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;; JACAL: Symbolic Mathematics System. -*-scheme-*-
;; Copyright (C) 1989, 1990, 1991, 1992, 1993, 1995, 1997, 2007, 2009, 2010, 2020, 2021 Aubrey Jaffer.
;;
;; 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, write to the Free Software
;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
(define tran:translations
'((last-expression-lost . "; Last expression lost.")
(bad-arglist . "bad arglist ")
(column-of-non-matrix?:-- . "Column of non-matrix?: ")
(coordinate-out-of-range:-- . "Coordinate out of range: ")
(funny-length-vectors . "funny length vectors ")
(unequal-length-vectors . "unequal length vectors ")
(did-not-verify: . "Did not verify:")
(error . "ERROR")
(expt-of-equation?:-- . "Expt of equation?: ")
(inexact-number-to-eval:- . "Inexact number to eval: ")
(non-rational-radicand:-- . "Non-rational radicand: ")
(not-a-number . "Not a Number")
(not-a-matrix:-- . "Not a matrix: ")
(not-a-square-matrix:-- . "Not a square matrix: ")
(row-of-non-matrix?:-- . "Row of non-matrix?: ")
(application . "application ")
(argument . " argument ")
(arguments . " arguments ")
(bad-info-entry . "bad info entry")
(bunch . "bunch")
(can-not-be-read . "can not be read")
(can-not-be-set . "can not be set")
(cannot-be-coerced-to-expl:-- . "cannot be coerced to expl:")
(cannot-be-coerced-to-expr:-- . "cannot be coerced to expr: ")
(cannot-be-coerced-to-implicit:-- . "cannot be coerced to implicit: ")
(cannot-be-coerced-to-poly-eqn:-- . "cannot be coerced to poly eqn: ")
(cannot-extract-denominator- . "cannot extract denominator ")
(cannot-extract-numerator- . "cannot extract numerator ")
(cannot-read-null-grammar . "cannot read null grammar")
(cannot-suchthat-a-vector . "cannot suchthat a vector")
(cc-of . "cc of ")
(column-vector . "column vector")
(delimiter-expected--ignoring-rest . "delimiter expected-ignoring rest")
(determinant-of-non-square-matrix . "determinant of non-square matrix")
(differential- . "differential ")
(does-not-appear-in- . " does not appear in ")
(does-not-divide- . " does not divide ")
(does-not-udivide- . " does not udivide ")
(dotproduct-of-unequal-size-matrices:-- . "dotproduct of unequal size matrices: ")
(elim-bunch?- . "elim bunch?")
(eliminating-from-more-than-one-expression?- . "eliminating from more than one expression?")
(eliminating: . "eliminating:")
(elimination-type-not-handled . "elimination type not handled")
(equation . "equation")
(expected-boolean . "expected boolean")
(expected-boolean-or-number . "expected boolean or number")
(expected-simple-symbol . "expected simple symbol")
(expression-missing . "expression missing")
(extra-delimiter . "extra delimiter")
(extra-separator . "extra separator")
(false . "false")
(file-not-found . "file not found")
(flag . "flag")
(for-help. . " for help.")
(free-var-to-var:elim . "free var to var:elim")
(from: . " from:")
(function-of- . " function of ")
(grammar . "grammar")
(implicit-expression . "implicit expression")
(is-not-defined . "is not defined")
(matrix . "matrix")
(matrix-product-of-unequal-size-matrices:-- . "matrix product of unequal size matrices: ")
(mismatched-delimiter . "mismatched delimiter")
(more . "--more--")
(nested-labels? . "nested labels? ")
(no-example-for . "no example for ")
(no-value-to-set . "no value to set")
(no-variables? . "no variables?")
(non-integer-power?-- . "non-integer power? ")
(normalize-symbol?- . "normalize symbol? ")
(normalizing: . "normalizing:")
(not-a-function? . "not a function?")
(not-a-scalar-expression-or-equation:-- . "not a scalar expression or equation")
(not-a-polynomial-equation . "not a polynomial equation")
(not-a-polynomial? . "not a polynomial?")
