-yank C-_ 4 calc-undo M-k 27 calc-copy-as-kill M-w 27 calc-copy-region-as-kill [ [... [.. a b ] [a,b] ( (... (.. a b ) (a,b) , vector or rect complex ; matrix or polar complex .. interval ~ calc-num-prefix < 4 calc-scroll-left > 4 calc-scroll-right { 4 calc-scroll-down } 4 calc-scroll-up ? calc-help a n 1 neg(a) -a o 4 calc-realign p precision 31 calc-precision q calc-quit w calc-why x command M-x calc-command a y 1,28,49 calc-copy-to-buffer a A 1 abs(a) a b B 2 log(a,b) a b I B 2 alog(a,b) b^a a C 1 cos(a) a I C 1 arccos(a) a H C 1 cosh(a) a I H C 1 arccosh(a) D 4 calc-redo a E 1 exp(a) a H E 1 exp10(a) 10.^a a F 1,11 floor(a,d) a I F 1,11 ceil(a,d) a H F 1,11 ffloor(a,d) a I H F 1,11 fceil(a,d) a G 1 arg(a) H command 32 Hyperbolic I command 32 Inverse a J 1 conj(a) K command 32 Keep-args a L 1 ln(a) a H L 1 log10(a) M calc-more-recursion-depth I M calc-less-recursion-depth a N 5 evalvn(a) P pi I P gamma H P e I H P phi a Q 1 sqrt(a) a I Q 1 sqr(a) a^2 a R 1,11 round(a,d) a I R 1,11 trunc(a,d) a H R 1,11 fround(a,d) a I H R 1,11 ftrunc(a,d) a S 1 sin(a) a I S 1 arcsin(a) a H S 1 sinh(a) a I H S 1 arcsinh(a) a T 1 tan(a) a I T 1 arctan(a) a H T 1 tanh(a) a I H T 1 arctanh(a) U 4 calc-undo X 4 calc-call-last-kbd-macro a b a = 2 eq(a,b) a=b a b a # 2 neq(a,b) a!=b a b a < 2 lt(a,b) a 2 gt(a,b) a>b a b a [ 2 leq(a,b) a<=b a b a ] 2 geq(a,b) a>=b a b a { 2 in(a,b) a b a & 2,45 land(a,b) a&&b a b a | 2,45 lor(a,b) a||b a a ! 1,45 lnot(a) !a a b c a : 45 if(a,b,c) a?b:c a a . 1 rmeq(a) a a " 7,8 calc-expand-formula a a + i, l, h 6,38 sum(a,i,l,h) a a - i, l, h 6,38 asum(a,i,l,h) a a * i, l, h 6,38 prod(a,i,l,h) a b a _ 2 subscr(a,b) a_b a b a \ 2 pdiv(a,b) a b a % 2 prem(a,b) a b a / 2 pdivrem(a,b) [q,r] a b H a / 2 pdivide(a,b) q+r/b a a a 1 apart(a) a a b old, new 38 subst(a,old,new) a a c v 38 collect(a,v) a a d v 4,38 deriv(a,v) a H a d v 4,38 tderiv(a,v) a a e esimplify(a) a a f 1 factor(a) a H a f 1 factors(a) a b a g 2 pgcd(a,b) a a i v 38 integ(a,v) a a m pats 38 match(a,pats) a I a m pats 38 matchnot(a,pats) data x a p 28 polint(data,x) data x H a p 28 ratint(data,x) a a n 1 nrat(a) a a r rules 4,8,38 rewrite(a,rules,n) a a s simplify(a) a a t v, n 31,39 taylor(a,v,n) a a v 7,8 calc-alg-evaluate a a x 4,8 expand(a) data a F model, vars 48 fit(m,iv,pv,data) data I a F model, vars 48 xfit(m,iv,pv,data) data H a F model, vars 48 efit(m,iv,pv,data) a a I v, l, h 38 ninteg(a,v,l,h) a b a M op 22 mapeq(op,a,b) a b I a M op 22 mapeqr(op,a,b) a b H a M op 22 mapeqp(op,a,b) a g a N v 38 minimize(a,v,g) a g H a N v 38 wminimize(a,v,g) a a P v 38 roots(a,v) a g a R v 38 root(a,v,g) a g H a R v 38 wroot(a,v,g) a a S v 38 solve(a,v) a I a S v 38 finv(a,v) a H a S v 38 fsolve(a,v) a I H a S v 38 ffinv(a,v) a a T i, l, h 6,38 table(a,i,l,h) a g a X v 38 maximize(a,v,g) a g H a X v 38 wmaximize(a,v,g) a b b a 9 and(a,b,w) a b c 9 clip(a,w) a b b d 9 diff(a,b,w) a b l 10 lsh(a,n,w) a n H b l 9 lsh(a,n,w) a b n 9 not(a,w) a b b o 9 or(a,b,w) v b p 1 vpack(v) a b r 10 rsh(a,n,w) a n H b r 9 rsh(a,n,w) a b t 10 rot(a,n,w) a n H b t 9 rot(a,n,w) a b u 1 vunpack(a) b w w 9,50 calc-word-size a b b x 9 xor(a,b,w) c s l p b D ddb(c,s,l,p) r n p b F fv(r,n,p) r n p I b F fvb(r,n,p) r n p H b F fvl(r,n,p) v b I 19 irr(v) v I b I 19 irrb(v) a b L 10 ash(a,n,w) a n H b L 9 ash(a,n,w) r n a b M pmt(r,n,a) r n a I b M pmtb(r,n,a) r n a H b M pmtl(r,n,a) r v b N 19 npv(r,v) r v I b N 19 npvb(r,v) r n p b P pv(r,n,p) r n p I b P pvb(r,n,p) r n p H b P pvl(r,n,p) a b R 10 rash(a,n,w) a n H b R 9 rash(a,n,w) c s l b S sln(c,s,l) n p a b T rate(n,p,a) n p a I b T rateb(n,p,a) n p a H b T ratel(n,p,a) c s l p b Y syd(c,s,l,p) r p a b # nper(r,p,a) r p a I b # nperb(r,p,a) r p a H b # nperl(r,p,a) a b b % relch(a,b) a c c 5 pclean(a,p) a c 0-9 pclean(a,p) a H c c 5 clean(a,p) a H c 0-9 clean(a,p) a c d 1 deg(a) a c f 1 pfloat(a) a H c f 1 float(a) a c h 1 hms(a) a c p polar(a) a I c p rect(a) a c r 1 rad(a) a c F 5 pfrac(a,p) a H c F 5 frac(a,p) a c % percent(a*100) d . char 50 calc-point-char d , char 50 calc-group-char d < 13,50 calc-left-justify d = 13,50 calc-center-justify d > 13,50 calc-right-justify d { label 50 calc-left-label d } label 50 calc-right-label d [ 4 calc-truncate-up d ] 4 calc-truncate-down d " 12,50 calc-display-strings d SPC calc-refresh d RET 1 calc-refresh-top d 0 50 calc-decimal-radix d 2 50 calc-binary-radix d 6 50 calc-hex-radix d 8 50 calc-octal-radix d b 12,13,50 calc-line-breaking d c 50 calc-complex-notation d d format 50 calc-date-notation d e 5,50 calc-eng-notation d f num 31,50 calc-fix-notation d g 12,13,50 calc-group-digits d h format 50 calc-hms-notation d i 50 calc-i-notation d j 50 calc-j-notation d l 12,50 calc-line-numbering d n 5,50 calc-normal-notation d o format 50 calc-over-notation d p 12,50 calc-show-plain d r radix 31,50 calc-radix d s 5,50 calc-sci-notation d t 27 calc-truncate-stack d w 12,13 calc-auto-why d z 12,50 calc-leading-zeros d B 50 calc-big-language d C 50 calc-c-language d E 50 calc-eqn-language d F 50 calc-fortran-language d M 50 calc-mathematica-language d N 50 calc-normal-language d O 50 calc-flat-language d P 50 calc-pascal-language d T 50 calc-tex-language d L 50 calc-latex-language d U 50 calc-unformatted-language d W 50 calc-maple-language a f [ 4 decr(a,n) a f ] 4 incr(a,n) a b f b 2 beta(a,b) a f e 1 erf(a) a I f e 1 erfc(a) a f g 1 gamma(a) a b f h 2 hypot(a,b) a f i 1 im(a) n a f j 2 besJ(n,a) a b f n 2 min(a,b) a f r 1 re(a) a f s 1 sign(a) a b f x 2 max(a,b) n a f y 2 besY(n,a) a f A 1 abssqr(a) x a b f B betaI(x,a,b) x a b H f B betaB(x,a,b) a f E 1 expm1(a) a x f G 2 gammaP(a,x) a x I f G 2 gammaQ(a,x) a x H f G 2 gammag(a,x) a x I H f G 2 gammaG(a,x) a b f I 2 ilog(a,b) a b I f I 2 alog(a,b) b^a a f L 1 lnp1(a) a f M 1 mant(a) a f Q 1 isqrt(a) a I f Q 1 sqr(a) a^2 a n f S 2 scf(a,n) y x f T arctan2(y,x) a f X 1 xpon(a) x y g a 28,40 calc-graph-add g b 12 calc-graph-border g c calc-graph-clear g d 41 calc-graph-delete x y g f 28,40 calc-graph-fast g g 12 calc-graph-grid g h title calc-graph-header g j 4 calc-graph-juggle g k 12 calc-graph-key g l 12 calc-graph-log-x g n name calc-graph-name g p 42 calc-graph-plot g q calc-graph-quit g r range calc-graph-range-x g s 12,13 calc-graph-line-style g t title calc-graph-title-x g v calc-graph-view-commands g x display calc-graph-display g z 12 calc-graph-zero-x x y z g A 28,40 calc-graph-add-3d g C command calc-graph-command g D device 43,44 calc-graph-device x y z g F 28,40 calc-graph-fast-3d g H 12 calc-graph-hide g K calc-graph-kill g L 12 calc-graph-log-y g N number 43,51 calc-graph-num-points g O filename 43,44 calc-graph-output g P 42 calc-graph-print g R range calc-graph-range-y g S 12,13 calc-graph-point-style g T title calc-graph-title-y g V calc-graph-view-trail g X format calc-graph-geometry