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emacs/lisp/calc/calc-lang.el
Paul Eggert 0e963201d0 Update copyright year to 2016 
Run admin/update-copyright.
2016-01-01 01:34:24 -08:00

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;;; calc-lang.el --- calc language functions
;; Copyright (C) 1990-1993, 2001-2016 Free Software Foundation, Inc.
;; Author: David Gillespie <daveg@synaptics.com>
;; This file is part of GNU Emacs.
;; GNU Emacs 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.
;; GNU Emacs 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 GNU Emacs. If not, see <http://www.gnu.org/licenses/>.
;;; Commentary:
;;; Code:
;; This file is autoloaded from calc-ext.el.
(require 'calc-ext)
(require 'calc-macs)
;; Declare functions which are defined elsewhere.
(declare-function math-compose-vector "calccomp" (a sep prec))
(declare-function math-compose-var "calccomp" (a))
(declare-function math-tex-expr-is-flat "calccomp" (a))
(declare-function math-read-factor "calc-aent" ())
(declare-function math-read-expr-level "calc-aent" (exp-prec &optional exp-term))
;; Declare variables which are defined elsewhere.
(defvar calc-lang-slash-idiv)
(defvar calc-lang-allow-underscores)
(defvar calc-lang-allow-percentsigns)
(defvar math-comp-left-bracket)
(defvar math-comp-right-bracket)
(defvar math-comp-comma)
(defvar math-comp-vector-prec)
;;; Alternate entry/display languages.
(defun calc-set-language (lang &optional option no-refresh)
(setq math-expr-opers (or (get lang 'math-oper-table) (math-standard-ops))
math-expr-function-mapping (get lang 'math-function-table)
math-expr-variable-mapping (get lang 'math-variable-table)
calc-language-input-filter (get lang 'math-input-filter)
calc-language-output-filter (get lang 'math-output-filter)
calc-vector-brackets (or (get lang 'math-vector-brackets) "[]")
calc-complex-format (get lang 'math-complex-format)
calc-radix-formatter (get lang 'math-radix-formatter)
calc-function-open (or (get lang 'math-function-open) "(")
calc-function-close (or (get lang 'math-function-close) ")"))
(if no-refresh
(setq calc-language lang
calc-language-option option)
(calc-change-mode '(calc-language calc-language-option)
(list lang option) t)))
(defun calc-normal-language ()
(interactive)
(calc-wrapper
(calc-set-language nil)
(message "Normal language mode")))
(defun calc-flat-language ()
(interactive)
(calc-wrapper
(calc-set-language 'flat)
(message "Flat language mode (all stack entries shown on one line)")))
(defun calc-big-language ()
(interactive)
(calc-wrapper
(calc-set-language 'big)
(message "\"Big\" language mode")))
(defun calc-unformatted-language ()
(interactive)
(calc-wrapper
(calc-set-language 'unform)
(message "Unformatted language mode")))
(defun calc-c-language ()
(interactive)
(calc-wrapper
(calc-set-language 'c)
(message "C language mode")))
(put 'c 'math-oper-table
'( ( "u!" calcFunc-lnot -1 1000 )
( "~" calcFunc-not -1 1000 )
( "u+" ident -1 197 )
( "u-" neg -1 197 )
( "*" * 190 191 )
( "/" / 190 191 )
( "%" % 190 191 )
( "+" + 180 181 )
( "-" - 180 181 )
( "<<" calcFunc-lsh 170 171 )
( ">>" calcFunc-rsh 170 171 )
( "<" calcFunc-lt 160 161 )
( ">" calcFunc-gt 160 161 )
( "<=" calcFunc-leq 160 161 )
( ">=" calcFunc-geq 160 161 )
( "==" calcFunc-eq 150 151 )
( "!=" calcFunc-neq 150 151 )
( "&" calcFunc-and 140 141 )
( "^" calcFunc-xor 131 130 )
( "|" calcFunc-or 120 121 )
( "&&" calcFunc-land 110 111 )
( "||" calcFunc-lor 100 101 )
( "?" (math-read-if) 91 90 )
( "!!!" calcFunc-pnot -1 88 )
( "&&&" calcFunc-pand 85 86 )
( "|||" calcFunc-por 75 76 )
( "=" calcFunc-assign 51 50 )
( ":=" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 ))) ; should support full assignments
(put 'c 'math-function-table
'( ( acos . calcFunc-arccos )
( acosh . calcFunc-arccosh )
( asin . calcFunc-arcsin )
( asinh . calcFunc-arcsinh )
( atan . calcFunc-arctan )
( atan2 . calcFunc-arctan2 )
( atanh . calcFunc-arctanh )
( fma . (math-C-parse-fma))
( fmax . calcFunc-max )
( j0 . (math-C-parse-bess))
( jn . calcFunc-besJ )
( j1 . (math-C-parse-bess))
( yn . calcFunc-besY )
( y0 . (math-C-parse-bess))
( y1 . (math-C-parse-bess))
( tgamma . calcFunc-gamma )))
(defun math-C-parse-bess (f val)
"Parse C's j0, j1, y0, y1 functions."
(let ((args (math-read-expr-list)))
(math-read-token)
(append
(cond ((eq val 'j0) '(calcFunc-besJ 0))
((eq val 'j1) '(calcFunc-besJ 1))
((eq val 'y0) '(calcFunc-besY 0))
((eq val 'y1) '(calcFunc-besY 1)))
args)))
(defun math-C-parse-fma (f val)
"Parse C's fma function fma(x,y,z) => (x * y + z)."
(let ((args (math-read-expr-list)))
(math-read-token)
(list 'calcFunc-add
(list 'calcFunc-mul
(nth 0 args)
(nth 1 args))
(nth 2 args))))
(put 'c 'math-variable-table
'( ( M_PI . var-pi )
( M_E . var-e )))
(put 'c 'math-vector-brackets "{}")
(put 'c 'math-radix-formatter
(function (lambda (r s)
(if (= r 16) (format "0x%s" s)
(if (= r 8) (format "0%s" s)
(format "%d#%s" r s))))))
(put 'c 'math-compose-subscr
(function
(lambda (a)
(let ((args (cdr (cdr a))))
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"["
(math-compose-vector args ", " 0)
"]")))))
(add-to-list 'calc-lang-slash-idiv 'c)
(add-to-list 'calc-lang-allow-underscores 'c)
(add-to-list 'calc-lang-c-type-hex 'c)
(add-to-list 'calc-lang-brackets-are-subscripts 'c)
(defun calc-pascal-language (n)
(interactive "P")
(calc-wrapper
(and n (setq n (prefix-numeric-value n)))
(calc-set-language 'pascal n)
(message (if (and n (/= n 0))
(if (> n 0)
"Pascal language mode (all uppercase)"
"Pascal language mode (all lowercase)")
"Pascal language mode"))))
(put 'pascal 'math-oper-table
'( ( "not" calcFunc-lnot -1 1000 )
( "*" * 190 191 )
( "/" / 190 191 )
( "and" calcFunc-and 190 191 )
( "div" calcFunc-idiv 190 191 )
( "mod" % 190 191 )
( "u+" ident -1 185 )
( "u-" neg -1 185 )
( "+" + 180 181 )
( "-" - 180 181 )
( "or" calcFunc-or 180 181 )
( "xor" calcFunc-xor 180 181 )
( "shl" calcFunc-lsh 180 181 )
( "shr" calcFunc-rsh 180 181 )
( "in" calcFunc-in 160 161 )
( "<" calcFunc-lt 160 161 )
( ">" calcFunc-gt 160 161 )
( "<=" calcFunc-leq 160 161 )
( ">=" calcFunc-geq 160 161 )
( "=" calcFunc-eq 160 161 )
( "<>" calcFunc-neq 160 161 )
( "!!!" calcFunc-pnot -1 85 )
( "&&&" calcFunc-pand 80 81 )
( "|||" calcFunc-por 75 76 )
( ":=" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 )))
(put 'pascal 'math-input-filter 'calc-input-case-filter)
(put 'pascal 'math-output-filter 'calc-output-case-filter)
(put 'pascal 'math-radix-formatter
(function (lambda (r s)
(if (= r 16) (format "$%s" s)
(format "%d#%s" r s)))))
(put 'pascal 'math-lang-read-symbol
'((?\$
(eq (string-match
"\\(\\$[0-9a-fA-F]+\\)\\($\\|[^0-9a-zA-Zα-ωΑ-Ω]\\)"
math-exp-str math-exp-pos)
math-exp-pos)
(setq math-exp-token 'number
math-expr-data (math-match-substring math-exp-str 1)
math-exp-pos (match-end 1)))))
(put 'pascal 'math-compose-subscr
(function
(lambda (a)
(let ((args (cdr (cdr a))))
(while (eq (car-safe (nth 1 a)) 'calcFunc-subscr)
(setq args (append (cdr (cdr (nth 1 a))) args)
a (nth 1 a)))
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"["
(math-compose-vector args ", " 0)
"]")))))
(add-to-list 'calc-lang-allow-underscores 'pascal)
(add-to-list 'calc-lang-brackets-are-subscripts 'pascal)
(defun calc-input-case-filter (str)
(cond ((or (null calc-language-option) (= calc-language-option 0))
str)
(t
(downcase str))))
(defun calc-output-case-filter (str)
(cond ((or (null calc-language-option) (= calc-language-option 0))
str)
((> calc-language-option 0)
(upcase str))
(t
(downcase str))))
(defun calc-fortran-language (n)
(interactive "P")
(calc-wrapper
(and n (setq n (prefix-numeric-value n)))
(calc-set-language 'fortran n)
(message (if (and n (/= n 0))
(if (> n 0)
"FORTRAN language mode (all uppercase)"
"FORTRAN language mode (all lowercase)")
"FORTRAN language mode"))))
(put 'fortran 'math-oper-table
'( ( "u/" (math-parse-fortran-vector) -1 1 )
( "/" (math-parse-fortran-vector-end) 1 -1 )
( "**" ^ 201 200 )
( "u+" ident -1 191 )
( "u-" neg -1 191 )
( "*" * 190 191 )
( "/" / 190 191 )
( "+" + 180 181 )
( "-" - 180 181 )
( ".LT." calcFunc-lt 160 161 )
( ".GT." calcFunc-gt 160 161 )
( ".LE." calcFunc-leq 160 161 )
( ".GE." calcFunc-geq 160 161 )
( ".EQ." calcFunc-eq 160 161 )
( ".NE." calcFunc-neq 160 161 )
( ".NOT." calcFunc-lnot -1 121 )
( ".AND." calcFunc-land 110 111 )
( ".OR." calcFunc-lor 100 101 )
( "!!!" calcFunc-pnot -1 85 )
( "&&&" calcFunc-pand 80 81 )
( "|||" calcFunc-por 75 76 )
( "=" calcFunc-assign 51 50 )
( ":=" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 )))
(put 'fortran 'math-vector-brackets "//")
(put 'fortran 'math-function-table
'( ( acos . calcFunc-arccos )
( acosh . calcFunc-arccosh )
( aimag . calcFunc-im )
( aint . calcFunc-ftrunc )
( asin . calcFunc-arcsin )
( asinh . calcFunc-arcsinh )
( atan . calcFunc-arctan )
( atan2 . calcFunc-arctan2 )
( atanh . calcFunc-arctanh )
( conjg . calcFunc-conj )
( log . calcFunc-ln )
( nint . calcFunc-round )
( real . calcFunc-re )))
(put 'fortran 'math-input-filter 'calc-input-case-filter)
(put 'fortran 'math-output-filter 'calc-output-case-filter)
(put 'fortran 'math-lang-read-symbol
'((?\.