(not-a-simple-variable:- . "not a simple variable: ")
(not-an-integer- . "not an integer ")
(not-an-operator . "not an operator")
(not-canonical . "not canonical ")
(not-enough-equations . "not enough equations")
(not-known . "not known")
(not-s-expression . " not s-expression")
(number . "number")
(of- . " of ")
(off . "off")
(on . "on")
(or- . " or ")
(partial-with-respect-to? . "partial with respect to?")
(polynomial . "polynomial")
(q-to-quit-space-for-more:- . " q to quit, space for more: ")
(radical . "radical")
(rational-expression . "rational expression")
(redefined-from- . " redefined from ")
(redefined-to- . " redefined to ")
(row-vector . "row vector")
(to- . " to ")
(to-return-to- . " to return to ")
(trouble-with . "trouble with ")
(transcendental-function-of-1-argument . "transcendental function of 1 argument")
(true . "true")
(type . "type ")
(type- . ", type ")
(unknown . "unknown")
(value-expected-equation-found:-- . "value expected, equation found: ")
(variable . "variable ")
(wna . ": Wrong number of args ")
(wta . ": Wrong type ")
(yielding: . "yielding:")))
;;;; Here are the templates for 2 dimensional output
(define tps:2d
'(
(template:default 140 #d0140 "(" #d1010 #(rest ", " #d2010) ")")
(template:bunch 140 "[" #d0010 #(rest ", " break #d1010) "]")
(template:matrix 140 (#\[) (#\ ) #d0010 #(rest " " #d1010) (#\ ) (#\]))
(template:parenthesis 200 "(" #d1010 ")")
(- 100 #d1100 " - " break #d2101 #(rest " - " break #d3101))
(negate 100 "- " #d1100)
(+ 100 #d1100 #(rest " + " break #d2101))
(* 120 #d1120 #(rest " " #d2121))
(/ 120 #d1120 "/" #d2121)
(over 120 ((-1 #d1040)
(0 #\-)
(1 #d2040)))
(^ 140 #d1141 ((-1 #d2100)))
(= 80 #d1080 " = " break #d2080 #(rest " = " break #d3080))
(differential 170 #d1170 "'")
(partial 130 " " ((-1 "%")
(0 #\-)
(1 "%" #d2140)) " " #d1140)
(suchthat 40 "{" #d1190 " | " #d2040 "}")
(satisfying 40 "{" #d1190 " :: " #d2040 "}")
(define 200 #d1120 ": " ((0 #d2010)))
(rapply 200 #d1200 ((1 #d2030 #(rest "," #d3010))))
(abs 200 (#\|) #d1010 (#\|))
(box 200 ((-1 #\")
(0 (#\") #d1010 (#\"))
(1 #\")))
(factorial 160 #d1160 "!")
(integrate 120 ((-3 #(optional #d4090))
(-2 "/ ")
(-1 "! ")
(0 "! ")
(1 "! ")
(2 "/ ")
(3 #(optional #d3090)))
#d1090 "d" #d2120)
(limit 90 ((0 "limit ")
(1 #d2090 "->" #d3090))
#d1090)
(sum 90 ((-3 #(optional #d4090))
(-2 "====")
(-1 "\\ ")
(0 " > ")
(1 "/ ")
(2 "====")
(3 #(optional #d2090 #(optional" = " #d3090))))
#d1090)
(prod 90 ((-3 " " #(optional #d4090))
(-2 "/===/")
(-1 " ! ! ")
(0 " ! ! ")
(1 " ! ! ")
(2 #(optional #d2090 #(optional" = " #d3090))))
#d1090)
(at 90 #d1090
((-2 "!")
(-1 "!")
(0 "!")
(1 "!")
(2 "!"))