g Z 12 calc-graph-zero-y g C-l 12 calc-graph-log-z g C-r range calc-graph-range-z g C-t title calc-graph-title-z h b calc-describe-bindings h c key calc-describe-key-briefly h f function calc-describe-function h h calc-full-help h i calc-info h k key calc-describe-key h n calc-view-news h s calc-info-summary h t calc-tutorial h v var calc-describe-variable j 1-9 calc-select-part j RET 27 calc-copy-selection j DEL 27 calc-del-selection j ' formula 27 calc-enter-selection j ` editing 27,30 calc-edit-selection j " 7,27 calc-sel-expand-formula j + formula 27 calc-sel-add-both-sides j - formula 27 calc-sel-sub-both-sides j * formula 27 calc-sel-mul-both-sides j / formula 27 calc-sel-div-both-sides j & 27 calc-sel-invert j a 27 calc-select-additional j b 12 calc-break-selections j c calc-clear-selections j d 12,50 calc-show-selections j e 12 calc-enable-selections j l 4,27 calc-select-less j m 4,27 calc-select-more j n 4 calc-select-next j o 4,27 calc-select-once j p 4 calc-select-previous j r rules 4,8,27 calc-rewrite-selection j s 4,27 calc-select-here j u 27 calc-unselect j v 7,27 calc-sel-evaluate j C 27 calc-sel-commute j D 4,27 calc-sel-distribute j E 27 calc-sel-jump-equals j I 27 calc-sel-isolate H j I 27 calc-sel-isolate (full) j L 4,27 calc-commute-left j M 27 calc-sel-merge j N 27 calc-sel-negate j O 4,27 calc-select-once-maybe j R 4,27 calc-commute-right j S 4,27 calc-select-here-maybe j U 27 calc-sel-unpack k a calc-random-again n k b 1 bern(n) n x H k b 2 bern(n,x) n m k c 2 choose(n,m) n m H k c 2 perm(n,m) n k d 1 dfact(n) n!! n k e 1 euler(n) n x H k e 2 euler(n,x) n k f 4 prfac(n) n m k g 2 gcd(n,m) m n k h 14 shuffle(n,m) n m k l 2 lcm(n,m) n k m 1 moebius(n) n k n 4 nextprime(n) n I k n 4 prevprime(n) n k p 4,28 calc-prime-test m k r 14 random(m) n m k s 2 stir1(n,m) n m H k s 2 stir2(n,m) n k t 1 totient(n) n p x k B utpb(x,n,p) n p x I k B ltpb(x,n,p) v x k C utpc(x,v) v x I k C ltpc(x,v) n m k E egcd(n,m) v1 v2 x k F utpf(x,v1,v2) v1 v2 x I k F ltpf(x,v1,v2) m s x k N utpn(x,m,s) m s x I k N ltpn(x,m,s) m x k P utpp(x,m) m x I k P ltpp(x,m) v x k T utpt(x,v) v x I k T ltpt(x,v) m a 12,13 calc-algebraic-mode m d calc-degrees-mode m e calc-embedded-preserve-modes m f 12 calc-frac-mode m g 52 calc-get-modes m h calc-hms-mode m i 12,13 calc-infinite-mode m m calc-save-modes m p 12 calc-polar-mode m r calc-radians-mode m s 12 calc-symbolic-mode m t 12 calc-total-algebraic-mode m v 12,13 calc-matrix-mode m w 13 calc-working m x calc-always-load-extensions m A 12 calc-alg-simplify-mode m B 12 calc-bin-simplify-mode m C 12 calc-auto-recompute m D calc-default-simplify-mode m E 12 calc-ext-simplify-mode m F filename 13 calc-settings-file-name m N 12 calc-num-simplify-mode m O 12 calc-no-simplify-mode m R 12,13 calc-mode-record-mode m S 12 calc-shift-prefix m U 12 calc-units-simplify-mode r s register 27 calc-copy-to-register r i register calc-insert-register s c var1, var2 29 calc-copy-variable s d var, decl calc-declare-variable s e var, editing 29,30 calc-edit-variable s i buffer calc-insert-variables s k const, var 29 calc-copy-special-constant a b s l var 29 a (letting var=b) a ... s m op, var 22,29 calc-store-map s n var 29,47 calc-store-neg (v/-1) s p var 29 calc-permanent-variable s r var 29 v (recalled value) r 0-9 calc-recall-quick a s s var 28,29 calc-store a s 0-9 calc-store-quick a s t var 29 calc-store-into a t 0-9 calc-store-into-quick s u var 29 calc-unstore a s x var 29 calc-store-exchange s A editing 30 calc-edit-AlgSimpRules s D editing 30 calc-edit-Decls s E editing 30 calc-edit-EvalRules s F editing 30 calc-edit-FitRules s G editing 30 calc-edit-GenCount s H editing 30 calc-edit-Holidays s I editing 30 calc-edit-IntegLimit s L editing 30 calc-edit-LineStyles s P editing 30 calc-edit-PointStyles s R editing 30 calc-edit-PlotRejects s T editing 30 calc-edit-TimeZone s U editing 30 calc-edit-Units s X editing 30 calc-edit-ExtSimpRules a s + var 29,47 calc-store-plus (v+a) a s - var 29,47 calc-store-minus (v-a) a s * var 29,47 calc-store-times (v*a) a s / var 29,47 calc-store-div (v/a) a s ^ var 29,47 calc-store-power (v^a) a s | var 29,47 calc-store-concat (v|a) s & var 29,47 calc-store-inv (v^-1) s [ var 29,47 calc-store-decr (v-1) s ] var 29,47 calc-store-incr (v-(-1)) a b s : 2 assign(a,b) a := b a s = 1 evalto(a,b) a => t [ 4 calc-trail-first t ] 4 calc-trail-last t < 4 calc-trail-scroll-left t > 4 calc-trail-scroll-right t . 12 calc-full-trail-vectors t b 4 calc-trail-backward t d 12,50 calc-trail-display t f 4 calc-trail-forward t h calc-trail-here t i calc-trail-in t k 4 calc-trail-kill t m string calc-trail-marker t n 4 calc-trail-next t o calc-trail-out t p 4 calc-trail-previous t r string calc-trail-isearch-backward t s string calc-trail-isearch-forward t y 4 calc-trail-yank d t C oz, nz tzconv(d,oz,nz) d oz nz t C $ tzconv(d,oz,nz) d t D 15 date(d) d t I 4 incmonth(d,n) d t J 16 julian(d,z) d t M 17 newmonth(d,n) t N 16 now(z) d t P 1 31 year(d) d t P 2 31 month(d) d t P 3 31 day(d) d t P 4 31 hour(d) d t P 5 31 minute(d) d t P 6 31 second(d) d t P 7 31 weekday(d) d t P 8 31 yearday(d) d t P 9 31 time(d) d t U 16 unixtime(d,z) d t W 17 newweek(d,w) d t Y 17 newyear(d,n) a b t + 2 badd(a,b) a b t - 2 bsub(a,b) u a 12 calc-autorange-units a u b calc-base-units a u c units 18 calc-convert-units defn u d unit, descr calc-define-unit u e calc-explain-units u g unit calc-get-unit-definition u p calc-permanent-units a u r calc-remove-units a u s usimplify(a) a u t units 18 calc-convert-temperature u u unit calc-undefine-unit u v calc-enter-units-table a u x calc-extract-units a u 0-9 calc-quick-units v1 v2 u C 20 vcov(v1,v2) v1 v2 I u C 20 vpcov(v1,v2) v1 v2 H u C 20 vcorr(v1,v2) v u G 19 vgmean(v) a b H u G 2 agmean(a,b) v u M 19 vmean(v) v I u M 19 vmeane(v) v H u M 19 vmedian(v) v I H u M 19 vhmean(v) v u N 19 vmin(v) v u S 19 vsdev(v) v I u S 19 vpsdev(v) v H u S 19 vvar(v) v I H u S 19 vpvar(v) u V calc-view-units-table v u X 19 vmax(v) v u + 19 vsum(v) v u * 19 vprod(v) v u # 19 vcount(v) V ( 50 calc-vector-parens V { 50 calc-vector-braces V [ 50 calc-vector-brackets V ] ROCP 50 calc-matrix-brackets V , 50 calc-vector-commas V < 50 calc-matrix-left-justify V = 50 calc-matrix-center-justify V > 50 calc-matrix-right-justify V / 12,50 calc-break-vectors V . 