(eq (string-match "\\.[a-zA-Zα-ωΑ-Ω][a-zA-Zα-ωΑ-Ω][a-zA-Zα-ωΑ-Ω]?\\."
math-exp-str math-exp-pos) math-exp-pos)
(setq math-exp-token 'punc
math-expr-data (upcase (math-match-substring math-exp-str 0))
math-exp-pos (match-end 0)))))
(put 'fortran 'math-compose-subscr
(function
(lambda (a)
(let ((args (cdr (cdr a))))
(while (eq (car-safe (nth 1 a)) 'calcFunc-subscr)
(setq args (append (cdr (cdr (nth 1 a))) args)
a (nth 1 a)))
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"("
(math-compose-vector args ", " 0)
")")))))
(add-to-list 'calc-lang-slash-idiv 'fortran)
(add-to-list 'calc-lang-allow-underscores 'fortran)
(add-to-list 'calc-lang-parens-are-subscripts 'fortran)
;; The next few variables are local to math-read-exprs in calc-aent.el
;; and math-read-expr in calc-ext.el, but are set in functions they call.
(defvar math-exp-token)
(defvar math-expr-data)
(defvar math-exp-old-pos)
(defvar math-parsing-fortran-vector nil)
(defun math-parse-fortran-vector (op)
(let ((math-parsing-fortran-vector '(end . "\000")))
(prog1
(math-read-brackets t "]")
(setq math-exp-token (car math-parsing-fortran-vector)
math-expr-data (cdr math-parsing-fortran-vector)))))
(defun math-parse-fortran-vector-end (x op)
(if math-parsing-fortran-vector
(progn
(setq math-parsing-fortran-vector (cons math-exp-token math-expr-data)
math-exp-token 'end
math-expr-data "\000")
x)
(throw 'syntax "Unmatched closing `/'")))
(defun math-parse-fortran-subscr (sym args)
(setq sym (math-build-var-name sym))
(while args
(setq sym (list 'calcFunc-subscr sym (car args))
args (cdr args)))
sym)
(defun calc-tex-language (n)
(interactive "P")
(calc-wrapper
(and n (setq n (prefix-numeric-value n)))
(calc-set-language 'tex n)
(cond ((not n)
(message "TeX language mode"))
((= n 0)
(message "TeX language mode with multiline matrices"))
((= n 1)
(message "TeX language mode with \\hbox{func}(\\hbox{var})"))
((> n 1)
(message
"TeX language mode with \\hbox{func}(\\hbox{var}) and multiline matrices"))
((= n -1)
(message "TeX language mode with \\func(\\hbox{var})"))
((< n -1)
(message
"TeX language mode with \\func(\\hbox{var}) and multiline matrices")))))
(defun calc-latex-language (n)
(interactive "P")
(calc-wrapper
(and n (setq n (prefix-numeric-value n)))
(calc-set-language 'latex n)
(cond ((not n)
(message "LaTeX language mode"))
((= n 0)
(message "LaTeX language mode with multiline matrices"))
((= n 1)
(message "LaTeX language mode with \\text{func}(\\text{var})"))
((> n 1)
(message
"LaTeX language mode with \\text{func}(\\text{var}) and multiline matrices"))
((= n -1)
(message "LaTeX language mode with \\func(\\text{var})"))
((< n -1)
(message
"LaTeX language mode with \\func(\\text{var}) and multiline matrices")))))
(put 'tex 'math-lang-name "TeX")
(put 'latex 'math-lang-name "LaTeX")
(put 'tex 'math-oper-table
'( ( "\\hat" calcFunc-hat -1 950 )
( "\\check" calcFunc-check -1 950 )
( "\\tilde" calcFunc-tilde -1 950 )
( "\\acute" calcFunc-acute -1 950 )
( "\\grave" calcFunc-grave -1 950 )
( "\\dot" calcFunc-dot -1 950 )
( "\\ddot" calcFunc-dotdot -1 950 )
( "\\breve" calcFunc-breve -1 950 )
( "\\bar" calcFunc-bar -1 950 )
( "\\vec" calcFunc-Vec -1 950 )
( "\\underline" calcFunc-under -1 950 )
( "u|" calcFunc-abs -1 0 )
( "|" closing 0 -1 )
( "\\lfloor" calcFunc-floor -1 0 )
( "\\rfloor" closing 0 -1 )
( "\\lceil" calcFunc-ceil -1 0 )
( "\\rceil" closing 0 -1 )
( "\\pm" sdev 300 300 )
( "!" calcFunc-fact 210 -1 )
( "^" ^ 201 200 )
( "_" calcFunc-subscr 201 200 )
( "u+" ident -1 197 )
( "u-" neg -1 197 )
( "\\times" * 191 190 )
( "*" * 191 190 )
( "2x" * 191 190 )
( "+" + 180 181 )
( "-" - 180 181 )
( "\\over" / 170 171 )
( "/" / 170 171 )
( "\\choose" calcFunc-choose 170 171 )
( "\\mod" % 170 171 )
( "<" calcFunc-lt 160 161 )
( ">" calcFunc-gt 160 161 )
( "\\leq" calcFunc-leq 160 161 )
( "\\geq" calcFunc-geq 160 161 )
( "=" calcFunc-eq 160 161 )
( "\\neq" calcFunc-neq 160 161 )
( "\\ne" calcFunc-neq 160 161 )
( "\\lnot" calcFunc-lnot -1 121 )
( "\\land" calcFunc-land 110 111 )
( "\\lor" calcFunc-lor 100 101 )
( "?" (math-read-if) 91 90 )
( "!!!" calcFunc-pnot -1 85 )
( "&&&" calcFunc-pand 80 81 )
( "|||" calcFunc-por 75 76 )
( "\\gets" calcFunc-assign 51 50 )
( ":=" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 )
( "\\to" calcFunc-evalto 40 41 )
( "\\to" calcFunc-evalto 40 -1 )
( "=>" calcFunc-evalto 40 41 )
( "=>" calcFunc-evalto 40 -1 )))
(put 'tex 'math-function-table
'( ( \\arccos . calcFunc-arccos )
( \\arcsin . calcFunc-arcsin )
( \\arctan . calcFunc-arctan )
( \\arg . calcFunc-arg )
( \\cos . calcFunc-cos )
( \\cosh . calcFunc-cosh )
( \\cot . calcFunc-cot )
( \\coth . calcFunc-coth )
( \\csc . calcFunc-csc )
( \\det . calcFunc-det )
( \\exp . calcFunc-exp )
( \\gcd . calcFunc-gcd )
( \\ln . calcFunc-ln )
( \\log . calcFunc-log10 )
( \\max . calcFunc-max )
( \\min . calcFunc-min )
( \\sec . calcFunc-sec )
( \\sin . calcFunc-sin )
( \\sinh . calcFunc-sinh )
( \\sqrt . calcFunc-sqrt )
( \\tan . calcFunc-tan )
( \\tanh . calcFunc-tanh )
( \\phi . calcFunc-totient )
( \\mu . calcFunc-moebius )))
(put 'tex 'math-special-function-table
'((calcFunc-sum . (math-compose-tex-sum "\\sum"))
(calcFunc-prod . (math-compose-tex-sum "\\prod"))
(calcFunc-sqrt . math-compose-tex-sqrt)
(intv . math-compose-tex-intv)))
(put 'tex 'math-variable-table
'(
;; The Greek letters
( \\alpha . var-alpha )
( \\beta . var-beta )
( \\gamma . var-gamma )
( \\Gamma . var-Gamma )
( \\delta . var-delta )
( \\Delta . var-Delta )
( \\epsilon . var-epsilon )
( \\varepsilon . var-varepsilon)
( \\zeta . var-zeta )
( \\eta . var-eta )
( \\theta . var-theta )
( \\vartheta . var-vartheta )
( \\Theta . var-Theta )
( \\iota . var-iota )
( \\kappa . var-kappa )
( \\lambda . var-lambda )
( \\Lambda . var-Lambda )
( \\mu . var-mu )
( \\nu . var-nu )
( \\xi . var-xi )
( \\Xi . var-Xi )
( \\pi . var-pi )
( \\varpi . var-varpi )
( \\Pi . var-Pi )
( \\rho . var-rho )
( \\varrho . var-varrho )
( \\sigma . var-sigma )
( \\sigma . var-varsigma )
( \\Sigma . var-Sigma )
( \\tau . var-tau )
( \\upsilon . var-upsilon )
( \\Upsilon . var-Upsilon )
( \\phi . var-phi )
( \\varphi . var-varphi )
( \\Phi . var-Phi )
( \\chi . var-chi )
( \\psi . var-psi )
( \\Psi . var-Psi )
( \\omega . var-omega )
( \\Omega . var-Omega )
;; Units
( pt . var-texpt )
( pc . var-texpc )
( bp . var-texbp )
( dd . var-texdd )
( cc . var-texcc )
( sp . var-texsp )
( pint . var-pt )
( parsec . var-pc)
;; Others
( \\ell . var-ell )
( \\infty . var-inf )
( \\infty . var-uinf )
( \\sum . (math-parse-tex-sum calcFunc-sum) )
( \\prod . (math-parse-tex-sum calcFunc-prod) )))
(put 'tex 'math-punc-table
'((?\{ . ?\()
(?\} . ?\))
(?\& . ?\,)))
(put 'tex 'math-complex-format 'i)
(put 'tex 'math-input-filter 'math-tex-input-filter)
(put 'tex 'math-matrix-formatter
(function
(lambda (a)
(if (and (integerp calc-language-option)
(or (= calc-language-option 0)
(> calc-language-option 1)
(< calc-language-option -1)))
(append '(vleft 0 "\\matrix{")
(math-compose-tex-matrix (cdr a))
'("}"))
(append '(horiz "\\matrix{ ")
(math-compose-tex-matrix (cdr a))
'(" }"))))))
(put 'tex 'math-var-formatter 'math-compose-tex-var)
(put 'tex 'math-func-formatter 'math-compose-tex-func)
(put 'tex 'math-dots "\\ldots")
(put 'tex 'math-big-parens '("\\left( " . " \\right)"))
(put 'tex 'math-evalto '("\\evalto " . " \\to "))
(defconst math-tex-ignore-words
'( ("\\hbox") ("\\mbox") ("\\text") ("\\left") ("\\right")
("\\,") ("\\>") ("\\:") ("\\;") ("\\!") ("\\ ")
("\\quad") ("\\qquad") ("\\hfil") ("\\hfill")
("\\displaystyle") ("\\textstyle") ("\\dsize") ("\\tsize")
("\\scriptstyle") ("\\scriptscriptstyle") ("\\ssize") ("\\sssize")
("\\rm") ("\\bf") ("\\it") ("\\sl")
("\\roman") ("\\bold") ("\\italic") ("\\slanted")
("\\cal") ("\\mit") ("\\Cal") ("\\Bbb") ("\\frak") ("\\goth")
("\\evalto")
("\\matrix" mat) ("\\bmatrix" mat) ("\\pmatrix" mat)
("\\begin" begenv)
("\\cr" punc ";") ("\\\\" punc ";") ("\\*" punc "*")
("\\{" punc "[") ("\\}" punc "]")))
(defconst math-latex-ignore-words
(append math-tex-ignore-words
'(("\\begin" begenv))))
(put 'tex 'math-lang-read-symbol
'((?\\
(< math-exp-pos (1- (length math-exp-str)))
(progn
(or (string-match "\\\\hbox *{\\([a-zA-Zα-ωΑ-Ω0-9]+\\)}"
math-exp-str math-exp-pos)
(string-match "\\(\\\\\\([a-zA-Zα-ωΑ-Ω]+\\|[^a-zA-Zα-ωΑ-Ω]\\)\\)"
math-exp-str math-exp-pos))
(setq math-exp-token 'symbol
math-exp-pos (match-end 0)
math-expr-data (math-restore-dashes
(math-match-substring math-exp-str 1)))
(let ((code (assoc math-expr-data math-latex-ignore-words)))
(cond ((null code))
((null (cdr code))
(math-read-token))
((eq (nth 1 code) 'punc)
(setq math-exp-token 'punc
math-expr-data (nth 2 code)))
((and (eq (nth 1 code) 'mat)
(string-match " *{" math-exp-str math-exp-pos))
(setq math-exp-pos (match-end 0)
math-exp-token 'punc
math-expr-data "[")
(let ((right (string-match "}" math-exp-str math-exp-pos)))
(and right
(setq math-exp-str (copy-sequence math-exp-str))
(aset math-exp-str right ?\]))))))))))
(defun math-compose-tex-matrix (a &optional ltx)
(if (cdr a)
(cons (append (math-compose-vector (cdr (car a)) " & " 0)
(if ltx '(" \\\\ ") '(" \\cr ")))
(math-compose-tex-matrix (cdr a) ltx))
(list (math-compose-vector (cdr (car a)) " & " 0))))
(defun math-compose-tex-sum (a fn)
(cond
((nth 4 a)
(list 'horiz (nth 1 fn)
"_{" (math-compose-expr (nth 2 a) 0)
"=" (math-compose-expr (nth 3 a) 0)
"}^{" (math-compose-expr (nth 4 a) 0)
"}{" (math-compose-expr (nth 1 a) 0) "}"))
((nth 3 a)
(list 'horiz (nth 1 fn)
"_{" (math-compose-expr (nth 2 a) 0)
"=" (math-compose-expr (nth 3 a) 0)
"}{" (math-compose-expr (nth 1 a) 0) "}"))
(t
(list 'horiz (nth 1 fn)
"_{" (math-compose-expr (nth 2 a) 0)
"}{" (math-compose-expr (nth 1 a) 0) "}"))))
(defun math-parse-tex-sum (f val)
(let (low high save)
(or (equal math-expr-data "_") (throw 'syntax "Expected `_'"))
(math-read-token)
(setq save math-exp-old-pos)
(setq low (math-read-factor))
(or (eq (car-safe low) 'calcFunc-eq)
(progn
(setq math-exp-old-pos (1+ save))
(throw 'syntax "Expected equation")))
(or (equal math-expr-data "^") (throw 'syntax "Expected `^'"))
(math-read-token)
(setq high (math-read-factor))
(list (nth 2 f) (math-read-factor) (nth 1 low) (nth 2 low) high)))
(defun math-tex-input-filter (str) ; allow parsing of 123\,456\,789.