((2 #d2010 #(rest ", " #d3010))))
(help 100 "help;")
(qed 100 "qed;")
(% 200 "%")
(ncmult 110 #d1109 " . " #d2109)
(^^ 210 #d1211 "^^" #d2210)
))
(define tps:c
'(
(template:default 140 #d0140 "(" #d1010 #(rest ", " #d2010) ")")
(template:bunch 140 "{" #d0010 #(rest ", " #d1010) "}")
(template:parenthesis 200 "(" #d1010 ")")
(= 80 #d1080 " == " break #d2080 #(rest "==" break #d3080))
(- 100 #d1100 " - " break #d2101 #(rest " - " break #d3101))
(+ 100 #d1100 #(rest " + " break #d2101))
(* 120 #d1120 #(rest " * " #d2121))
(negate 90 "- " #d1090)
(/ 120 #d1120 "/" #d2121)
(over 120 #d1120 "/" #d2121)
(^ 140 "pow(" #d1141 ", " #d2100 ")")
(rapply 200 #d1200 "[" #d2030 #(rest "," #d3010) "]")
(box 200 ((-1 #\")
(0 (#\") #d1010 (#\"))
(1 #\")))
(define 200 #d1120 " = " #d2010)
(set 20 "set " #d1120 " " #d2010)
(show 20 "show " #d1120)
))
(define tps:standard
'(
(template:default 140 #d0140 "(" #d1010 #(rest ", " #d2010) ")")
(template:bunch 140 "[" #d0010 #(rest ", " break #d1010) "]")
(template:parenthesis 200 "(" #d1010 ")")
(= 80 #d1080 " = " break #d2080 #(rest " = " break #d3080))
(- 100 #d1100 " - " break #d2101 #(rest " - " break #d3101))
(+ 100 #d1100 #(rest " + " break #d2101))
(* 120 #d1120 #(rest " * " #d2121))
(negate 90 "- " #d1090)
(/ 120 #d1120 "/" #d2121)
(over 120 #d1120 "/" #d2121)
(^ 140 #d1141 "^" #d2140)
(differential 170 #d1170 "'")
(suchthat 40 "{" #d1190 " | " #d2040 "}")
(satisfying 40 "{" #d1190 " :: " #d2040 "}")
(rapply 200 #d1200 "[" #d2030 #(rest "," #d3010) "]")
(box 200 ((-1 #\")
(0 (#\") #d1010 (#\"))
(1 #\")))
(define 200 #d1120 ": " #d2010)
(set 20 "set " #d1120 " " #d2010)
(show 20 "show " #d1120)
(factorial 160 #d1160 "!")
(help 100 "help;")
(qed 100 "qed;")
(% 200 "%")
(ncmult 110 #d1109 " . " #d2109)
(^^ 210 #d1211 "^^" #d2210)
))
(define tps:std
'(
(template:default 140 #d0140 "(" #d1010 #(rest "," #d2010) ")")
(template:bunch 140 "[" #d0010 #(rest "," break #d1010) "]")
(template:parenthesis 200 "(" #d1010 ")")
(= 80 #d1080 "=" break #d2080 #(rest "=" break #d3080))
(- 100 #d1100 "-" break #d2101 #(rest "-" break #d3101))
(+ 100 #d1100 #(rest "+" break #d2101))
(* 120 #d1120 #(rest "*" #d2121))
(negate 90 "-" #d1090)
(/ 120 #d1120 "/" #d2121)
(over 120 #d1120 "/" #d2121)
(^ 140 #d1141 "^" #d2140)
(differential 170 #d1170 "'")
(suchthat 40 "{" #d1190 "|" #d2040 "}")
(satisfying 40 "{" #d1190 "::" #d2040 "}")
(rapply 200 #d1200 "[" #d2030 #(rest "," #d3010) "]")
(box 200 ((-1 #\")
(0 (#\") #d1010 (#\"))
(1 #\")))
(define 200 #d1120 ":" #d2010)
(set 20 "set " #d1120 " " #d2010)
(show 20 "show " #d1120)
(factorial 160 #d1160 "!")