12,50 calc-full-vectors s t V ^ 2 vint(s,t) s t V - 2 vdiff(s,t) s V ~ 1 vcompl(s) s V # 1 vcard(s) s V : 1 vspan(s) s V + 1 rdup(s) m V & 1 inv(m) 1/m v v a n arrange(v,n) a v b n cvec(a,n) v v c n >0 21,31 mcol(v,n) v v c n <0 31 mrcol(v,-n) m v c 0 31 getdiag(m) v v d 25 diag(v,n) v m v e 2 vexp(v,m) v m f H v e 2 vexp(v,m,f) v a v f 26 find(v,a,n) v v h 1 head(v) v I v h 1 tail(v) v H v h 1 rhead(v) v I H v h 1 rtail(v) v i n 31 idn(1,n) v i 0 31 idn(1) h t v k 2 cons(h,t) h t H v k 2 rcons(h,t) v v l 1 vlen(v) v H v l 1 mdims(v) v m v m 2 vmask(v,m) v v n 1 rnorm(v) a b c v p 24 calc-pack v v r n >0 21,31 mrow(v,n) v v r n <0 31 mrrow(v,-n) m v r 0 31 getdiag(m) v i j v s subvec(v,i,j) v i j I v s rsubvec(v,i,j) m v t 1 trn(m) v v u 24 calc-unpack v v v 1 rev(v) v x n 31 index(n) n s i C-u v x index(n,s,i) v V A op 22 apply(op,v) v1 v2 V C 2 cross(v1,v2) m V D 1 det(m) s V E 1 venum(s) s V F 1 vfloor(s) v V G grade(v) v I V G rgrade(v) v V H n 31 histogram(v,n) v w H V H n 31 histogram(v,w,n) v1 v2 V I mop aop 22 inner(mop,aop,v1,v2) m V J 1 ctrn(m) m1 m2 V K kron(m1,m2) m V L 1 lud(m) v V M op 22,23 map(op,v) v V N 1 cnorm(v) v1 v2 V O op 22 outer(op,v1,v2) v V R op 22,23 reduce(op,v) v I V R op 22,23 rreduce(op,v) a n H V R op 22 nest(op,a,n) a I H V R op 22 fixp(op,a) v V S sort(v) v I V S rsort(v) m V T 1 tr(m) v V U op 22 accum(op,v) v I V U op 22 raccum(op,v) a n H V U op 22 anest(op,a,n) a I H V U op 22 afixp(op,a) s t V V 2 vunion(s,t) s t V X 2 vxor(s,t) Y user commands z user commands c Z [ 45 calc-kbd-if c Z | 45 calc-kbd-else-if Z : calc-kbd-else Z ] calc-kbd-end-if Z { 4 calc-kbd-loop c Z / 45 calc-kbd-break Z } calc-kbd-end-loop n Z < calc-kbd-repeat Z > calc-kbd-end-repeat n m Z ( calc-kbd-for s Z ) calc-kbd-end-for Z C-g cancel if/loop command Z ` calc-kbd-push Z ' calc-kbd-pop Z # calc-kbd-query comp Z C func, args 50 calc-user-define-composition Z D key, command calc-user-define Z E key, editing 30 calc-user-define-edit defn Z F k, c, f, a, n 28 calc-user-define-formula Z G key calc-get-user-defn Z I calc-user-define-invocation Z K key, command calc-user-define-kbd-macro Z P key calc-user-define-permanent Z S 30 calc-edit-user-syntax Z T 12 calc-timing Z U key calc-user-undefine NOTES 1. Positive prefix arguments apply to `n' stack entries. Negative prefix arguments apply to the `-n'th stack entry. A prefix of zero applies to the entire stack. (For and `M-', the meaning of the sign is reversed.) 2. Positive prefix arguments apply to `n' stack entries. Negative prefix arguments apply to the top stack entry and the next `-n' stack entries. 3. Positive prefix arguments rotate top `n' stack entries by one. Negative prefix arguments rotate the entire stack by `-n'. A prefix of zero reverses the entire stack. 4. Prefix argument specifies a repeat count or distance. 5. Positive prefix arguments specify a precision `p'. Negative prefix arguments reduce the current precision by `-p'. 6. A prefix argument is interpreted as an additional step-size parameter. A plain `C-u' prefix means to prompt for the step size. 7. A prefix argument specifies simplification level and depth. 1=Default, 2=like `a s', 3=like `a e'. 8. A negative prefix operates only on the top level of the input formula. 9. Positive prefix arguments specify a word size of `w' bits, unsigned. Negative prefix arguments specify a word size of `w' bits, signed. 10. Prefix arguments specify the shift amount `n'. The `w' argument cannot be specified in the keyboard version of this command. 11. From the keyboard, `d' is omitted and defaults to zero. 12. Mode is toggled; a positive prefix always sets the mode, and a negative prefix always clears the mode. 13. Some prefix argument values provide special variations of the mode. 14. A prefix argument, if any, is used for `m' instead of taking `m' from the stack. `M' may take any of these values: Integer Random integer in the interval `[0 .. m)'. Float Random floating-point number in the interval `[0 .. m)'. 0.0 Gaussian with mean 1 and standard deviation 0. Error form Gaussian with specified mean and standard deviation. Interval Random integer or floating-point number in that interval. Vector Random element from the vector. 15. A prefix argument from 1 to 6 specifies number of date components to remove from the stack. *Note Date Conversions::. 16. A prefix argument specifies a time zone; `C-u' says to take the time zone number or name from the top of the stack. *Note Time Zones::. 17. A prefix argument specifies a day number (0-6, 0-31, or 0-366). 18. If the input has no units, you will be prompted for both the old and the new units. 19. With a prefix argument, collect that many stack entries to form the input data set. Each entry may be a single value or a vector of values. 20. With a prefix argument of 1, take a single Nx2 matrix from the stack instead of two separate data vectors. 21. The row or column number `n' may be given as a numeric prefix argument instead. A plain `C-u' prefix says to take `n' from the top of the stack. If `n' is a vector or interval, a subvector/submatrix of the input is created. 22. The `op' prompt can be answered with the key sequence for the desired function, or with `x' or `z' followed by a function name, or with `$' to take a formula from the top of the stack, or with `'' and a typed formula. In the last two cases, the formula may be a nameless function like `<#1+#2>' or `', or it may include `$', `$$', etc. (where `$' will correspond to the last argument of the created function), or otherwise you will be prompted for an argument list. The number of vectors popped from the stack by `V M' depends on the number of arguments of the function. 23. One of the mapping direction keys `_' (horizontal, i.e., map by rows or reduce across), `:' (vertical, i.e., map by columns or reduce down), or `=' (map or reduce by rows) may be used before entering `op'; these modify the function name by adding the letter `r' for "rows," `c' for "columns," `a' for "across," or `d' for "down." 24. The prefix argument specifies a packing mode. A nonnegative mode is the number of items (for `v p') or the number of levels (for `v u'). A negative mode is as described below. With no prefix argument, the mode is taken from the top of the stack and may be an integer or a vector of integers. `-1' (2) Rectangular complex number. `-2' (2) Polar complex number. `-3' (3) HMS form. `-4' (2) Error form. `-5' (2) Modulo form. `-6' (2) Closed interval. `-7' (2) Closed .. open interval. `-8' (2) Open .. closed interval. `-9' (2) Open interval. `-10' (2) Fraction. `-11' (2) Float with integer mantissa. `-12' (2) Float with mantissa in `[1 .. 10)'. `-13' (1) Date form (using date numbers). `-14' (3) Date form (using year, month, day). `-15' (6) Date form (using year, month, day, hour, minute, second). 25. A prefix argument specifies the size `n' of the matrix. With no prefix argument, `n' is omitted and the size is inferred from the input vector. 26. The prefix argument specifies the starting position `n' (default 1). 27. Cursor position within stack buffer affects this command. 28. Arguments are not actually removed from the stack by this command. 