(while (string-match "[0-9]\\\\,[0-9]" str)
(setq str (concat (substring str 0 (1+ (match-beginning 0)))
(substring str (1- (match-end 0))))))
str)
(defun math-compose-tex-sqrt (a)
(list 'horiz
"\\sqrt{"
(math-compose-expr (nth 1 a) 0)
"}"))
(defun math-compose-tex-intv (a)
(list 'horiz
(if (memq (nth 1 a) '(0 1)) "(" "[")
(math-compose-expr (nth 2 a) 0)
" \\ldots "
(math-compose-expr (nth 3 a) 0)
(if (memq (nth 1 a) '(0 2)) ")" "]")))
(defun math-compose-tex-var (a prec)
(if (and calc-language-option
(not (= calc-language-option 0))
(string-match "\\`[a-zA-Zα-ωΑ-Ω][a-zA-Zα-ωΑ-Ω0-9]+\\'"
(symbol-name (nth 1 a))))
(if (eq calc-language 'latex)
(format "\\text{%s}" (symbol-name (nth 1 a)))
(format "\\hbox{%s}" (symbol-name (nth 1 a))))
(math-compose-var a)))
(defun math-compose-tex-func (func a)
(let (left right)
(if (and calc-language-option
(not (= calc-language-option 0))
(string-match "\\`[a-zA-Zα-ωΑ-Ω][a-zA-Zα-ωΑ-Ω0-9]+\\'" func))
(if (< (prefix-numeric-value calc-language-option) 0)
(setq func (format "\\%s" func))
(setq func (if (eq calc-language 'latex)
(format "\\text{%s}" func)
(format "\\hbox{%s}" func)))))
(cond ((or (> (length a) 2)
(not (math-tex-expr-is-flat (nth 1 a))))
(setq left "\\left( "
right " \\right)"))
((and (eq (aref func 0) ?\\)
(not (or
(string-match "\\hbox{" func)
(string-match "\\text{" func)))
(= (length a) 2)
(or (Math-realp (nth 1 a))
(memq (car (nth 1 a)) '(var *))))
(setq left "{" right "}"))
(t (setq left calc-function-open
right calc-function-close)))
(list 'horiz func
left
(math-compose-vector (cdr a) ", " 0)
right)))
(put 'latex 'math-oper-table
(append (get 'tex 'math-oper-table)
'(( "\\Hat" calcFunc-Hat -1 950 )
( "\\Check" calcFunc-Check -1 950 )
( "\\Tilde" calcFunc-Tilde -1 950 )
( "\\Acute" calcFunc-Acute -1 950 )
( "\\Grave" calcFunc-Grave -1 950 )
( "\\Dot" calcFunc-Dot -1 950 )
( "\\Ddot" calcFunc-Dotdot -1 950 )
( "\\Breve" calcFunc-Breve -1 950 )
( "\\Bar" calcFunc-Bar -1 950 )
( "\\Vec" calcFunc-VEC -1 950 )
( "\\dddot" calcFunc-dddot -1 950 )
( "\\ddddot" calcFunc-ddddot -1 950 )
( "\\div" / 170 171 )
( "\\le" calcFunc-leq 160 161 )
( "\\leqq" calcFunc-leq 160 161 )
( "\\leqsland" calcFunc-leq 160 161 )
( "\\ge" calcFunc-geq 160 161 )
( "\\geqq" calcFunc-geq 160 161 )
( "\\geqslant" calcFunc-geq 160 161 )
( "=" calcFunc-eq 160 161 )
( "\\neq" calcFunc-neq 160 161 )
( "\\ne" calcFunc-neq 160 161 )
( "\\lnot" calcFunc-lnot -1 121 )
( "\\land" calcFunc-land 110 111 )
( "\\lor" calcFunc-lor 100 101 )
( "?" (math-read-if) 91 90 )
( "!!!" calcFunc-pnot -1 85 )
( "&&&" calcFunc-pand 80 81 )
( "|||" calcFunc-por 75 76 )
( "\\gets" calcFunc-assign 51 50 )
( ":=" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 )
( "\\to" calcFunc-evalto 40 41 )
( "\\to" calcFunc-evalto 40 -1 )
( "=>" calcFunc-evalto 40 41 )
( "=>" calcFunc-evalto 40 -1 ))))
(put 'latex 'math-function-table
(append
(get 'tex 'math-function-table)
'(( \\frac . (math-latex-parse-frac))
( \\tfrac . (math-latex-parse-frac))
( \\dfrac . (math-latex-parse-frac))
( \\binom . (math-latex-parse-two-args calcFunc-choose))
( \\tbinom . (math-latex-parse-two-args calcFunc-choose))
( \\dbinom . (math-latex-parse-two-args calcFunc-choose))
( \\phi . calcFunc-totient )
( \\mu . calcFunc-moebius ))))
(put 'latex 'math-special-function-table
'((/ . (math-compose-latex-frac "\\frac"))
(calcFunc-choose . (math-compose-latex-frac "\\binom"))
(calcFunc-sum . (math-compose-tex-sum "\\sum"))
(calcFunc-prod . (math-compose-tex-sum "\\prod"))
(calcFunc-sqrt . math-compose-tex-sqrt)
(intv . math-compose-tex-intv)))
(put 'latex 'math-variable-table
(get 'tex 'math-variable-table))
(put 'latex 'math-punc-table
'((?\{ . ?\()
(?\} . ?\))
(?\& . ?\,)))
(put 'latex 'math-complex-format 'i)
(put 'latex 'math-matrix-formatter
(function
(lambda (a)
(if (and (integerp calc-language-option)
(or (= calc-language-option 0)
(> calc-language-option 1)
(< calc-language-option -1)))
(append '(vleft 0 "\\begin{pmatrix}")
(math-compose-tex-matrix (cdr a) t)
'("\\end{pmatrix}"))
(append '(horiz "\\begin{pmatrix} ")
(math-compose-tex-matrix (cdr a) t)
'(" \\end{pmatrix}"))))))
(put 'latex 'math-var-formatter 'math-compose-tex-var)
(put 'latex 'math-func-formatter 'math-compose-tex-func)
(put 'latex 'math-dots "\\ldots")
(put 'latex 'math-big-parens '("\\left( " . " \\right)"))
(put 'latex 'math-evalto '("\\evalto " . " \\to "))
(put 'latex 'math-lang-read-symbol
'((?\\
(< math-exp-pos (1- (length math-exp-str)))
(progn
(or (string-match "\\\\hbox *{\\([a-zA-Zα-ωΑ-Ω0-9]+\\)}"
math-exp-str math-exp-pos)
(string-match "\\\\text *{\\([a-zA-Zα-ωΑ-Ω0-9]+\\)}"
math-exp-str math-exp-pos)
(string-match "\\(\\\\\\([a-zA-Zα-ωΑ-Ω]+\\|[^a-zA-Zα-ωΑ-Ω]\\)\\)"
math-exp-str math-exp-pos))
(setq math-exp-token 'symbol
math-exp-pos (match-end 0)
math-expr-data (math-restore-dashes
(math-match-substring math-exp-str 1)))
(let ((code (assoc math-expr-data math-tex-ignore-words))
envname)
(cond ((null code))
((null (cdr code))
(math-read-token))
((eq (nth 1 code) 'punc)
(setq math-exp-token 'punc
math-expr-data (nth 2 code)))
((and (eq (nth 1 code) 'begenv)
(string-match " *{\\([^}]*\\)}" math-exp-str math-exp-pos))
(setq math-exp-pos (match-end 0)
envname (match-string 1 math-exp-str)
math-exp-token 'punc
math-expr-data "[")
(cond ((or (string= envname "matrix")
(string= envname "bmatrix")
(string= envname "smallmatrix")
(string= envname "pmatrix"))
(if (string-match (concat "\\\\end{" envname "}")
math-exp-str math-exp-pos)
(setq math-exp-str
(replace-match "]" t t math-exp-str))
(error "%s" (concat "No closing \\end{" envname "}"))))))
((and (eq (nth 1 code) 'mat)
(string-match " *{" math-exp-str math-exp-pos))
(setq math-exp-pos (match-end 0)
math-exp-token 'punc
math-expr-data "[")
(let ((right (string-match "}" math-exp-str math-exp-pos)))
(and right
(setq math-exp-str (copy-sequence math-exp-str))
(aset math-exp-str right ?\]))))))))))
(defun math-latex-parse-frac (f val)
(let (numer denom)
(setq numer (car (math-read-expr-list)))
(math-read-token)
(setq denom (math-read-factor))
(if (and (Math-num-integerp numer)
(Math-num-integerp denom))
(list 'frac numer denom)
(list '/ numer denom))))
(defun math-latex-parse-two-args (f val)
(let (first second)
(setq first (car (math-read-expr-list)))
(math-read-token)
(setq second (math-read-factor))
(list (nth 2 f) first second)))
(defun math-compose-latex-frac (a fn)
(list 'horiz (nth 1 fn) "{" (math-compose-expr (nth 1 a) -1)
"}{"
(math-compose-expr (nth 2 a) -1)
"}"))
(put 'latex 'math-input-filter 'math-tex-input-filter)
(defun calc-eqn-language (n)
(interactive "P")
(calc-wrapper
(calc-set-language 'eqn)
(message "Eqn language mode")))
(put 'eqn 'math-oper-table
'( ( "prime" (math-parse-eqn-prime) 950 -1 )
( "prime" calcFunc-Prime 950 -1 )
( "dot" calcFunc-dot 950 -1 )
( "dotdot" calcFunc-dotdot 950 -1 )
( "hat" calcFunc-hat 950 -1 )