(help 100 "help;")
(qed 100 "qed;")
(% 200 "%")
(ncmult 110 #d1109 " . " #d2109)
(^^ 210 #d1211 "^^" #d2210)
))
(define tps:tex
'(
(template:top 0 "$" #d1000 "$")
(template:default 140 #d0140 "\\left(" #d1010
#(rest ", " #d2010) "\\right)")
(template:bunch 140 "\\left[" #d0010 #(rest ", " break #d1010) "\\right]")
;;; (template:matrix 140 "\\left({\matrix{" #d0010 #(rest "&" #d1010)
;;; (#\\)(#\c)(#\r) "}}\\right)")
(template:parenthesis 200 "\\left(" #d1010 "\\right)")
(= 80 #d1080 "=" break #d2080 #(rest "=" break #d3080))
(- 100 #d1100 "-" break #d2101 #(rest "-" break #d3101))
(+ 100 #d1100 #(rest "+" break #d2101))
(* 120 #d1120 #(rest "\\," #d2121))
(negate 100 "-" #d1100)
(/ 120 #d1120 "/{" break #d2121 "}")
(over 120 "{{" #d1040 "}\\over{" break #d2041 "}}")
(^ 140 #d1141 "^{" #d2100 "}")
(differential 170 "{" #d1170 "}'")
(suchthat 40 "\\left\\{ " #d1190 " | " break #d2040 "\\right\\}")
(satisfying 40 "\\left\\{ " #d1190 " :: " break #d2040 "\\right\\}")
(rapply 200 #d1200 "\\left[" #d2030 #(rest "," break #d3010) "\\right]")
(abs 200 "\\left|" #d1010 "\\right|")
;;; (box 200 ((-1 #\")
;;; (0 (#\") #d1010 (#\"))
;;; (1 #\")))
(define 200 #d1120 ": " #d2010)
(set 20 "set " #d1120 " " #d2010)
(show 20 "show " #d1120)
(factorial 160 #d1160 "!")
(help 100 "help;")
(qed 100 "qed;")
(% 200 "%")
))
;;;;The parse tables.
;;; Definitions accumulate in top-level variable *SYN-DEFS*.
;;;Syntax definitions for STANDARD GRAMMAR
;;; Begin by Ignoring whitespace characters.
(set! *syn-defs* *syn-ignore-whitespace*)
(define (list2string dyn lst) (list->string lst))
;;; Character classes
(prec:define-grammar (tok:char-group 70 #\^ list2string))
(prec:define-grammar (tok:char-group 49 #\* list2string))
(prec:define-grammar (tok:char-group 50 #\/ list2string))
(prec:define-grammar (tok:char-group 51 '(#\+ #\-) list2string))
(prec:define-grammar (tok:char-group 20 '(#\|) list2string))
(prec:define-grammar (tok:char-group 30 '(#\< #\> #\= #\: #\~) list2string))
(prec:define-grammar (tok:char-group
40
(string-append "." tok:decimal-digits)
(lambda (dyn l)
(if (equal? '(#\.) l)
#\.
(string->number (list->string l))))))
(prec:define-grammar (tok:char-group
41
(string-append tok:upper-case tok:lower-case "@%?_")
list2string))
(prec:define-grammar (tok:char-group
(lambda (chr) (or (eqv? #\" chr) (eof-object? chr)))
#\"
(lambda (dyn l)
(tok:read-char dyn)
(list->string (cdr l)))))
;;; Delimiters and Separators
;;; Delimiters used to be defined here, but now are defined
;;; dynamically by parse functions.