29. Variable name may be a single digit or a full name. 30. Editing occurs in a separate buffer. Press `C-c C-c' (or , or in some cases ) to finish the edit, or kill the buffer with `C-x k' to cancel the edit. The key prevents evaluation of the result of the edit. 31. The number prompted for can also be provided as a prefix argument. 32. Press this key a second time to cancel the prefix. 33. With a negative prefix, deactivate all formulas. With a positive prefix, deactivate and then reactivate from scratch. 34. Default is to scan for nearest formula delimiter symbols. With a prefix of zero, formula is delimited by mark and point. With a non-zero prefix, formula is delimited by scanning forward or backward by that many lines. 35. Parse the region between point and mark as a vector. A nonzero prefix parses N lines before or after point as a vector. A zero prefix parses the current line as a vector. A `C-u' prefix parses the region between point and mark as a single formula. 36. Parse the rectangle defined by point and mark as a matrix. A positive prefix N divides the rectangle into columns of width N. A zero or `C-u' prefix parses each line as one formula. A negative prefix suppresses special treatment of bracketed portions of a line. 37. A numeric prefix causes the current language mode to be ignored. 38. Responding to a prompt with a blank line answers that and all later prompts by popping additional stack entries. 39. Answer for `v' may also be of the form `v = v_0' or `v - v_0'. 40. With a positive prefix argument, stack contains many `y''s and one common `x'. With a zero prefix, stack contains a vector of `y's and a common `x'. With a negative prefix, stack contains many `[x,y]' vectors. (For 3D plots, substitute `z' for `y' and `x,y' for `x'.) 41. With any prefix argument, all curves in the graph are deleted. 42. With a positive prefix, refines an existing plot with more data points. With a negative prefix, forces recomputation of the plot data. 43. With any prefix argument, set the default value instead of the value for this graph. 44. With a negative prefix argument, set the value for the printer. 45. Condition is considered "true" if it is a nonzero real or complex number, or a formula whose value is known to be nonzero; it is "false" otherwise. 46. Several formulas separated by commas are pushed as multiple stack entries. Trailing `)', `]', `}', `>', and `"' delimiters may be omitted. The notation `$$$' refers to the value in stack level three, and causes the formula to replace the top three stack levels. The notation `$3' refers to stack level three without causing that value to be removed from the stack. Use in place of to prevent evaluation; use `M-=' in place of to evaluate variables. 47. The variable is replaced by the formula shown on the right. The Inverse flag reverses the order of the operands, e.g., `I s - x' assigns `x := a-x'. 48. Press `?' repeatedly to see how to choose a model. Answer the variables prompt with `iv' or `iv;pv' to specify independent and parameter variables. A positive prefix argument takes N+1 vectors from the stack; a zero prefix takes a matrix and a vector from the stack. 49. With a plain `C-u' prefix, replace the current region of the destination buffer with the yanked text instead of inserting. 50. All stack entries are reformatted; the `H' prefix inhibits this. The `I' prefix sets the mode temporarily, redraws the top stack entry, then restores the original setting of the mode. 51. A negative prefix sets the default 3D resolution instead of the default 2D resolution. 52. This grabs a vector of the form [PREC, WSIZE, SSIZE, RADIX, FLFMT, ANG, FRAC, SYMB, POLAR, MATRIX, SIMP, INF]. A prefix argument from 1 to 12 grabs the Nth mode value only.  File: calc, Node: Key Index, Next: Command Index, Prev: Summary, Up: Top Index of Key Sequences ********************** [index] * Menu: * !: Combinatorial Functions. (line 24) * ": Strings. (line 6) * " (HMS forms): HMS Forms. (line 13) * #: Integers. (line 18) * $: Algebraic Entry. (line 57) * %: Basic Arithmetic. (line 146) * &: Basic Arithmetic. (line 184) * & (matrices): Vector and Matrix Arithmetic. (line 42) * ': Algebraic Entry. (line 6) * ' (HMS forms): HMS Forms. (line 13) * (: Incomplete Objects. (line 6) * ): Incomplete Objects. (line 6) * *: Basic Arithmetic. (line 70) * +: Basic Arithmetic. (line 6) * ,: Incomplete Objects. (line 6) * -: Basic Arithmetic. (line 65) * .: Numeric Entry. (line 6) * ..: Incomplete Objects. (line 32) * /: Basic Arithmetic. (line 89) * 0-9: Numeric Entry. (line 6) * :: Basic Arithmetic. (line 153) * ;: Incomplete Objects. (line 27) * <: Basic Commands. (line 95) * : Stack Manipulation. (line 23) * : Stack Manipulation. (line 16) * : Stack Manipulation. (line 6) * : Stack Manipulation. (line 6) * : Stack Manipulation. (line 39) * =: Variables. (line 30) * >: Basic Commands. (line 95) * ?: Help Commands. (line 6) * @: HMS Forms. (line 13) * [: Incomplete Objects. (line 6) * \: Basic Arithmetic. (line 139) * ]: Incomplete Objects. (line 6) * ^: Basic Arithmetic. (line 128) * _: Numeric Entry. (line 12) * `: Editing Stack Entries. (line 6) * A: Basic Arithmetic. (line 165) * a !: Logical Operations. (line 86) * a ": Algebraic Manipulation. (line 59) * a #: Logical Operations. (line 46) * a %: Polynomials. (line 133) * a &: Logical Operations. (line 75) * A (vectors): Vector and Matrix Arithmetic. (line 19) * a *: Summations. (line 116) * a +: Summations. (line 6) * a -: Summations. (line 104) * a .: Logical Operations. (line 65) * a /: Polynomials. (line 139) * a :: Logical Operations. (line 90) * a <: Logical Operations. (line 51) * a =: Logical Operations. (line 20) * a >: Logical Operations. (line 51) * a ?: Help Commands. (line 6) * a [: Logical Operations. (line 51) * a \: Polynomials. (line 119) * a ]: Logical Operations. (line 51) * a _: Extracting Elements. (line 24) * a a: Polynomials. (line 105) * a b: Algebraic Manipulation. (line 109) * a c: Polynomials. (line 68) * a d: Differentiation. (line 6) * a e: Unsafe Simplifications. (line 6) * a F: Linear Fits. (line 6) * a f: Polynomials. (line 13) * a g: Polynomials. (line 145) * a I: Numerical Integration. (line 6) * a i: Integration. (line 6) * a m: Matching Commands. (line 6) * a M: Algebraic Manipulation. (line 73) * a N: Minimization. (line 6) * a n: Polynomials. (line 112) * a p: Interpolation. (line 6) * a P: Multiple Solutions. (line 63) * a r: Rewrite Rules. (line 6) * a R: Root Finding. (line 6) * a S: Solving Equations. (line 6) * a s: Simplifying Formulas. (line 6) * a T: Summations. (line 122) * a t: Taylor Series. (line 6) * a v: Algebraic Manipulation. (line 15) * a X: Minimization. (line 6) * a x: Polynomials. (line 83) * a {: Logical Operations. (line 109) * a |: Logical Operations. (line 81) * B: Logarithmic Functions. (line 22) * b #: Related Financial Functions. (line 21) * b %: Percentages. (line 44) * b ?: Help