( "tilde" calcFunc-tilde 950 -1 )
( "vec" calcFunc-Vec 950 -1 )
( "dyad" calcFunc-dyad 950 -1 )
( "bar" calcFunc-bar 950 -1 )
( "under" calcFunc-under 950 -1 )
( "sub" calcFunc-subscr 931 930 )
( "sup" ^ 921 920 )
( "sqrt" calcFunc-sqrt -1 910 )
( "over" / 900 901 )
( "u|" calcFunc-abs -1 0 )
( "|" closing 0 -1 )
( "left floor" calcFunc-floor -1 0 )
( "right floor" closing 0 -1 )
( "left ceil" calcFunc-ceil -1 0 )
( "right ceil" closing 0 -1 )
( "+-" sdev 300 300 )
( "!" calcFunc-fact 210 -1 )
( "u+" ident -1 197 )
( "u-" neg -1 197 )
( "times" * 191 190 )
( "*" * 191 190 )
( "2x" * 191 190 )
( "/" / 180 181 )
( "%" % 180 181 )
( "+" + 170 171 )
( "-" - 170 171 )
( "<" calcFunc-lt 160 161 )
( ">" calcFunc-gt 160 161 )
( "<=" calcFunc-leq 160 161 )
( ">=" calcFunc-geq 160 161 )
( "=" calcFunc-eq 160 161 )
( "==" calcFunc-eq 160 161 )
( "!=" calcFunc-neq 160 161 )
( "u!" calcFunc-lnot -1 121 )
( "&&" calcFunc-land 110 111 )
( "||" calcFunc-lor 100 101 )
( "?" (math-read-if) 91 90 )
( "!!!" calcFunc-pnot -1 85 )
( "&&&" calcFunc-pand 80 81 )
( "|||" calcFunc-por 75 76 )
( "<-" calcFunc-assign 51 50 )
( ":=" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 )
( "->" calcFunc-evalto 40 41 )
( "->" calcFunc-evalto 40 -1 )
( "=>" calcFunc-evalto 40 41 )
( "=>" calcFunc-evalto 40 -1 )))
(put 'eqn 'math-function-table
'( ( arc\ cos . calcFunc-arccos )
( arc\ cosh . calcFunc-arccosh )
( arc\ sin . calcFunc-arcsin )
( arc\ sinh . calcFunc-arcsinh )
( arc\ tan . calcFunc-arctan )
( arc\ tanh . calcFunc-arctanh )
( GAMMA . calcFunc-gamma )
( phi . calcFunc-totient )
( mu . calcFunc-moebius )
( matrix . (math-parse-eqn-matrix) )))
(put 'eqn 'math-special-function-table
'((intv . math-compose-eqn-intv)))
(put 'eqn 'math-punc-table
'((?\{ . ?\()
(?\} . ?\))))
(put 'eqn 'math-variable-table
'( ( inf . var-uinf )))
(put 'eqn 'math-complex-format 'i)
(put 'eqn 'math-big-parens '("{left ( " . " right )}"))
(put 'eqn 'math-evalto '("evalto " . " -> "))
(put 'eqn 'math-matrix-formatter
(function
(lambda (a)
(append '(horiz "matrix { ")
(math-compose-eqn-matrix
(cdr (math-transpose a)))
'("}")))))
(put 'eqn 'math-var-formatter
(function
(lambda (a prec)
(let (v)
(if (and math-compose-hash-args
(let ((p calc-arg-values))
(setq v 1)
(while (and p (not (equal (car p) a)))
(setq p (and (eq math-compose-hash-args t) (cdr p))
v (1+ v)))
p))
(if (eq math-compose-hash-args 1)
"#"
(format "#%d" v))
(if (string-match ".'\\'" (symbol-name (nth 2 a)))
(math-compose-expr
(list 'calcFunc-Prime
(list
'var
(intern (substring (symbol-name (nth 1 a)) 0 -1))
(intern (substring (symbol-name (nth 2 a)) 0 -1))))
prec)
(symbol-name (nth 1 a))))))))
(defconst math-eqn-special-funcs
'( calcFunc-log
calcFunc-ln calcFunc-exp
calcFunc-sin calcFunc-cos calcFunc-tan
calcFunc-sec calcFunc-csc calcFunc-cot
calcFunc-sinh calcFunc-cosh calcFunc-tanh
calcFunc-sech calcFunc-csch calcFunc-coth
calcFunc-arcsin calcFunc-arccos calcFunc-arctan
calcFunc-arcsinh calcFunc-arccosh calcFunc-arctanh))
(put 'eqn 'math-func-formatter
(function
(lambda (func a)
(let (left right)
(if (string-match "[^']'+\\'" func)
(let ((n (- (length func) (match-beginning 0) 1)))
(setq func (substring func 0 (- n)))
(while (>= (setq n (1- n)) 0)
(setq func (concat func " prime")))))
(cond ((or (> (length a) 2)
(not (math-tex-expr-is-flat (nth 1 a))))
(setq left "{left ( "
right " right )}"))
((and
(memq (car a) math-eqn-special-funcs)
(= (length a) 2)
(or (Math-realp (nth 1 a))
(memq (car (nth 1 a)) '(var *))))
(setq left "~{" right "}"))
(t
(setq left " ( "
right " )")))
(list 'horiz func left
(math-compose-vector (cdr a) " , " 0)
right)))))
(put 'eqn 'math-lang-read-symbol
'((?\"
(string-match "\\(\"\\([^\"\\]\\|\\\\.\\)*\\)\\(\"\\|\\'\\)"
math-exp-str math-exp-pos)
(progn
(setq math-exp-str (copy-sequence math-exp-str))
(aset math-exp-str (match-beginning 1) ?\{)
(if (< (match-end 1) (length math-exp-str))
(aset math-exp-str (match-end 1) ?\}))
(math-read-token)))))
(defconst math-eqn-ignore-words
'( ("roman") ("bold") ("italic") ("mark") ("lineup") ("evalto")
("left" ("floor") ("ceil"))
("right" ("floor") ("ceil"))
("arc" ("sin") ("cos") ("tan") ("sinh") ("cosh") ("tanh"))
("size" n) ("font" n) ("fwd" n) ("back" n) ("up" n) ("down" n)
("above" punc ",")))
(put 'eqn 'math-lang-adjust-words
(function
(lambda ()
(let ((code (assoc math-expr-data math-eqn-ignore-words)))
(cond ((null code))
((null (cdr code))
(math-read-token))
((consp (nth 1 code))
(math-read-token)
(if (assoc math-expr-data (cdr code))
(setq math-expr-data (format "%s %s"
(car code) math-expr-data))))
((eq (nth 1 code) 'punc)
(setq math-exp-token 'punc
math-expr-data (nth 2 code)))
(t
(math-read-token)
(math-read-token)))))))
(put 'eqn 'math-lang-read
'((eq (string-match "->\\|<-\\|+-\\|\\\\dots\\|~\\|\\^"
math-exp-str math-exp-pos)
math-exp-pos)
(progn
(setq math-exp-token 'punc
math-expr-data (math-match-substring math-exp-str 0)
math-exp-pos (match-end 0))
(and (eq (string-match "\\\\dots\\." math-exp-str math-exp-pos)
math-exp-pos)
(setq math-exp-pos (match-end 0)))
(if (memq (aref math-expr-data 0) '(?~ ?^))
(math-read-token)))))
(defun math-compose-eqn-matrix (a)
(if a
(cons
(cond ((eq calc-matrix-just 'right) "rcol ")
((eq calc-matrix-just 'center) "ccol ")
(t "lcol "))
(cons
(list 'break math-compose-level)
(cons
"{ "
(cons
(let ((math-compose-level (1+ math-compose-level)))
(math-compose-vector (cdr (car a)) " above " 1000))
(cons
" } "
(math-compose-eqn-matrix (cdr a)))))))
nil))
(defun math-parse-eqn-matrix (f sym)
(let ((vec nil))
(while (assoc math-expr-data '(("ccol") ("lcol") ("rcol")))
(math-read-token)
(or (equal math-expr-data calc-function-open)
(throw 'syntax "Expected `{'"))
(math-read-token)
(setq vec (cons (cons 'vec (math-read-expr-list)) vec))
(or (equal math-expr-data calc-function-close)
(throw 'syntax "Expected `}'"))
(math-read-token))
(or (equal math-expr-data calc-function-close)
(throw 'syntax "Expected `}'"))
(math-read-token)
(math-transpose (cons 'vec (nreverse vec)))))
(defun math-parse-eqn-prime (x sym)
(if (eq (car-safe x) 'var)
(if (equal math-expr-data calc-function-open)
(progn
(math-read-token)
(let ((args (if (or (equal math-expr-data calc-function-close)
(eq math-exp-token 'end))
nil
(math-read-expr-list))))
(if (not (or (equal math-expr-data calc-function-close)
(eq math-exp-token 'end)))
(throw 'syntax "Expected `)'"))
(math-read-token)
(cons (intern (format "calcFunc-%s'" (nth 1 x))) args)))
(list 'var
(intern (concat (symbol-name (nth 1 x)) "'"))
(intern (concat (symbol-name (nth 2 x)) "'"))))
(list 'calcFunc-Prime x)))
(defun math-compose-eqn-intv (a)
(list 'horiz
(if (memq (nth 1 a) '(0 1)) "(" "[")
(math-compose-expr (nth 2 a) 0)
" ... "
(math-compose-expr (nth 3 a) 0)
(if (memq (nth 1 a) '(0 2)) ")" "]")))
;;; Yacas
(defun calc-yacas-language ()
"Change the Calc language to be Yacas-like."