(prec:define-grammar (prec:delim #\])
;;(prec:delim #\;)
;;(prec:delim #\,)
;;(prec:postfix #\$ (lambda (x) (write x)) 0)
)
;;;prefix operators
(prec:define-grammar (prec:prefix '+ #f 100))
(prec:define-grammar (prec:prefix '- 'negate 120))
(prec:define-grammar (prec:prefix "+/-" 'u+/- 100))
(prec:define-grammar (prec:prefix "-/+" 'u-/+ 100))
(prec:define-grammar (prec:prefix '(not ~) 'impl:not 70))
(prec:define-grammar (prec:prefix ":" 'settemplate! 20))
;;;nary operators
(prec:define-grammar (prec:nary '* '* 120))
(prec:define-grammar (prec:nary '+ '+ 100))
(prec:define-grammar (prec:nary '- '- 100))
(prec:define-grammar (prec:nary "+/-" 'b+/- 100))
(prec:define-grammar (prec:nary "-/+" 'b-/+ 100))
(prec:define-grammar (prec:nary '/ '/ 120))
(prec:define-grammar (prec:nary '(and #\&) '& 60))
(prec:define-grammar (prec:nary 'or 'or 50))
(prec:define-grammar (prec:nary "||" 'parallel 110))
;;;infix operators
;(prec:infix 'x 'crossproduct 111 110)
(prec:define-grammar (prec:infix #\. 'ncmult 110 109))
(prec:define-grammar (prec:infix '(^ **) '^ 140 139))
(prec:define-grammar (prec:infix '^^ '^^ 210 210))
(prec:define-grammar (prec:infix '(":=" ":") 'define 180 20))
(prec:define-grammar (prec:infix '= '= 80 80))
;(prec:define-grammar (prec:infix '(~= <>) 'make-not-equal 80 80))
(prec:define-grammar (prec:infix 'mod 'mod 70 70))
(prec:define-grammar (prec:infix ':: 'satisfying 190 40))
(prec:define-grammar (prec:infix "|" 'suchthat 190 40))
;;; I don't remember what I had in mind here.
;(prec:define-grammar (prec:infix "" '* 120 120)) ;null operator
;;;postfix operators
(prec:define-grammar (prec:postfix #\! 'factorial 160))
(prec:define-grammar (prec:postfix #\' 'differential 170))
;;;matchfix operators
(prec:define-grammar (prec:matchfix #\( identity #f #\)))
(prec:define-grammar (prec:matchfix #\[ vector #\, #\]))
(prec:define-grammar (prec:matchfix #\{ 'or #\, #\}
(prec:infix "|" 'suchthat 190 40)))
(prec:define-grammar (prec:matchfix #\\ 'lambda #\, #\;))
(prec:define-grammar (prec:matchfix "|" 'abs #f "|"))
;;;special operators
(prec:define-grammar (prec:inmatchfix #\( list #\, #\) 200))
(prec:define-grammar (prec:inmatchfix #\[ 'rapply #\, #\] 200))
;;;rest operator reads expressions up to next delimiter.
(prec:define-grammar (prec:prestfix 'set 'set 10))
(prec:define-grammar (prec:prestfix 'show 'show 10))
;;;miscellany
;(prec:define-grammar (prec:prefix 'load 'load 50))
(prec:define-grammar (prec:nofix '% '%))
(prec:define-grammar (prec:nofix 'help 'help))
(prec:define-grammar (prec:nofix 'qed 'qed))
(prec:define-grammar (prec:commentfix
"/*"
(lambda (str)
(and str
(not (eq? (get-grammar 'null) *echo-grammar*))
(display str)))
"*/"))
(define (grm-reader grm column)
(define cip (current-input-port))
(prec:parse (grammar-read-tab grm)
#\;
(+ column (flush-input-whitespace cip))
cip))
(defgrammar 'std
(make-grammar
'std ;name
grm-reader ;reader
*syn-defs* ;read-tab
print-using-grammar ;writer
tps:std)) ;write-tab
(defgrammar 'standard
(make-grammar
'standard ;name
grm-reader ;reader
*syn-defs* ;read-tab
print-using-grammar ;writer
tps:standard)) ;write-tab
(defgrammar 'disp2d
(make-grammar
'disp2d ;name
grm-reader ;reader
*syn-defs* ;read-tab
print-using-grammar ;writer
tps:2d)) ;write-tab
(set! *input-grammar* (get-grammar 'standard))
(set! *output-grammar* (get-grammar 'disp2d))
;;;; Syntax definitions for TEX GRAMMAR
;;; built-in functions:
;; \arccos \arcsin \arctan \cos \cosh \cot \coth \csc \exp \gcd \lg \ln \log \sec \sin \sinh \tan \tanh
;;; Begin by Ignoring whitespace characters.