Commands. (line 6) * b a: Binary Functions. (line 57) * b c: Binary Functions. (line 26) * b d: Binary Functions. (line 71) * b D: Depreciation Functions. (line 29) * b F: Future Value. (line 6) * b I: Related Financial Functions. (line 50) * b L: Binary Functions. (line 97) * b l: Binary Functions. (line 78) * b M: Related Financial Functions. (line 9) * b n: Binary Functions. (line 75) * b N: Present Value. (line 46) * b o: Binary Functions. (line 63) * b p: Set Operations. (line 111) * b P: Present Value. (line 6) * b R: Binary Functions. (line 102) * b r: Binary Functions. (line 93) * b S: Depreciation Functions. (line 16) * b t: Binary Functions. (line 111) * b T: Related Financial Functions. (line 38) * b u: Set Operations. (line 111) * b w: Binary Functions. (line 35) * b x: Binary Functions. (line 67) * b Y: Depreciation Functions. (line 22) * C: Trigonometric and Hyperbolic Functions. (line 44) * c %: Percentages. (line 34) * c 0-9: Conversions. (line 101) * c ?: Help Commands. (line 6) * c c: Conversions. (line 81) * c d: Conversions. (line 56) * c F: Conversions. (line 40) * c f: Conversions. (line 9) * c h: Conversions. (line 64) * c p: Conversions. (line 73) * c r: Conversions. (line 61) * C-_: Undo. (line 6) * C-d: Stack Manipulation. (line 23) * C-k: Killing From Stack. (line 6) * C-w: Killing From Stack. (line 6) * C-x * ': More About Embedded Mode. (line 115) * C-x * *: Basic Commands. (line 19) * C-x * 0: Basic Commands. (line 105) * C-x * :: Grabbing From Buffers. (line 77) * C-x * _: Grabbing From Buffers. (line 77) * C-x * `: More About Embedded Mode. (line 134) * C-x * a: Assignments in Embedded Mode. (line 93) * C-x * b: Basic Commands. (line 53) * C-x * c: Basic Commands. (line 19) * C-x * d: More About Embedded Mode. (line 84) * C-x * e: Basic Embedded Mode. (line 6) * C-x * f: More About Embedded Mode. (line 115) * C-x * g: Grabbing From Buffers. (line 6) * C-x * i: Help Commands. (line 20) * C-x * j: Assignments in Embedded Mode. (line 51) * C-x * k: Keypad Mode. (line 6) * C-x * L: Autoloading Problems. (line 12) * C-x * m: Naming Keyboard Macros. (line 39) * C-x * n: More About Embedded Mode. (line 123) * C-x * o: Basic Commands. (line 61) * C-x * p: More About Embedded Mode. (line 123) * C-x * q: Quick Calculator. (line 6) * C-x * r: Grabbing From Buffers. (line 37) * C-x * s: Help Commands. (line 37) * C-x * t: Help Commands. (line 29) * C-x * u: Assignments in Embedded Mode. (line 64) * C-x * w: Basic Embedded Mode. (line 53) * C-x * x: Basic Commands. (line 84) * C-x * y: Yanking Into Buffers. (line 50) * C-x * z: Invocation Macros. (line 6) * C-xC-t: Stack Manipulation. (line 72) * C-y: Yanking Into Stack. (line 6) * D: Undo. (line 23) * d ": Strings. (line 25) * d ,: Grouping Digits. (line 20) * d .: Float Formats. (line 50) * d 0: Radix Modes. (line 12) * d 2: Radix Modes. (line 12) * d 6: Radix Modes. (line 12) * d 8: Radix Modes. (line 12) * d <: Justification. (line 6) * d : Display Modes. (line 19) * d : Basic Commands. (line 88) * d =: Justification. (line 6) * d >: Justification. (line 6) * d ?: Help Commands. (line 6) * d [: Truncating the Stack. (line 25) * d ]: Truncating the Stack. (line 25) * d A: Giac Language Mode. (line 6) * d B: Normal Language Modes. (line 24) * d b: Normal Language Modes. (line 16) * d C: C FORTRAN Pascal. (line 6) * d c: Complex Formats. (line 6) * d d: Date Formats. (line 6) * d E: Eqn Language Mode. (line 6) * d e: Float Formats. (line 34) * d F: C FORTRAN Pascal. (line 40) * d f: Float Formats. (line 20) * d g: Grouping Digits. (line 6) * d h: HMS Formats. (line 6) * d i: Complex Formats. (line 11) * d j: Complex Formats. (line 11) * d L: TeX and LaTeX Language Modes. (line 6) * d l: Stack Basics. (line 24) * d M: Mathematica Language Mode. (line 6) * d N: Normal Language Modes. (line 6) * d n: Float Formats. (line 12) * d O: Normal Language Modes. (line 11) * d o: Fraction Formats. (line 6) * d p: More About Embedded Mode. (line 19) * d P: C FORTRAN Pascal. (line 30) * d r: Radix Modes. (line 19) * d s: Float Formats. (line 28) * d T: TeX and LaTeX Language Modes. (line 6) * d t: Truncating the Stack. (line 6) * d U: Normal Language Modes. (line 67) * d W: Maple Language Mode. (line 6) * d w: Error Messages. (line 20) * d X: Maxima Language Mode. (line 6) * d Y: Yacas Language Mode. (line 6) * d z: Radix Modes. (line 23) * d {: Labels. (line 6) * d }: Labels. (line 16) * E: Logarithmic Functions. (line 11) * e: Numeric Entry. (line 6) * F: Integer Truncation. (line 15) * f ?: Help Commands. (line 6) * f [: Basic Arithmetic. (line 227) * f ]: Basic Arithmetic. (line 227) * f A: Basic Arithmetic. (line 175) * f B: Advanced Math Functions. (line 47) * f b: Advanced Math Functions. (line 42) * f e: Advanced Math Functions. (line 53) * f E: Logarithmic Functions. (line 37) * f G: Advanced Math Functions. (line 25) * f g: Advanced Math Functions. (line 18) * f h: Basic Arithmetic. (line 192) * f I: Logarithmic Functions. (line 29) * f i: Complex Number Functions. (line 29) * f j: Advanced Math Functions. (line 58) * f L: Logarithmic Functions. (line 41) * f M: Basic Arithmetic. (line 210) * f n: Basic Arithmetic. (line 204) * f Q: Basic Arithmetic. (line 197) * f r: Complex Number Functions. (line 24) * f S: Basic Arithmetic. (line 221) * f s: Basic Arithmetic. (line 178) * f T: Trigonometric and Hyperbolic Functions. (line 49) * f X: Basic Arithmetic. (line 210) * f x: Basic Arithmetic. (line 204) * f y: Advanced Math Functions. (line 58) * G: Complex Number Functions. (line 12) * g ?: Help Commands. (line 6) * g A: Managing Curves. (line 62) * g a: Managing Curves. (line 11) * g b: Graphics Options. (line 13) * g C: Devices. (line 111) * g c: Basic Graphics. (line 68) * g C-l: Graphics Options. (line 78) * g C-r: Graphics Options. (line 78) * g C-t: Graphics Options. (line 78) * g D: Devices. (line 6) * g d: Managing Curves. (line 78) * g F: Three Dimensional Graphics. (line 6) * g f: Basic Graphics. (line 6) * g g: Graphics Options. (line 6) * g h: Graphics Options. (line 45) * g H: Managing Curves. (line 83) * g j: Managing Curves. (line 88) * g K: Devices. (line 149) * g k: Graphics Options. (line 17) * g L: Graphics Options. (line 74) * g l: Graphics Options. (line 74) * g n: Graphics Options. (line 49) * g N: Graphics Options. (line 22) * g O: Devices. (line 45) * g P: Managing Curves. (line 126) * g p: Managing Curves. (line 95) * g q: Devices. (line 142) * g R: Graphics Options. (line 65) * g r: Graphics Options. (line 65) * g S: Graphics Options. (line 98) * g s: Graphics Options. (line 89) * g T: Graphics Options. (line 57) * g t: Graphics Options. (line 57) * g V: Devices. (line 117) * g v: Devices. (line 117) * g X: Devices. (line 97) * g x: Devices. (line 92) * g Z: Graphics Options. (line 82) * g z: Graphics Options. (line 82) * H: Inverse and Hyperbolic. (line 12) * h (HMS forms): HMS Forms. (line 13) * H a /: Polynomials. (line 139) * H a d: Differentiation. (line 6) * H a F: Error Estimates for Fits. (line 6) * H a f: Polynomials. (line 56) * H a M: Algebraic Manipulation. (line 98) * H a N: Minimization. (line 6) * H a p: Interpolation. (line 35) * H a R: Root Finding. (line 52) * H a S: Multiple Solutions. (line 6) * H a s: Simplifying Formulas. (line 6) * H a X: Minimization. (line 6) * h b: Help Commands. (line 77) * H b #: Related Financial Functions. (line 32) * H b F: Future Value. (line 24) * H b L: Binary Functions. (line 86) * H b l: Binary Functions. (line 86) * H b M: Related Financial Functions. (line 18) * H b P: Present Value. (line 34) * H b R: Binary Functions. (line 86) * H b r: Binary Functions. (line 86) * H b t: Binary Functions. (line 86) * H b T: Related Financial Functions. (line 43) * H C: Trigonometric and Hyperbolic Functions. (line 44) * h c: Help Commands. (line 52) * H c 0-9: Conversions. (line 126) * H c c: Conversions. (line 126) * H c F: Conversions. (line 52) * H c f: Conversions. (line 30) * h C-c: Help Commands. (line 84) * h C-d: Help Commands. (line 84) * h C-w: Help Commands. (line 84) * H E: Logarithmic Functions. (line 16) * H F: Integer Truncation. (line 15) * h f: Help Commands. (line 67) * H f B: Advanced Math Functions. (line 47) * H f G: Advanced Math Functions. (line 25) * h h: Help Commands. (line 12) * h i: Help Commands. (line 20) * H I a S: Multiple Solutions. (line 56) * H I C: Trigonometric and Hyperbolic Functions. (line 44) * H I E: Logarithmic Functions. (line 16) * H I F: Integer Truncation. (line 19) * H I f G: Advanced Math Functions. (line 25) * H I L: Logarithmic Functions. (line 16) * H I P: Scientific Functions. (line 12) * H I R: Integer Truncation. (line 29) * H I S: Trigonometric and Hyperbolic Functions. (line 39) * H I T: Trigonometric and Hyperbolic Functions. (line 44) * H I u M: Single-Variable Statistics. (line 99) * H I u S: Single-Variable Statistics. (line 143) * H I V h: Building Vectors. (line 98) * H I v h: Building Vectors. (line 98) * H I V R: Nesting and Fixed Points. (line 18) * H I v R: Nesting and Fixed Points. (line 18) * H I V U: Nesting and Fixed Points. (line 22) * H I v U: Nesting and Fixed Points. (line 22) * H I |: Building Vectors. (line 28) * H j I: Rearranging with Selections. (line 109) * h k: Help Commands. (line 41) * H k b: Combinatorial Functions. (line 52) * H k c: Combinatorial Functions. (line 49) * H k e: Combinatorial Functions. (line 60) * H k s: Combinatorial Functions. (line 64) * H L: Logarithmic Functions. (line 16) * h n: Help Commands. (line 80) * H P: Scientific Functions. (line 12) * H R: Integer Truncation. (line 23) * H S: Trigonometric and Hyperbolic Functions. (line 39) * h s: Help Commands. (line 37) * H T: Trigonometric and Hyperbolic Functions. (line 44) * h t: Help Commands. (line 29) * H u C: Paired-Sample Statistics. (line 28) * H u G: Single-Variable Statistics. (line 108) * H u M: Single-Variable Statistics. (line 85) * H u S: Single-Variable Statistics. (line 143) * h v: Help Commands. (line 74) * H V e: Manipulating Vectors. (line 125) * H v e: Manipulating Vectors. (line 125) * H V H: Manipulating Vectors. (line 89) * H v H: Manipulating Vectors. (line 89) * H V h: Building Vectors. (line 98) * H v h: Building Vectors. (line 98) * H V k: Building Vectors. (line 98) * H v k: Building Vectors. (line 98) * H V l: Manipulating Vectors. (line 11) * H v l: Manipulating Vectors. (line 11) * H V R: Nesting and Fixed Points. (line 6) * H v R: Nesting and Fixed Points. (line 6) * H V U: Nesting and Fixed Points. (line 13) * H v U: Nesting and Fixed Points. (line 13) * H |: Building Vectors. (line 22) * I: Inverse and Hyperbolic. (line 6) * i: Help Commands. (line 20) * I ^: Basic Arithmetic. (line 135) * I a F: Error Estimates for Fits. (line 50) * I a m: Matching Commands. (line 26) * I a M: Algebraic Manipulation. (line 104) * I a S: Multiple Solutions. (line 56) * I a s: Simplifying Formulas. (line 6) * I B: Logarithmic Functions. (line 22) * I b #: Related Financial Functions. (line 27) * I b F: Future Value. (line 15) * I b I: Related Financial Functions. (line 55) * I b M: Related Financial Functions. (line 14) * I b N: Present Value. (line 65) * I b P: Present Value. (line 28) * I b T: Related Financial Functions. (line 43) * I C: Trigonometric and Hyperbolic Functions. (line 44) * I c p: Conversions. (line 73) * I E: Logarithmic Functions. (line 6) * I F: Integer Truncation. (line 19) * I f e: Advanced Math Functions. (line 53) * I f G: Advanced Math Functions. (line 25) * I k B: Probability Distribution Functions. (line 22) * I k C: Probability Distribution Functions. (line 40) * I k F: Probability Distribution Functions. (line 44) * I k N: Probability Distribution Functions. (line 49) * I k n: Combinatorial Functions. (line 115) * I k P: Probability Distribution Functions. (line 53) * I k T: Probability Distribution Functions. (line 57) * I L: Logarithmic Functions. (line 11) * I M: Recursion Depth. (line 6) * I P: Scientific Functions. (line 12) * I Q: Scientific Functions. (line 23) * I R: Integer Truncation. (line 29) * I S: Trigonometric and Hyperbolic Functions. (line 34) * I T: Trigonometric and Hyperbolic Functions. (line 44) * I u C: Paired-Sample Statistics. (line 24) * I u M: Single-Variable Statistics. (line 73) * I u S: Single-Variable Statistics. (line 130) * I V G: Manipulating Vectors. (line 53) * I v G: Manipulating Vectors. (line 53) * I V h: Building Vectors. (line 87) * I v h: Building Vectors. (line 87) * I V R: Reducing. (line 15) * I v R: Reducing. (line 15) * I V S: Manipulating Vectors. (line 39) * I v S: Manipulating Vectors. (line 39) * I V s: Extracting Elements. (line 73) * I v s: Extracting Elements. (line 73) * I V U: Reducing. (line 27) * I v U: Reducing. (line 27) * I |: Building Vectors. (line 28) * J: Complex Number Functions. (line 6) * j ": Rearranging with Selections. (line 189) * j &: Rearranging with Selections. (line 98) * j ': Operating on Selections. (line 43) * j *: Rearranging with Selections. (line 116) * j +: Rearranging with Selections. (line 161) * j -: Rearranging with Selections. (line 161) * j /: Rearranging with Selections. (line 116) * j 1-9: Changing Selections. (line 35) * j : Operating on Selections. (line 77) * j : Operating on Selections. (line 83) * j ?: Help Commands. (line 6) * j `: Operating on Selections. (line 53) * j a: Making Selections. (line 66) * j b: Making Selections. (line 96) * j C: Rearranging with Selections. (line 74) * j c: Making Selections. (line 118) * j D: Rearranging with Selections. (line 41) * j d: Displaying Selections. (line 6) * j E: Rearranging with Selections. (line 