(interactive)
(calc-wrapper
(calc-set-language 'yacas)
(message "Yacas language mode")))
(put 'yacas 'math-vector-brackets "{}")
(put 'yacas 'math-complex-format 'I)
(add-to-list 'calc-lang-brackets-are-subscripts 'yacas)
(put 'yacas 'math-variable-table
'(( Infinity . var-inf)
( Infinity . var-uinf)
( Undefined . var-nan)
( Pi . var-pi)
( E . var-e) ;; Not really in Yacas
( GoldenRatio . var-phi)
( Gamma . var-gamma)))
(put 'yacas 'math-parse-table
'((("Deriv(" 0 ")" 0)
calcFunc-deriv (var ArgB var-ArgB) (var ArgA var-ArgA))
(("D(" 0 ")" 0)
calcFunc-deriv (var ArgB var-ArgB) (var ArgA var-ArgA))
(("Integrate(" 0 ")" 0)
calcFunc-integ (var ArgB var-ArgB)(var ArgA var-ArgA))
(("Integrate(" 0 "," 0 "," 0 ")" 0)
calcFunc-integ (var ArgD var-ArgD) (var ArgA var-ArgA)
(var ArgB var-ArgB) (var ArgC var-ArgC))
(("Subst(" 0 "," 0 ")" 0)
calcFunc-subst (var ArgC var-ArgC) (var ArgA var-ArgA)
(var ArgB var-ArgB))
(("Taylor(" 0 "," 0 "," 0 ")" 0)
calcFunc-taylor (var ArgD var-ArgD)
(calcFunc-eq (var ArgA var-ArgA) (var ArgB var-ArgB))
(var ArgC var-ArgC))))
(put 'yacas 'math-oper-table
'(("+" + 30 30)
("-" - 30 60)
("*" * 60 60)
("/" / 70 70)
("u-" neg -1 60)
("^" ^ 80 80)
("u+" ident -1 30)
("<<" calcFunc-lsh 80 80)
(">>" calcFunc-rsh 80 80)
("!" calcFunc-fact 80 -1)
("!!" calcFunc-dfact 80 -1)
("X" calcFunc-cross 70 70)
("=" calcFunc-eq 10 10)
("!=" calcFunc-neq 10 10)
("<" calcFunc-lt 10 10)
(">" calcFunc-gt 10 10)
("<=" calcFunc-leq 10 10)
(">=" calcFunc-geq 10 10)
("And" calcFunc-land 5 5)
("Or" calcFunc-or 4 4)
("Not" calcFunc-lnot -1 3)
(":=" calcFunc-assign 1 1)))
(put 'yacas 'math-function-table
'(( Div . calcFunc-idiv)
( Mod . calcFunc-mod)
( Abs . calcFunc-abs)
( Sign . calcFunc-sign)
( Sqrt . calcFunc-sqrt)
( Max . calcFunc-max)
( Min . calcFunc-min)
( Floor . calcFunc-floor)
( Ceil . calcFunc-ceil)
( Round . calcFunc-round)
( Conjugate . calcFunc-conj)
( Arg . calcFunc-arg)
( Re . calcFunc-re)
( Im . calcFunc-im)
( Rationalize . calcFunc-pfrac)
( Sin . calcFunc-sin)
( Cos . calcFunc-cos)
( Tan . calcFunc-tan)
( Sec . calcFunc-sec)
( Csc . calcFunc-csc)
( Cot . calcFunc-cot)
( ArcSin . calcFunc-arcsin)
( ArcCos . calcFunc-arccos)
( ArcTan . calcFunc-arctan)
( Sinh . calcFunc-sinh)
( Cosh . calcFunc-cosh)
( Tanh . calcFunc-tanh)
( Sech . calcFunc-sech)
( Csch . calcFunc-csch)
( Coth . calcFunc-coth)
( ArcSinh . calcFunc-arcsinh)
( ArcCosh . calcFunc-arccosh)
( ArcTanh . calcFunc-arctanh)
( Ln . calcFunc-ln)
( Exp . calcFunc-exp)
( Gamma . calcFunc-gamma)
( Gcd . calcFunc-gcd)
( Lcm . calcFunc-lcm)
( Bin . calcFunc-choose)
( Bernoulli . calcFunc-bern)
( Euler . calcFunc-euler)
( StirlingNumber1 . calcFunc-stir1)
( StirlingNumber2 . calcFunc-stir2)
( IsPrime . calcFunc-prime)
( Factors . calcFunc-prfac)
( NextPrime . calcFunc-nextprime)
( Moebius . calcFunc-moebius)
( Random . calcFunc-random)
( Concat . calcFunc-vconcat)
( Head . calcFunc-head)
( Tail . calcFunc-tail)
( Length . calcFunc-vlen)
( Reverse . calcFunc-rev)
( CrossProduct . calcFunc-cross)
( Dot . calcFunc-mul)
( DiagonalMatrix . calcFunc-diag)
( Transpose . calcFunc-trn)
( Inverse . calcFunc-inv)
( Determinant . calcFunc-det)
( Trace . calcFunc-tr)
( RemoveDuplicates . calcFunc-rdup)
( Union . calcFunc-vunion)
( Intersection . calcFunc-vint)
( Difference . calcFunc-vdiff)
( Apply . calcFunc-apply)
( Map . calcFunc-map)
( Simplify . calcFunc-simplify)
( ExpandBrackets . calcFunc-expand)
( Solve . calcFunc-solve)
( Degree . calcFunc-pdeg)
( If . calcFunc-if)
( Contains . (math-lang-switch-args calcFunc-in))
( Sum . (math-yacas-parse-Sum calcFunc-sum))
( Factorize . (math-yacas-parse-Sum calcFunc-prod))))
(put 'yacas 'math-special-function-table
'(( calcFunc-sum . (math-yacas-compose-sum "Sum"))
( calcFunc-prod . (math-yacas-compose-sum "Factorize"))
( calcFunc-deriv . (math-yacas-compose-deriv "Deriv"))
( calcFunc-integ . (math-yacas-compose-deriv "Integrate"))
( calcFunc-taylor . math-yacas-compose-taylor)
( calcFunc-in . (math-lang-compose-switch-args "Contains"))))
(put 'yacas 'math-compose-subscr
(function
(lambda (a)
(let ((args (cdr (cdr a))))
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"["
(math-compose-vector args ", " 0)
"]")))))
(defun math-yacas-parse-Sum (f val)
"Read in the arguments to \"Sum\" in Calc's Yacas mode."
(let ((args (math-read-expr-list)))
(math-read-token)
(list (nth 2 f)
(nth 3 args)
(nth 0 args)
(nth 1 args)
(nth 2 args))))
(defun math-yacas-compose-sum (a fn)
"Compose the \"Sum\" function in Calc's Yacas mode."
(list 'horiz
(nth 1 fn)
"("
(math-compose-expr (nth 2 a) -1)
","
(math-compose-expr (nth 3 a) -1)
","
(math-compose-expr (nth 4 a) -1)
","
(math-compose-expr (nth 1 a) -1)
")"))
(defun math-yacas-compose-deriv (a fn)
"Compose the \"Deriv\" function in Calc's Yacas mode."
(list 'horiz
(nth 1 fn)
"("
(math-compose-expr (nth 2 a) -1)
(if (not (nth 3 a))
")"
(concat
","
(math-compose-expr (nth 3 a) -1)
","
(math-compose-expr (nth 4 a) -1)
")"))
" "
(math-compose-expr (nth 1 a) -1)))
(defun math-yacas-compose-taylor (a)
"Compose the \"Taylor\" function in Calc's Yacas mode."
(list 'horiz
"Taylor("
(if (eq (car-safe (nth 2 a)) 'calcFunc-eq)
(concat (math-compose-expr (nth 1 (nth 2 a)) -1)
","
(math-compose-expr (nth 2 (nth 2 a)) -1))
(concat (math-compose-expr (nth 2 a) -1) ",0"))
","
(math-compose-expr (nth 3 a) -1)
") "
(math-compose-expr (nth 1 a) -1)))
;;; Maxima
(defun calc-maxima-language ()
"Change the Calc language to be Maxima-like."
(interactive)
(calc-wrapper
(calc-set-language 'maxima)
(message "Maxima language mode")))
(put 'maxima 'math-oper-table
'(("+" + 100 100)
("-" - 100 134)
("*" * 120 120)
("." * 130 129)
("/" / 120 120)
("u-" neg -1 180)
("u+" ident -1 180)
("^" ^ 140 139)
("**" ^ 140 139)
("!" calcFunc-fact 160 -1)
("!!" calcFunc-dfact 160 -1)
("=" calcFunc-eq 80 80)
("#" calcFunc-neq 80 80)
("<" calcFunc-lt 80 80)
(">" calcFunc-gt 80 80)
("<=" calcFunc-leq 80 80)
(">=" calcFunc-geq 80 80)
("and" calcFunc-land 65 65)
("or" calcFunc-or 60 60)
("not" calcFunc-lnot -1 70)
(":" calcFunc-assign 180 20)))
(put 'maxima 'math-function-table
'(( matrix . vec)
( abs . calcFunc-abs)
( cabs . calcFunc-abs)
( signum . calcFunc-sign)
( floor . calcFunc-floor)
( entier . calcFunc-floor)
( fix . calcFunc-floor)
( conjugate . calcFunc-conj )
( carg . calcFunc-arg)
( realpart . calcFunc-re)
( imagpart . calcFunc-im)
( rationalize . calcFunc-pfrac)
( asin . calcFunc-arcsin)
( acos . calcFunc-arccos)
( atan . calcFunc-arctan)
( atan2 . calcFunc-arctan2)
( asinh . calcFunc-arcsinh)
( acosh . calcFunc-arccosh)
( atanh . calcFunc-arctanh)
( log . calcFunc-ln)
( plog . calcFunc-ln)
( bessel_j . calcFunc-besJ)
( bessel_y . calcFunc-besY)
( factorial . calcFunc-fact)
( binomial . calcFunc-choose)
( primep . calcFunc-prime)
( next_prime . calcFunc-nextprime)
( prev_prime . calcFunc-prevprime)
( append . calcFunc-vconcat)
( rest . calcFunc-tail)
( reverse . calcFunc-rev)
( innerproduct . calcFunc-mul)
( inprod . calcFunc-mul)
( row . calcFunc-mrow)
( columnvector . calcFunc-mcol)
( covect . calcFunc-mcol)
( transpose . calcFunc-trn)
( invert . calcFunc-inv)
( determinant . calcFunc-det)
( mattrace . calcFunc-tr)
( member . calcFunc-in)
( lmax . calcFunc-vmax)
( lmin . calcFunc-vmin)
( distrib . calcFunc-expand)
( partfrac . calcFunc-apart)
( rat . calcFunc-nrat)
( product . calcFunc-prod)
( diff . calcFunc-deriv)
( integrate . calcFunc-integ)
( quotient . calcFunc-pdiv)
( remainder . calcFunc-prem)
( divide . calcFunc-pdivrem)
( equal . calcFunc-eq)
( notequal . calcFunc-neq)
( rhs . calcFunc-rmeq)
( subst . (math-maxima-parse-subst))
( substitute . (math-maxima-parse-subst))
( taylor . (math-maxima-parse-taylor))))
(defun math-maxima-parse-subst (f val)
"Read in the arguments to \"subst\" in Calc's Maxima mode."
(let ((args (math-read-expr-list)))
(math-read-token)
(list 'calcFunc-subst
(nth 1 args)
(nth 2 args)
(nth 0 args))))
(defun math-maxima-parse-taylor (f val)
"Read in the arguments to \"taylor\" in Calc's Maxima mode."
(let ((args (math-read-expr-list)))
(math-read-token)
(list 'calcFunc-taylor
(nth 0 args)
(list 'calcFunc-eq
(nth 1 args)
(nth 2 args))
(nth 3 args))))
(put 'maxima 'math-parse-table
'((("if" 0 "then" 0 "else" 0)
calcFunc-if
(var ArgA var-ArgA)
(var ArgB var-ArgB)
(var ArgC var-ArgC))))
(put 'maxima 'math-special-function-table
'(( calcFunc-taylor . math-maxima-compose-taylor)
( calcFunc-subst . math-maxima-compose-subst)
( calcFunc-if . math-maxima-compose-if)))
(defun math-maxima-compose-taylor (a)
"Compose the \"taylor\" function in Calc's Maxima mode."
(list 'horiz
"taylor("
(math-compose-expr (nth 1 a) -1)
","
(if (eq (car-safe (nth 2 a)) 'calcFunc-eq)
(concat (math-compose-expr (nth 1 (nth 2 a)) -1)
","
(math-compose-expr (nth 2 (nth 2 a)) -1))
(concat (math-compose-expr (nth 2 a) -1) ",0"))
","
(math-compose-expr (nth 3 a) -1)
")"))
(defun math-maxima-compose-subst (a)
"Compose the \"subst\" function in Calc's Maxima mode."
(list 'horiz
"substitute("
(math-compose-expr (nth 2 a) -1)
","
(math-compose-expr (nth 3 a) -1)
","
(math-compose-expr (nth 1 a) -1)
")"))
(defun math-maxima-compose-if (a)
"Compose the \"if\" function in Calc's Maxima mode."