(set! *syn-defs* *syn-ignore-whitespace*)
(prec:define-grammar (tok:char-group
40
tok:decimal-digits
(lambda (dyn l) (string->number (list->string l)))))
(prec:define-grammar (tok:char-group
41
(string-append tok:upper-case tok:lower-case)
list2string))
(let ((seen1 #f))
(prec:define-grammar (tok:char-group
(lambda (chr)
(cond (seen1 (not (char-alphabetic? chr)))
((not (char-alphabetic? chr))
(set! seen1 chr) #t)
(else (set! seen1 #t) #f)))
'(#\\)
(lambda (dyn l)
(cond ((char? seen1)
(tok:read-char dyn)
(set! l (list #\\ seen1))))
(set! seen1 #f)
(list->string l)))))
(prec:define-grammar (prec:commentfix #\$ #f #\$))
(prec:define-grammar (prec:delim #\,))
(prec:define-grammar (prec:delim #\;))
(prec:define-grammar (prec:prefix #\+ #f 100))
(prec:define-grammar (prec:prefix #\- 'negate 100))
(prec:define-grammar (prec:postfix #\! 'factorial 160))
(prec:define-grammar (prec:postfix #\' 'differential 170))
(prec:define-grammar (prec:infix #\: 'define 180 20))
(prec:define-grammar (prec:infix #\= '= 80 80))
(prec:define-grammar (prec:nary '(#\* "\\,") '* 120))
(prec:define-grammar (prec:nary #\+ '+ 100))
(prec:define-grammar (prec:nary #\- '- 100))
(prec:define-grammar (prec:nary #\/ '/ 120))
(prec:define-grammar (prec:nary "\\over" '/ 120))
(prec:define-grammar (prec:nary #\& vector 50))
(prec:define-grammar (prec:nary "\\cr" vector 49))
(prec:define-grammar (prec:commentfix
'("\\left" "\\right"
"\\big" "\\bigm" "\\bigl" "\\bigr"
"\\bigg" "\\biggm" "\\biggl" "\\biggr"
"\\Big" "\\Bigm" "\\Bigl" "\\Bigr"
"\\Bigg" "\\Biggm" "\\Biggl" "\\Biggr")
#f
#f))
(prec:define-grammar (prec:commentfix #\% #f #\newline))
(prec:define-grammar (prec:inmatchfix #\( #f #\, #\) 200))
(prec:define-grammar (prec:matchfix #\( #f #f #\)))
(prec:define-grammar (prec:matchfix #\{ #f #f #\}))
(prec:define-grammar (prec:matchfix "\\lbrace" #f #f "\\rbrace"))
(prec:define-grammar (prec:inmatchfix #\[ 'rapply #\, #\] 200))
(prec:define-grammar (prec:inmatchfix "\\lbrack" 'rapply #\, "\\rbrack" 200))
(prec:define-grammar (prec:matchfix #\[ vector #\, #\]))
(prec:define-grammar (prec:infix '(#\| "\\vert") 'suchthat 190 40))
(prec:define-grammar (prec:infix #\^ '^ 140 139))
(prec:define-grammar (prec:prefix "\\sqrt" (lambda (arg) `(^ ,arg (/ 1 2))) 100))
(prec:define-grammar (prec:prefix "\\frac" '/ 100)) ;prefix2
;(prec:define-grammar (prec:delim "\\of"))
;(prec:define-grammar (prec:prefix "\\root" (lambda (arg) `(^ ,arg (/ 1 2))) 100))
(prec:define-grammar (prec:prefix 'load 'load 50))
(prec:define-grammar (prec:nofix '% '%))
(prec:define-grammar (prec:nofix 'help 'help))
(prec:define-grammar (prec:nofix '(qed bye exit) 'qed))
(prec:define-grammar (prec:prestfix 'set 'set 10))
(prec:define-grammar (prec:prestfix 'show 'show 10))
(defgrammar 'tex
(make-grammar
'tex ;name
grm-reader ;reader
*syn-defs* ;read-tab
print-using-grammar ;writer
tps:tex)) ;write-tab
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