103) * j e: Operating on Selections. (line 11) * j I: Rearranging with Selections. (line 109) * j L: Rearranging with Selections. (line 32) * j l: Changing Selections. (line 29) * j M: Rearranging with Selections. (line 68) * j m: Changing Selections. (line 6) * j N: Rearranging with Selections. (line 90) * j n: Changing Selections. (line 49) * j O: Making Selections. (line 83) * j o: Making Selections. (line 73) * j p: Changing Selections. (line 49) * j r: Selections with Rewrite Rules. (line 12) * j R: Rearranging with Selections. (line 6) * j S: Making Selections. (line 83) * j s: Making Selections. (line 6) * j U: Rearranging with Selections. (line 167) * j u: Making Selections. (line 113) * j v: Rearranging with Selections. (line 173) * K: Keep Arguments. (line 6) * k ?: Help Commands. (line 6) * k a: Random Numbers. (line 63) * k B: Probability Distribution Functions. (line 22) * k b: Combinatorial Functions. (line 52) * k C: Probability Distribution Functions. (line 40) * k c: Combinatorial Functions. (line 42) * k d: Combinatorial Functions. (line 34) * k e: Combinatorial Functions. (line 60) * k E: Combinatorial Functions. (line 20) * k F: Probability Distribution Functions. (line 44) * k f: Combinatorial Functions. (line 93) * k g: Combinatorial Functions. (line 9) * k h: Random Numbers. (line 67) * k l: Combinatorial Functions. (line 16) * k m: Combinatorial Functions. (line 122) * k N: Probability Distribution Functions. (line 49) * k n: Combinatorial Functions. (line 103) * k P: Probability Distribution Functions. (line 53) * k p: Combinatorial Functions. (line 71) * k r: Random Numbers. (line 6) * k s: Combinatorial Functions. (line 64) * k T: Probability Distribution Functions. (line 57) * k t: Combinatorial Functions. (line 118) * L: Logarithmic Functions. (line 6) * M: Recursion Depth. (line 6) * m (HMS forms): HMS Forms. (line 13) * M (modulo forms): Modulo Forms. (line 12) * m ?: Help Commands. (line 6) * m A: Simplification Modes. (line 48) * m a: Algebraic Entry. (line 28) * m B: Simplification Modes. (line 41) * m C <1>: Evaluates-To Operator. (line 41) * m C: Automatic Recomputation. (line 11) * m D: Simplification Modes. (line 36) * m d: Angular Modes. (line 20) * m e: Mode Settings in Embedded Mode. (line 6) * m E: Simplification Modes. (line 53) * m f: Fraction Mode. (line 13) * m F: General Mode Commands. (line 27) * m g: Modes Variable. (line 6) * m h: Angular Modes. (line 20) * m i: Infinite Mode. (line 10) * m m: General Mode Commands. (line 6) * m N: Simplification Modes. (line 26) * m O: Simplification Modes. (line 21) * m p: Polar Mode. (line 12) * m r: Angular Modes. (line 20) * m R: General Mode Commands. (line 18) * m s: Symbolic Mode. (line 12) * m S: General Mode Commands. (line 57) * m t: Algebraic Entry. (line 42) * m U: Simplification Modes. (line 57) * m v: Matrix Mode. (line 11) * m w: Working Message. (line 14) * m x: General Mode Commands. (line 48) * M-%: Percentages. (line 6) * M-: Stack Manipulation. (line 33) * M-: Undo. (line 31) * M-: Stack Manipulation. (line 49) * M-C-w: Killing From Stack. (line 6) * M-k: Killing From Stack. (line 6) * M-w: Killing From Stack. (line 6) * M-x: Basic Commands. (line 23) * n: Basic Arithmetic. (line 161) * N: Symbolic Mode. (line 17) * o: Stack Basics. (line 30) * o (HMS forms): HMS Forms. (line 13) * P: Scientific Functions. (line 12) * p: Precision. (line 6) * p (error forms): Error Forms. (line 47) * Q: Basic Arithmetic. (line 188) * q: Basic Commands. (line 77) * R: Integer Truncation. (line 23) * r 0-9: Recalling Variables. (line 18) * r ?: Help Commands. (line 6) * r i: Inserting From Registers. (line 6) * r s: Saving Into Registers. (line 6) * S: Trigonometric and Hyperbolic Functions. (line 6) * s &: Storing Variables. (line 41) * s (HMS forms): HMS Forms. (line 13) * s *: Storing Variables. (line 41) * s +: Storing Variables. (line 41) * s -: Storing Variables. (line 41) * s /: Storing Variables. (line 41) * s 0-9: Storing Variables. (line 37) * s :: Evaluates-To Operator. (line 90) * s =: Evaluates-To Operator. (line 22) * s ?: Help Commands. (line 6) * s [: Storing Variables. (line 41) * s ]: Storing Variables. (line 41) * s ^: Storing Variables. (line 41) * s A: Operations on Variables. (line 25) * s c: Storing Variables. (line 115) * s D: Operations on Variables. (line 25) * s d: Declaration Basics. (line 6) * s E: Operations on Variables. (line 25) * s e: Operations on Variables. (line 6) * s F: Operations on Variables. (line 25) * s G: Operations on Variables. (line 25) * s H: Operations on Variables. (line 25) * s i: Operations on Variables. (line 87) * s I: Operations on Variables. (line 25) * s k: Storing Variables. (line 137) * s l: Let Command. (line 6) * s L: Operations on Variables. (line 25) * s m: Storing Variables. (line 84) * s n: Storing Variables. (line 41) * s p: Operations on Variables. (line 70) * s P: Operations on Variables. (line 25) * s R: Operations on Variables. (line 25) * s r: Recalling Variables. (line 6) * s s: Storing Variables. (line 6) * s T: Operations on Variables. (line 25) * s t: Storing Variables. (line 12) * s U: Operations on Variables. (line 25) * s u: Storing Variables. (line 110) * s X: Operations on Variables. (line 25) * s x: Storing Variables. (line 102) * s |: Storing Variables. (line 41) * T: Trigonometric and Hyperbolic Functions. (line 44) * t +: Business Days. (line 13) * t -: Business Days. (line 13) * t .: Vector and Matrix Formats. (line 78) * t 0-9: Storing Variables. (line 37) * t <: Trail Commands. (line 36) * t >: Trail Commands. (line 36) * t ?: Help Commands. (line 6) * t [: Trail Commands. (line 47) * t ]: Trail Commands. (line 47) * t b: Trail Commands. (line 40) * t C: Date Conversions. (line 60) * t D: Date Conversions. (line 6) * t d: Trail Commands. (line 9) * t f: Trail Commands. (line 40) * t h: Trail Commands. (line 47) * t I: Date Functions. (line 98) * t i: Trail Commands. (line 19) * t J: Date Conversions. (line 35) * t k: Trail Commands. (line 66) * t M: Date Functions. (line 51) * t m: Trail Commands. (line 60) * t N: Date Functions. (line 6) * t n: Trail Commands. (line 40) * t o: Trail Commands. (line 19) * t P: Date Functions. (line 11) * t p: Trail Commands. (line 40) * t r: Trail Commands. (line 53) * t s: Trail Commands. (line 53) * t U: Date Conversions. (line 50) * t W: Date Functions. (line 68) * t Y: Date Functions. (line 59) * t y: Trail Commands. (line 30) * U: Undo. (line 6) * u #: Single-Variable Statistics. (line 36) * u *: Single-Variable Statistics. (line 42) * u +: Single-Variable Statistics. (line 42) * u 0-9: User-Defined Units. (line 9) * u ?: Help Commands. (line 6) * u a: Basic Operations on Units. (line 138) * u b: Basic Operations on Units. (line 116) * u c: Basic Operations on Units. (line 