(list 'horiz
"if "
(math-compose-expr (nth 1 a) -1)
" then "
(math-compose-expr (nth 2 a) -1)
" else "
(math-compose-expr (nth 3 a) -1)))
(put 'maxima 'math-variable-table
'(( infinity . var-uinf)
( %pi . var-pi)
( %e . var-e)
( %i . var-i)
( %phi . var-phi)
( %gamma . var-gamma)))
(put 'maxima 'math-complex-format '%i)
(add-to-list 'calc-lang-allow-underscores 'maxima)
(add-to-list 'calc-lang-allow-percentsigns 'maxima)
(add-to-list 'calc-lang-brackets-are-subscripts 'maxima)
(put 'maxima 'math-compose-subscr
(function
(lambda (a)
(let ((args (cdr (cdr a))))
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"["
(math-compose-vector args ", " 0)
"]")))))
(put 'maxima 'math-matrix-formatter
(function
(lambda (a)
(list 'horiz
"matrix("
(math-compose-vector (cdr a)
(concat math-comp-comma " ")
math-comp-vector-prec)
")"))))
;;; Giac
(defun calc-giac-language ()
"Change the Calc language to be Giac-like."
(interactive)
(calc-wrapper
(calc-set-language 'giac)
(message "Giac language mode")))
(put 'giac 'math-oper-table
'( ( "[" (math-read-giac-subscr) 250 -1 )
( "+" + 180 181 )
( "-" - 180 181 )
( "/" / 191 192 )
( "*" * 191 192 )
( "^" ^ 201 200 )
( "u+" ident -1 197 )
( "u-" neg -1 197 )
( "!" calcFunc-fact 210 -1 )
( ".." (math-read-maple-dots) 165 165 )
( "\\dots" (math-read-maple-dots) 165 165 )
( "intersect" calcFunc-vint 191 192 )
( "union" calcFunc-vunion 180 181 )
( "minus" calcFunc-vdiff 180 181 )
( "<" calcFunc-lt 160 160 )
( ">" calcFunc-gt 160 160 )
( "<=" calcFunc-leq 160 160 )
( ">=" calcFunc-geq 160 160 )
( "=" calcFunc-eq 160 160 )
( "==" calcFunc-eq 160 160 )
( "!=" calcFunc-neq 160 160 )
( "and" calcFunc-land 110 111 )
( "or" calcFunc-lor 100 101 )
( "&&" calcFunc-land 110 111 )
( "||" calcFunc-lor 100 101 )
( "not" calcFunc-lnot -1 121 )
( ":=" calcFunc-assign 51 50 )))
(put 'giac 'math-function-table
'(( rdiv . calcFunc-div)
( iquo . calcFunc-idiv)
( irem . calcFunc-mod)
( remain . calcFunc-mod)
( floor . calcFunc-floor)
( iPart . calcFunc-floor)
( ceil . calcFunc-ceil)
( ceiling . calcFunc-ceil)
( re . calcFunc-re)
( real . calcFunc-re)
( im . calcFunc-im)
( imag . calcFunc-im)
( float2rational . calcFunc-pfrac)
( exact . calcFunc-pfrac)
( evalf . calcFunc-pfloat)
( bitand . calcFunc-and)
( bitor . calcFunc-or)
( bitxor . calcFunc-xor)
( asin . calcFunc-arcsin)
( acos . calcFunc-arccos)
( atan . calcFunc-arctan)
( asinh . calcFunc-arcsinh)
( acosh . calcFunc-arccosh)
( atanh . calcFunc-arctanh)
( log . calcFunc-ln)
( logb . calcFunc-log)
( factorial . calcFunc-fact)
( comb . calcFunc-choose)
( binomial . calcFunc-choose)
( nCr . calcFunc-choose)
( perm . calcFunc-perm)
( nPr . calcFunc-perm)
( bernoulli . calcFunc-bern)
( is_prime . calcFunc-prime)
( isprime . calcFunc-prime)
( isPrime . calcFunc-prime)
( ifactors . calcFunc-prfac)
( euler . calcFunc-totient)
( phi . calcFunc-totient)
( rand . calcFunc-random)
( concat . calcFunc-vconcat)
( augment . calcFunc-vconcat)
( mid . calcFunc-subvec)
( length . calcFunc-length)
( size . calcFunc-length)
( nops . calcFunc-length)
( SortA . calcFunc-sort)
( SortB . calcFunc-rsort)
( revlist . calcFunc-rev)
( cross . calcFunc-cross)
( crossP . calcFunc-cross)
( crossproduct . calcFunc-cross)
( mul . calcFunc-mul)
( dot . calcFunc-mul)
( dotprod . calcFunc-mul)
( dotP . calcFunc-mul)
( scalar_product . calcFunc-mul)
( scalar_Product . calcFunc-mul)
( row . calcFunc-mrow)
( col . calcFunc-mcol)
( dim . calcFunc-mdims)
( tran . calcFunc-trn)
( transpose . calcFunc-trn)
( lu . calcFunc-lud)
( trace . calcFunc-tr)
( member . calcFunc-in)
( sum . calcFunc-vsum)
( add . calcFunc-vsum)
( product . calcFunc-vprod)
( mean . calcFunc-vmean)
( median . calcFunc-vmedian)
( stddev . calcFunc-vsdev)
( stddevp . calcFunc-vpsdev)
( variance . calcFunc-vpvar)
( map . calcFunc-map)
( apply . calcFunc-map)
( of . calcFunc-map)
( zip . calcFunc-map)
( expand . calcFunc-expand)
( fdistrib . calcFunc-expand)
( partfrac . calcFunc-apart)
( ratnormal . calcFunc-nrat)
( diff . calcFunc-deriv)
( derive . calcFunc-deriv)
( integrate . calcFunc-integ)
( int . calcFunc-integ)
( Int . calcFunc-integ)
( romberg . calcFunc-ninteg)
( nInt . calcFunc-ninteg)
( lcoeff . calcFunc-plead)
( content . calcFunc-pcont)
( primpart . calcFunc-pprim)
( quo . calcFunc-pdiv)
( rem . calcFunc-prem)
( quorem . calcFunc-pdivrem)
( divide . calcFunc-pdivrem)
( equal . calcFunc-eq)
( ifte . calcFunc-if)
( not . calcFunc-lnot)
( rhs . calcFunc-rmeq)
( right . calcFunc-rmeq)
( prepend . (math-lang-switch-args calcFunc-cons))
( contains . (math-lang-switch-args calcFunc-in))
( has . (math-lang-switch-args calcFunc-refers))))
(defun math-lang-switch-args (f val)
"Read the arguments to a Calc function in reverse order.
This is used for various language modes which have functions in reverse
order to Calc's."
(let ((args (math-read-expr-list)))
(math-read-token)
(list (nth 2 f)
(nth 1 args)
(nth 0 args))))
(put 'giac 'math-parse-table
'((("set" 0)
calcFunc-rdup
(var ArgA var-ArgA))))
(put 'giac 'math-special-function-table
'((calcFunc-cons . (math-lang-compose-switch-args "prepend"))
(calcFunc-in . (math-lang-compose-switch-args "contains"))
(calcFunc-refers . (math-lang-compose-switch-args "has"))
(intv . math-compose-maple-intv)))
(defun math-lang-compose-switch-args (a fn)
"Compose the arguments to a Calc function in reverse order.
This is used for various language modes which have functions in reverse
order to Calc's."
(list 'horiz (nth 1 fn)
"("
(math-compose-expr (nth 2 a) 0)
","
(math-compose-expr (nth 1 a) 0)
")"))
(put 'giac 'math-variable-table
'(( infinity . var-inf)
( infinity . var-uinf)))
(put 'giac 'math-complex-format 'i)
(add-to-list 'calc-lang-allow-underscores 'giac)
(put 'giac 'math-compose-subscr
(function
(lambda (a)
(let ((args (cdr (cdr a))))
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"["
(math-compose-expr
(calc-normalize (list '- (nth 2 a) 1)) 0)
"]")))))
(defun math-read-giac-subscr (x op)
(let ((idx (math-read-expr-level 0)))
(or (equal math-expr-data "]")
(throw 'syntax "Expected `]'"))
(math-read-token)
(list 'calcFunc-subscr x (calc-normalize (list '+ idx 1)))))
(add-to-list 'calc-lang-c-type-hex 'giac)
(defun calc-mathematica-language ()
(interactive)
(calc-wrapper
(calc-set-language 'math)
(message "Mathematica language mode")))
(put 'math 'math-oper-table
'( ( "[[" (math-read-math-subscr) 250 -1 )
( "!" calcFunc-fact 210 -1 )
( "!!" calcFunc-dfact 210 -1 )
( "^" ^ 201 200 )
( "u+" ident -1 197 )
( "u-" neg -1 197 )
( "/" / 195 196 )
( "*" * 190 191 )
( "2x" * 190 191 )
( "+" + 180 181 )
( "-" - 180 181 )
( "<" calcFunc-lt 160 161 )
( ">" calcFunc-gt 160 161 )
( "<=" calcFunc-leq 160 161 )
( ">=" calcFunc-geq 160 161 )
( "==" calcFunc-eq 150 151 )
( "!=" calcFunc-neq 150 151 )
( "u!" calcFunc-lnot -1 121 )
( "&&" calcFunc-land 110 111 )
( "||" calcFunc-lor 100 101 )
( "!!!" calcFunc-pnot -1 85 )
( "&&&" calcFunc-pand 80 81 )
( "|||" calcFunc-por 75 76 )
( ":=" calcFunc-assign 51 50 )
( "=" calcFunc-assign 51 50 )
( "->" calcFunc-assign 51 50 )
( ":>" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 )
))
(put 'math 'math-function-table
'( ( Abs . calcFunc-abs )
( ArcCos . calcFunc-arccos )
( ArcCosh . calcFunc-arccosh )
( ArcSin . calcFunc-arcsin )
( ArcSinh . calcFunc-arcsinh )
( ArcTan . calcFunc-arctan )
( ArcTanh . calcFunc-arctanh )
( Arg . calcFunc-arg )
( Binomial . calcFunc-choose )
( Ceiling . calcFunc-ceil )
( Conjugate . calcFunc-conj )
( Cos . calcFunc-cos )
( Cosh . calcFunc-cosh )
( Cot . calcFunc-cot )
( Coth . calcFunc-coth )
( Csc . calcFunc-csc )
( Csch . calcFunc-csch )
( D . calcFunc-deriv )
( Dt . calcFunc-tderiv )
( Det . calcFunc-det )
( Exp . calcFunc-exp )
( EulerPhi . calcFunc-totient )
( Floor . calcFunc-floor )
( Gamma . calcFunc-gamma )
( GCD . calcFunc-gcd )
( If . calcFunc-if )
( Im . calcFunc-im )
( Inverse . calcFunc-inv )
( Integrate . calcFunc-integ )
( Join . calcFunc-vconcat )
( LCM . calcFunc-lcm )
( Log . calcFunc-ln )
( Max . calcFunc-max )
( Min . calcFunc-min )
( Mod . calcFunc-mod )
( MoebiusMu . calcFunc-moebius )
( Random . calcFunc-random )
( Round . calcFunc-round )
( Re . calcFunc-re )
( Sec . calcFunc-sec )
( Sech . calcFunc-sech )
( Sign . calcFunc-sign )
( Sin . calcFunc-sin )
( Sinh . calcFunc-sinh )
( Sqrt . calcFunc-sqrt )
( Tan . calcFunc-tan )
( Tanh . calcFunc-tanh )
( Transpose . calcFunc-trn )
( Length . calcFunc-vlen )
))
(put 'math 'math-variable-table
'( ( I . var-i )
( Pi . var-pi )
( E . var-e )
( GoldenRatio . var-phi )
( EulerGamma . var-gamma )
( Infinity . var-inf )
( ComplexInfinity . var-uinf )
( Indeterminate . var-nan )
))
(put 'math 'math-vector-brackets "{}")
(put 'math 'math-complex-format 'I)
(put 'math 'math-function-open "[")
(put 'math 'math-function-close "]")
(put 'math 'math-radix-formatter
(function (lambda (r s) (format "%d^^%s" r s))))
(put 'math 'math-lang-read
'((eq (string-match "\\[\\[\\|->\\|:>" math-exp-str math-exp-pos)
math-exp-pos)
(setq math-exp-token 'punc
math-expr-data (math-match-substring math-exp-str 0)
math-exp-pos (match-end 0))))
(put 'math 'math-compose-subscr
(function
(lambda (a)
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"[["
(math-compose-expr (nth 2 a) 0)
"]]"))))
(defun math-read-math-subscr (x op)
(let ((idx (math-read-expr-level 0)))
(or (and (equal math-expr-data "]")
(progn
(math-read-token)
(equal math-expr-data "]")))
(throw 'syntax "Expected `]]'"))
(math-read-token)
(list 'calcFunc-subscr x idx)))
(defun calc-maple-language ()
(interactive)
(calc-wrapper
(calc-set-language 'maple)
(message "Maple language mode")))
(put 'maple 'math-oper-table
'( ( "matrix" ident -1 300 )
( "MATRIX" ident -1 300 )
( "!" calcFunc-fact 210 -1 )
( "^" ^ 201 200 )
( "**" ^ 201 200 )
( "u+" ident -1 197 )
( "u-" neg -1 197 )
( "/" / 191 192 )
( "*" * 191 192 )
( "intersect" calcFunc-vint 191 192 )
( "+" + 180 181 )
( "-" - 180 181 )
( "union" calcFunc-vunion 180 181 )
( "minus" calcFunc-vdiff 180 181 )
( "mod" % 170 170 )
( ".." (math-read-maple-dots) 165 165 )
( "\\dots" (math-read-maple-dots) 165 165 )
( "<" calcFunc-lt 160 160 )
( ">" calcFunc-gt 160 160 )
( "<=" calcFunc-leq 160 160 )
( ">=" calcFunc-geq 160 160 )
( "=" calcFunc-eq 160 160 )
( "<>" calcFunc-neq 160 160 )
( "not" calcFunc-lnot -1 121 )
( "and" calcFunc-land 110 111 )
( "or" calcFunc-lor 100 101 )
( "!!!" calcFunc-pnot -1 85 )
( "&&&" calcFunc-pand 80 81 )
( "|||" calcFunc-por 75 76 )
( ":=" calcFunc-assign 51 50 )
( "::" calcFunc-condition 45 46 )
))
(put 'maple 'math-function-table
'( ( bernoulli . calcFunc-bern )
( binomial . calcFunc-choose )
( diff . calcFunc-deriv )
( GAMMA . calcFunc-gamma )
( ifactor . calcFunc-prfac )
( igcd . calcFunc-gcd )
( ilcm . calcFunc-lcm )
( int . calcFunc-integ )
( modp . % )
( irem . % )
( iquo . calcFunc-idiv )
( isprime . calcFunc-prime )
( length . calcFunc-vlen )
( member . calcFunc-in )
( crossprod . calcFunc-cross )
( inverse . calcFunc-inv )
( trace . calcFunc-tr )
( transpose . calcFunc-trn )
( vectdim . calcFunc-vlen )
))
(put 'maple 'math-special-function-table
'((intv . math-compose-maple-intv)))
(put 'maple 'math-variable-table
'( ( I . var-i )
( Pi . var-pi )
( E . var-e )
( infinity . var-inf )
( infinity . var-uinf )
( infinity . var-nan )
))
(put 'maple 'math-complex-format 'I)
(put 'maple 'math-matrix-formatter
(function
(lambda (a)
(list 'horiz
"matrix("
math-comp-left-bracket
(math-compose-vector (cdr a)
(concat math-comp-comma " ")
math-comp-vector-prec)
math-comp-right-bracket
")"))))
(put 'maple 'math-compose-subscr
(function
(lambda (a)
(let ((args (cdr (cdr a))))
(list 'horiz
(math-compose-expr (nth 1 a) 1000)
"["
(math-compose-vector args ", " 0)
"]")))))
(add-to-list 'calc-lang-allow-underscores 'maple)
(add-to-list 'calc-lang-brackets-are-subscripts 'maple)
(defun math-compose-maple-intv (a)
(list 'horiz
(math-compose-expr (nth 2 a) 0)
" .. "
(math-compose-expr (nth 3 a) 0)))
(defun math-read-maple-dots (x op)
(list 'intv 3 x (math-read-expr-level (nth 3 op))))
;; The variable math-read-big-lines is local to math-read-big-expr in
;; calc-ext.el, but is used by math-read-big-rec, math-read-big-char,
;; math-read-big-emptyp, math-read-big-error and math-read-big-balance,
;; which are called (directly and indirectly) by math-read-big-expr.
;; It is also local to math-read-big-bigp in calc-ext.el, which calls
;; math-read-big-balance.
(defvar math-read-big-lines)
;; The variables math-read-big-baseline and math-read-big-h2 are
;; local to math-read-big-expr in calc-ext.el, but used by
;; math-read-big-rec.
(defvar math-read-big-baseline)
(defvar math-read-big-h2)
;; The variables math-rb-h1, math-rb-h2, math-rb-v1 and math-rb-v2
;; are local to math-read-big-rec, but are used by math-read-big-char,
;; math-read-big-emptyp and math-read-big-balance which are called by
;; math-read-big-rec.
;; math-rb-h2 is also local to math-read-big-bigp in calc-ext.el,
;; which calls math-read-big-balance.
(defvar math-rb-h1)
(defvar math-rb-h2)
(defvar math-rb-v1)
(defvar math-rb-v2)
(defun math-read-big-rec (math-rb-h1 math-rb-v1 math-rb-h2 math-rb-v2
&optional baseline prec short)
(or prec (setq prec 0))
;; Clip whitespace above or below.
(while (and (< math-rb-v1 math-rb-v2)
(math-read-big-emptyp math-rb-h1 math-rb-v1 math-rb-h2 (1+ math-rb-v1)))
(setq math-rb-v1 (1+ math-rb-v1)))
(while (and (< math-rb-v1 math-rb-v2)
(math-read-big-emptyp math-rb-h1 (1- math-rb-v2) math-rb-h2 math-rb-v2))
(setq math-rb-v2 (1- math-rb-v2)))
;; If formula is a single line high, normal parser can handle it.
(if (<= math-rb-v2 (1+ math-rb-v1))
(if (or (<= math-rb-v2 math-rb-v1)
(> math-rb-h1 (length (setq math-rb-v2
(nth math-rb-v1 math-read-big-lines)))))
(math-read-big-error math-rb-h1 math-rb-v1)
(setq math-read-big-baseline math-rb-v1
math-read-big-h2 math-rb-h2
math-rb-v2 (nth math-rb-v1 math-read-big-lines)
math-rb-h2 (math-read-expr
(substring math-rb-v2 math-rb-h1
(min math-rb-h2 (length math-rb-v2)))))
(if (eq (car-safe math-rb-h2) 'error)
(math-read-big-error (+ math-rb-h1 (nth 1 math-rb-h2))
math-rb-v1 (nth 2 math-rb-h2))
math-rb-h2))
;; Clip whitespace at left or right.
(while (and (< math-rb-h1 math-rb-h2)
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) math-rb-v2))
(setq math-rb-h1 (1+ math-rb-h1)))
(while (and (< math-rb-h1 math-rb-h2)
(math-read-big-emptyp (1- math-rb-h2) math-rb-v1 math-rb-h2 math-rb-v2))
(setq math-rb-h2 (1- math-rb-h2)))
;; Scan to find widest left-justified "----" in the region.
(let* ((widest nil)
(widest-h2 0)
(lines-v1 (nthcdr math-rb-v1 math-read-big-lines))
(p lines-v1)
(v math-rb-v1)
(other-v nil)
other-char line len h)
(while (< v math-rb-v2)
(setq line (car p)
len (min math-rb-h2 (length line)))
(and (< math-rb-h1 len)
(/= (aref line math-rb-h1) ?\ )
(if (and (= (aref line math-rb-h1) ?\-)
;; Make sure it's not a minus sign.
(or (and (< (1+ math-rb-h1) len)
(= (aref line (1+ math-rb-h1)) ?\-))
(/= (math-read-big-char math-rb-h1 (1- v)) ?\ )
(/= (math-read-big-char math-rb-h1 (1+ v)) ?\ )))
(progn
(setq h math-rb-h1)
(while (and (< (setq h (1+ h)) len)
(= (aref line h) ?\-)))
(if (> h widest-h2)
(setq widest v
widest-h2 h)))
(or other-v (setq other-v v other-char (aref line math-rb-h1)))))
(setq v (1+ v)
p (cdr p)))
(cond ((not (setq v other-v))
(math-read-big-error math-rb-h1 math-rb-v1)) ; Should never happen!
;; Quotient.
(widest
(setq h widest-h2
v widest)
(let ((num (math-read-big-rec math-rb-h1 math-rb-v1 h v))
(den (math-read-big-rec math-rb-h1 (1+ v) h math-rb-v2)))
(setq p (if (and (math-integerp num) (math-integerp den))
(math-make-frac num den)
(list '/ num den)))))
;; Big radical sign.
((= other-char ?\\)
(or (= (math-read-big-char (1+ math-rb-h1) v) ?\|)
(math-read-big-error (1+ math-rb-h1) v "Malformed root sign"))
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(while (= (math-read-big-char (1+ math-rb-h1) (setq v (1- v))) ?\|))
(or (= (math-read-big-char (setq h (+ math-rb-h1 2)) v) ?\_)
(math-read-big-error h v "Malformed root sign"))
(while (= (math-read-big-char (setq h (1+ h)) v) ?\_))
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ other-v) h math-rb-v2 nil t)
(setq p (list 'calcFunc-sqrt (math-read-big-rec
(+ math-rb-h1 2) (1+ v)
h (1+ other-v) baseline))
v math-read-big-baseline))
;; Small radical sign.
((and (= other-char ?V)
(= (math-read-big-char (1+ math-rb-h1) (1- v)) ?\_))
(setq h (1+ math-rb-h1))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h (1- v) nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(while (= (math-read-big-char (setq h (1+ h)) (1- v)) ?\_))
(setq p (list 'calcFunc-sqrt (math-read-big-rec
(1+ math-rb-h1) v h (1+ v) t))
v math-read-big-baseline))
;; Binomial coefficient.
((and (= other-char ?\()
(= (math-read-big-char (1+ math-rb-h1) v) ?\ )
(= (string-match "( *)" (nth v math-read-big-lines)
math-rb-h1) math-rb-h1))
(setq h (match-end 0))
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) (1+ math-rb-h1) math-rb-v2 nil t)
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(setq p (list 'calcFunc-choose
(math-read-big-rec (1+ math-rb-h1) math-rb-v1 (1- h) v)
(math-read-big-rec (1+ math-rb-h1) (1+ v)
(1- h) math-rb-v2))))
;; Minus sign.
((= other-char ?\-)
(setq p (list 'neg (math-read-big-rec (1+ math-rb-h1) math-rb-v1
math-rb-h2 math-rb-v2 v 250 t))
v math-read-big-baseline
h math-read-big-h2))
;; Parentheses.
((= other-char ?\()
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) (1+ math-rb-h1) math-rb-v2 nil t)
(setq h (math-read-big-balance (1+ math-rb-h1) v "(" t))
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(let ((sep (math-read-big-char (1- h) v))
hmid)
(if (= sep ?\.)