51) * u C: Paired-Sample Statistics. (line 13) * u d: User-Defined Units. (line 27) * u e: The Units Table. (line 45) * u g: The Units Table. (line 35) * u G: Single-Variable Statistics. (line 103) * u M: Single-Variable Statistics. (line 55) * u N: Single-Variable Statistics. (line 48) * u p: User-Defined Units. (line 63) * u r: Basic Operations on Units. (line 131) * u s: Basic Operations on Units. (line 31) * u S: Single-Variable Statistics. (line 116) * u t: Basic Operations on Units. (line 126) * u u: User-Defined Units. (line 40) * u V: The Units Table. (line 27) * u v: The Units Table. (line 6) * u x: Basic Operations on Units. (line 131) * u X: Single-Variable Statistics. (line 48) * V #: Set Operations. (line 95) * v #: Set Operations. (line 95) * V (: Vector and Matrix Formats. (line 17) * v (: Vector and Matrix Formats. (line 17) * v ): Vector and Matrix Formats. (line 28) * V ): Vector and Matrix Formats. (line 28) * V +: Set Operations. (line 34) * v +: Set Operations. (line 34) * V ,: Vector and Matrix Formats. (line 59) * v ,: Vector and Matrix Formats. (line 59) * V -: Set Operations. (line 55) * v -: Set Operations. (line 55) * V .: Vector and Matrix Formats. (line 71) * v .: Vector and Matrix Formats. (line 71) * V /: Vector and Matrix Formats. (line 86) * v /: Vector and Matrix Formats. (line 86) * V :: Set Operations. (line 89) * v :: Set Operations. (line 89) * V <: Vector and Matrix Formats. (line 12) * v <: Vector and Matrix Formats. (line 12) * V =: Vector and Matrix Formats. (line 12) * v =: Vector and Matrix Formats. (line 12) * V >: Vector and Matrix Formats. (line 12) * v >: Vector and Matrix Formats. (line 12) * V ?: Help Commands. (line 6) * v ?: Help Commands. (line 6) * V [: Vector and Matrix Formats. (line 17) * v [: Vector and Matrix Formats. (line 17) * v ]: Vector and Matrix Formats. (line 28) * V ]: Vector and Matrix Formats. (line 28) * V ^: Set Operations. (line 47) * v ^: Set Operations. (line 47) * V A: Reducing and Mapping. (line 9) * v A: Reducing and Mapping. (line 9) * V a: Manipulating Vectors. (line 23) * v a: Manipulating Vectors. (line 23) * V b: Building Vectors. (line 80) * v b: Building Vectors. (line 80) * V C: Vector and Matrix Arithmetic. (line 38) * v C: Vector and Matrix Arithmetic. (line 38) * V c: Extracting Elements. (line 44) * v c: Extracting Elements. (line 44) * V D: Vector and Matrix Arithmetic. (line 53) * v D: Vector and Matrix Arithmetic. (line 53) * V d: Building Vectors. (line 32) * v d: Building Vectors. (line 32) * V E: Set Operations. (line 84) * v E: Set Operations. (line 84) * V e: Manipulating Vectors. (line 115) * v e: Manipulating Vectors. (line 115) * V F: Set Operations. (line 75) * v F: Set Operations. (line 75) * V f: Manipulating Vectors. (line 16) * v f: Manipulating Vectors. (line 16) * V G: Manipulating Vectors. (line 53) * v G: Manipulating Vectors. (line 53) * V H: Manipulating Vectors. (line 79) * v H: Manipulating Vectors. (line 79) * V h: Building Vectors. (line 87) * v h: Building Vectors. (line 87) * V I: Generalized Products. (line 14) * v I: Generalized Products. (line 14) * V i: Building Vectors. (line 45) * v i: Building Vectors. (line 45) * V J: Vector and Matrix Arithmetic. (line 16) * v J: Vector and Matrix Arithmetic. (line 16) * V K: Vector and Matrix Arithmetic. (line 67) * v K: Vector and Matrix Arithmetic. (line 67) * V k: Building Vectors. (line 92) * v k: Building Vectors. (line 92) * V L: Vector and Matrix Arithmetic. (line 56) * v L: Vector and Matrix Arithmetic. (line 56) * V l: Manipulating Vectors. (line 6) * v l: Manipulating Vectors. (line 6) * V M: Mapping. (line 6) * v M: Mapping. (line 6) * V m: Manipulating Vectors. (line 107) * v m: Manipulating Vectors. (line 107) * V N: Vector and Matrix Arithmetic. (line 31) * v N: Vector and Matrix Arithmetic. (line 31) * V n: Vector and Matrix Arithmetic. (line 25) * v n: Vector and Matrix Arithmetic. (line 25) * V O: Generalized Products. (line 6) * v O: Generalized Products. (line 6) * V p: Packing and Unpacking. (line 11) * v p: Packing and Unpacking. (line 11) * V p (complex): Complex Number Functions. (line 33) * v p (complex): Complex Number Functions. (line 33) * V R: Reducing. (line 6) * v R: Reducing. (line 6) * V r: Extracting Elements. (line 6) * v r: Extracting Elements. (line 6) * V S: Manipulating Vectors. (line 39) * v S: Manipulating Vectors. (line 39) * V s: Extracting Elements. (line 57) * v s: Extracting Elements. (line 57) * V T: Vector and Matrix Arithmetic. (line 63) * v T: Vector and Matrix Arithmetic. (line 63) * V t: Manipulating Vectors. (line 96) * v t: Manipulating Vectors. (line 96) * V U: Reducing. (line 21) * v U: Reducing. (line 21) * V u: Packing and Unpacking. (line 124) * v u: Packing and Unpacking. (line 124) * V u (complex): Complex Number Functions. (line 39) * v u (complex): Complex Number Functions. (line 39) * V V: Set Operations. (line 42) * v V: Set Operations. (line 42) * V v: Manipulating Vectors. (line 101) * v v: Manipulating Vectors. (line 101) * V X: Set Operations. (line 65) * v X: Set Operations. (line 65) * V x: Building Vectors. (line 61) * v x: Building Vectors. (line 61) * V {: Vector and Matrix Formats. (line 17) * v {: Vector and Matrix Formats. (line 17) * v }: Vector and Matrix Formats. (line 28) * V }: Vector and Matrix Formats. (line 28) * V ~: Set Operations. (line 70) * v ~: Set Operations. (line 70) * w: Error Messages. (line 6) * X: Keyboard Macros. (line 6) * x: Basic Commands. (line 23) * Y: Defining Simple Commands. (line 87) * y: Yanking Into Buffers. (line 6) * Y ?: Defining Simple Commands. (line 87) * z: Programming. (line 30) * Z #: Queries in Macros. (line 6) * Z ': Local Values in Macros. (line 11) * Z (: Loops in Macros. (line 33) * Z ): Loops in Macros. (line 33) * Z /: Loops in Macros. (line 26) * Z :: Conditionals in Macros. (line 31) * Z <: Loops in Macros. (line 6) * Z >: Loops in Macros. (line 6) * Z ?: Help Commands. (line 6) * z ?: Help Commands. (line 6) * Z [: Conditionals in Macros. (line 6) * Z ]: Conditionals in Macros. (line 6) * Z `: Local Values in Macros. (line 11) * Z C: User-Defined Compositions. (line 6) * Z C-g: Conditionals in Macros. (line 60) * Z D: Creating User Keys. (line 6) * Z E: Creating User Keys. (line 60) * Z F: Algebraic Definitions. (line 6) * Z G: Algebraic Definitions. (line 75) * Z I: Invocation Macros. (line 6) * Z K: Naming Keyboard Macros. (line 6) * Z P: Creating User Keys. (line 36) * Z S: Syntax Tables. (line 13) * Z T: Debugging Calc. (line 10) * Z U: Creating User Keys. (line 32) * Z {: Loops in Macros. (line 56) * Z |: Conditionals in Macros. (line 38) * Z }: Loops in Macros. (line 56) * {: Basic Commands. (line 101) * |: Building Vectors. (line 9) * }: Basic Commands. (line 101) * ~: Prefix Arguments. (line 39)