(setq h (1+ h)))
(if (= sep ?\])
(math-read-big-error (1- h) v "Expected `)'"))
(if (= sep ?\))
(setq p (math-read-big-rec
(1+ math-rb-h1) math-rb-v1 (1- h) math-rb-v2 v))
(setq hmid (math-read-big-balance h v "(")
p (list p
(math-read-big-rec h math-rb-v1 (1- hmid) math-rb-v2 v))
h hmid)
(cond ((= sep ?\.)
(setq p (cons 'intv (cons (if (= (math-read-big-char
(1- h) v)
?\))
0 1)
p))))
((= (math-read-big-char (1- h) v) ?\])
(math-read-big-error (1- h) v "Expected `)'"))
((= sep ?\,)
(or (and (math-realp (car p)) (math-realp (nth 1 p)))
(math-read-big-error
math-rb-h1 v "Complex components must be real"))
(setq p (cons 'cplx p)))
((= sep ?\;)
(or (and (math-realp (car p)) (math-anglep (nth 1 p)))
(math-read-big-error
math-rb-h1 v "Complex components must be real"))
(setq p (cons 'polar p)))))))
;; Matrix.
((and (= other-char ?\[)
(or (= (math-read-big-char (setq h math-rb-h1) (1+ v)) ?\[)
(= (math-read-big-char (setq h (1+ h)) v) ?\[)
(and (= (math-read-big-char h v) ?\ )
(= (math-read-big-char (setq h (1+ h)) v) ?\[)))
(= (math-read-big-char h (1+ v)) ?\[))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(let ((vtop v)
(hleft h)
(hright nil))
(setq p nil)
(while (progn
(setq h (math-read-big-balance (1+ hleft) v "["))
(if hright
(or (= h hright)
(math-read-big-error hright v "Expected `]'"))
(setq hright h))
(setq p (cons (math-read-big-rec
hleft v h (1+ v)) p))
(and (memq (math-read-big-char h v) '(?\ ?\,))
(= (math-read-big-char hleft (1+ v)) ?\[)))
(setq v (1+ v)))
(or (= hleft math-rb-h1)
(progn
(if (= (math-read-big-char h v) ?\ )
(setq h (1+ h)))
(and (= (math-read-big-char h v) ?\])
(setq h (1+ h))))
(math-read-big-error (1- h) v "Expected `]'"))
(if (= (math-read-big-char h vtop) ?\,)
(setq h (1+ h)))
(math-read-big-emptyp math-rb-h1 (1+ v) (1- h) math-rb-v2 nil t)
(setq v (+ vtop (/ (- v vtop) 2))
p (cons 'vec (nreverse p)))))
;; Square brackets.
((= other-char ?\[)
(math-read-big-emptyp math-rb-h1 math-rb-v1 (1+ math-rb-h1) v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) (1+ math-rb-h1) math-rb-v2 nil t)
(setq p nil
h (1+ math-rb-h1))
(while (progn
(setq widest (math-read-big-balance h v "[" t))
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(setq p (cons (math-read-big-rec
h math-rb-v1 (1- widest) math-rb-v2 v) p)
h widest)
(= (math-read-big-char (1- h) v) ?\,)))
(setq widest (math-read-big-char (1- h) v))
(if (or (memq widest '(?\; ?\)))
(and (eq widest ?\.) (cdr p)))
(math-read-big-error (1- h) v "Expected `]'"))
(if (= widest ?\.)
(setq h (1+ h)
widest (math-read-big-balance h v "[")
p (nconc p (list (math-read-big-rec
h math-rb-v1 (1- widest) math-rb-v2 v)))
h widest
p (cons 'intv (cons (if (= (math-read-big-char (1- h) v)
?\])
3 2)
p)))
(setq p (cons 'vec (nreverse p)))))
;; Date form.
((= other-char ?\<)
(setq line (nth v math-read-big-lines))
(string-match ">" line math-rb-h1)
(setq h (match-end 0))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)
(setq p (math-read-big-rec math-rb-h1 v h (1+ v) v)))
;; Variable name or function call.
((or (and (>= other-char ?a) (<= other-char ?z))
(and (>= other-char ?A) (<= other-char ?Z))
(and (>= other-char ?α) (<= other-char ?ω))
(and (>= other-char ?Α) (<= other-char ?Ω)))
(setq line (nth v math-read-big-lines))
(string-match "\\([a-zA-Zα-ωΑ-Ω'_]+\\) *" line math-rb-h1)
(setq h (match-end 1)
widest (match-end 0)
p (math-match-substring line 1))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)
(if (= (math-read-big-char widest v) ?\()
(progn
(setq line (if (string-match "-" p)
(intern p)
(intern (concat "calcFunc-" p)))
h (1+ widest)
p nil)
(math-read-big-emptyp widest math-rb-v1 h v nil t)
(math-read-big-emptyp widest (1+ v) h math-rb-v2 nil t)
(while (progn
(setq widest (math-read-big-balance h v "(" t))
(math-read-big-emptyp (1- h) math-rb-v1 h v nil t)
(math-read-big-emptyp (1- h) (1+ v) h math-rb-v2 nil t)
(setq p (cons (math-read-big-rec
h math-rb-v1 (1- widest) math-rb-v2 v) p)
h widest)
(= (math-read-big-char (1- h) v) ?\,)))
(or (= (math-read-big-char (1- h) v) ?\))
(math-read-big-error (1- h) v "Expected `)'"))
(setq p (cons line (nreverse p))))
(setq p (list 'var
(intern (math-remove-dashes p))
(if (string-match "-" p)
(intern p)
(intern (concat "var-" p)))))))
;; Number.
(t
(setq line (nth v math-read-big-lines))
(or (= (string-match "_?\\([0-9]+.?0*@ *\\)?\\([0-9]+.?0*' *\\)?\\([0-9]+\\(#\\|\\^\\^\\)[0-9a-zA-Z:]+\\|[0-9]+:[0-9:]+\\|[0-9.]+\\([eE][-+_]?[0-9]+\\)?\"?\\)?" line math-rb-h1) math-rb-h1)
(math-read-big-error h v "Expected a number"))
(setq h (match-end 0)
p (math-read-number (math-match-substring line 0)))
(math-read-big-emptyp math-rb-h1 math-rb-v1 h v nil t)
(math-read-big-emptyp math-rb-h1 (1+ v) h math-rb-v2 nil t)))
;; Now left term is bounded by math-rb-h1, math-rb-v1, h, math-rb-v2;
;; baseline = v.
(if baseline
(or (= v baseline)
(math-read-big-error math-rb-h1 v "Inconsistent baseline in formula"))
(setq baseline v))
;; Look for superscripts or subscripts.
(setq line (nth baseline math-read-big-lines)
len (min math-rb-h2 (length line))
widest h)
(while (and (< widest len)
(= (aref line widest) ?\ ))
(setq widest (1+ widest)))
(and (>= widest len) (setq widest math-rb-h2))
(if (math-read-big-emptyp h v widest math-rb-v2)
(if (math-read-big-emptyp h math-rb-v1 widest v)
(setq h widest)
(setq p (list '^ p (math-read-big-rec h math-rb-v1 widest v))
h widest))
(if (math-read-big-emptyp h math-rb-v1 widest v)
(setq p (list 'calcFunc-subscr p
(math-read-big-rec h v widest math-rb-v2))
h widest)))
;; Look for an operator name and grab additional terms.
(while (and (< h len)
(if (setq widest (and (math-read-big-emptyp
h math-rb-v1 (1+ h) v)
(math-read-big-emptyp
h (1+ v) (1+ h) math-rb-v2)
(string-match "<=\\|>=\\|\\+/-\\|!=\\|&&\\|||\\|:=\\|=>\\|." line h)
(assoc (math-match-substring line 0)
(math-standard-ops))))
(and (>= (nth 2 widest) prec)
(setq h (match-end 0)))
(and (not (eq (string-match ",\\|;\\|\\.\\.\\|)\\|\\]\\|:" line h)
h))
(setq widest '("2x" * 196 195)))))
(cond ((eq (nth 3 widest) -1)
(setq p (list (nth 1 widest) p)))
((equal (car widest) "?")
(let ((y (math-read-big-rec h math-rb-v1 math-rb-h2
math-rb-v2 baseline nil t)))
(or (= (math-read-big-char math-read-big-h2 baseline) ?\:)
(math-read-big-error math-read-big-h2 baseline
"Expected `:'"))
(setq p (list (nth 1 widest) p y
(math-read-big-rec
(1+ math-read-big-h2) math-rb-v1 math-rb-h2 math-rb-v2
baseline (nth 3 widest) t))
h math-read-big-h2)))
(t
(setq p (list (nth 1 widest) p
(math-read-big-rec h math-rb-v1 math-rb-h2 math-rb-v2
baseline (nth 3 widest) t))
h math-read-big-h2))))
;; Return all relevant information to caller.
(setq math-read-big-baseline baseline
math-read-big-h2 h)
(or short (= math-read-big-h2 math-rb-h2)
(math-read-big-error h baseline))
p)))
(defun math-read-big-char (h v)
(or (and (>= h math-rb-h1)
(< h math-rb-h2)
(>= v math-rb-v1)
(< v math-rb-v2)
(let ((line (nth v math-read-big-lines)))
(and line
(< h (length line))
(aref line h))))
?\ ))
(defun math-read-big-emptyp (eh1 ev1 eh2 ev2 &optional what error)
(and (< ev1 math-rb-v1) (setq ev1 math-rb-v1))
(and (< eh1 math-rb-h1) (setq eh1 math-rb-h1))
(and (> ev2 math-rb-v2) (setq ev2 math-rb-v2))
(and (> eh2 math-rb-h2) (setq eh2 math-rb-h2))
(or what (setq what ?\ ))
(let ((p (nthcdr ev1 math-read-big-lines))
h)
(while (and (< ev1 ev2)
(progn
(setq h (min eh2 (length (car p))))
(while (and (>= (setq h (1- h)) eh1)
(= (aref (car p) h) what)))
(and error (>= h eh1)
(math-read-big-error h ev1 (if (stringp error)
error
"Whitespace expected")))
(< h eh1)))
(setq ev1 (1+ ev1)
p (cdr p)))
(>= ev1 ev2)))
;; math-read-big-err-msg is local to math-read-big-expr in calc-ext.el,
;; but is used by math-read-big-error which is called (indirectly) by
;; math-read-big-expr.
(defvar math-read-big-err-msg)
(defun math-read-big-error (h v &optional msg)
(let ((pos 0)
(p math-read-big-lines))
(while (> v 0)
(setq pos (+ pos 1 (length (car p)))
p (cdr p)
v (1- v)))
(setq h (+ pos (min h (length (car p))))
math-read-big-err-msg (list 'error h (or msg "Syntax error")))
(throw 'syntax nil)))
(defun math-read-big-balance (h v what &optional commas)
(let* ((line (nth v math-read-big-lines))
(len (min math-rb-h2 (length line)))
(count 1))
(while (> count 0)
(if (>= h len)
(if what
(math-read-big-error nil v (format-message
"Unmatched `%s'" what))
(setq count 0))
(if (memq (aref line h) '(?\( ?\[))
(setq count (1+ count))
(if (if (and commas (= count 1))
(or (memq (aref line h) '(?\) ?\] ?\, ?\;))
(and (eq (aref line h) ?\.)
(< (1+ h) len)
(eq (aref line (1+ h)) ?\.)))
(memq (aref line h) '(?\) ?\])))
(setq count (1- count))))
(setq h (1+ h))))
h))
(provide 'calc-lang)
;;; calc-lang.el ends here
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