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[Emacs-diffs] Changes to emacs/lisp/calc/calc-alg.el [emacs-unicode-2]
|
From: |
Miles Bader |
|
Subject: |
[Emacs-diffs] Changes to emacs/lisp/calc/calc-alg.el [emacs-unicode-2] |
|
Date: |
Fri, 19 Nov 2004 02:02:27 -0500 |
Index: emacs/lisp/calc/calc-alg.el
diff -c emacs/lisp/calc/calc-alg.el:1.7.4.1 emacs/lisp/calc/calc-alg.el:1.7.4.2
*** emacs/lisp/calc/calc-alg.el:1.7.4.1 Fri Apr 16 12:50:11 2004
--- emacs/lisp/calc/calc-alg.el Fri Nov 19 06:55:08 2004
***************
*** 3,10 ****
;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
;; Author: David Gillespie <address@hidden>
! ;; Maintainers: D. Goel <address@hidden>
! ;; Colin Walters <address@hidden>
;; This file is part of GNU Emacs.
--- 3,9 ----
;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
;; Author: David Gillespie <address@hidden>
! ;; Maintainer: Jay Belanger <address@hidden>
;; This file is part of GNU Emacs.
***************
*** 121,139 ****
(calc-slow-wrapper
(calc-binary-op "pgcd" 'calcFunc-pgcd arg)))
(defun calc-poly-div (arg)
(interactive "P")
(calc-slow-wrapper
! (setq calc-poly-div-remainder nil)
! (calc-binary-op "pdiv" 'calcFunc-pdiv arg)
! (if (and calc-poly-div-remainder (null arg))
! (progn
! (calc-clear-command-flag 'clear-message)
! (calc-record calc-poly-div-remainder "prem")
! (if (not (Math-zerop calc-poly-div-remainder))
! (message "(Remainder was %s)"
! (math-format-flat-expr calc-poly-div-remainder 0))
! (message "(No remainder)"))))))
(defun calc-poly-rem (arg)
(interactive "P")
--- 120,139 ----
(calc-slow-wrapper
(calc-binary-op "pgcd" 'calcFunc-pgcd arg)))
+
(defun calc-poly-div (arg)
(interactive "P")
(calc-slow-wrapper
! (let ((calc-poly-div-remainder nil))
! (calc-binary-op "pdiv" 'calcFunc-pdiv arg)
! (if (and calc-poly-div-remainder (null arg))
! (progn
! (calc-clear-command-flag 'clear-message)
! (calc-record calc-poly-div-remainder "prem")
! (if (not (Math-zerop calc-poly-div-remainder))
! (message "(Remainder was %s)"
! (math-format-flat-expr calc-poly-div-remainder 0))
! (message "(No remainder)")))))))
(defun calc-poly-rem (arg)
(interactive "P")
***************
*** 184,189 ****
--- 184,194 ----
(memq (car name) '(vec calcFunc-assign calcFunc-condition))
name))
+ ;; math-eval-rules-cache and math-eval-rules-cache-other are
+ ;; declared in calc.el, but are used here by math-recompile-eval-rules.
+ (defvar math-eval-rules-cache)
+ (defvar math-eval-rules-cache-other)
+
(defun math-recompile-eval-rules ()
(setq math-eval-rules-cache (and (calc-has-rules 'var-EvalRules)
(math-compile-rewrites
***************
*** 266,274 ****
(defalias 'calcFunc-esimplify 'math-simplify-extended)
(defun math-simplify (top-expr)
(let ((math-simplifying t)
! (top-only (consp calc-simplify-mode))
(simp-rules (append (and (calc-has-rules 'var-AlgSimpRules)
'((var AlgSimpRules var-AlgSimpRules)))
(and math-living-dangerously
--- 271,283 ----
(defalias 'calcFunc-esimplify 'math-simplify-extended)
+ ;; math-top-only is local to math-simplify, but is used by
+ ;; math-simplify-step, which is called by math-simplify.
+ (defvar math-top-only)
+
(defun math-simplify (top-expr)
(let ((math-simplifying t)
! (math-top-only (consp calc-simplify-mode))
(simp-rules (append (and (calc-has-rules 'var-AlgSimpRules)
'((var AlgSimpRules var-AlgSimpRules)))
(and math-living-dangerously
***************
*** 281,287 ****
(calc-has-rules 'var-IntegSimpRules)
'((var IntegSimpRules var-IntegSimpRules)))))
res)
! (if top-only
(let ((r simp-rules))
(setq res (math-simplify-step (math-normalize top-expr))
calc-simplify-mode '(nil)
--- 290,296 ----
(calc-has-rules 'var-IntegSimpRules)
'((var IntegSimpRules var-IntegSimpRules)))))
res)
! (if math-top-only
(let ((r simp-rules))
(setq res (math-simplify-step (math-normalize top-expr))
calc-simplify-mode '(nil)
***************
*** 308,314 ****
(defun math-simplify-step (a)
(if (Math-primp a)
a
! (let ((aa (if (or top-only
(memq (car a) '(calcFunc-quote calcFunc-condition
calcFunc-evalto)))
a
--- 317,323 ----
(defun math-simplify-step (a)
(if (Math-primp a)
a
! (let ((aa (if (or math-top-only
(memq (car a) '(calcFunc-quote calcFunc-condition
calcFunc-evalto)))
a
***************
*** 328,479 ****
(defun math-need-std-simps ()
nil)
(math-defsimplify (+ -)
(math-simplify-plus))
(defun math-simplify-plus ()
! (cond ((and (memq (car-safe (nth 1 expr)) '(+ -))
! (Math-numberp (nth 2 (nth 1 expr)))
! (not (Math-numberp (nth 2 expr))))
! (let ((x (nth 2 expr))
! (op (car expr)))
! (setcar (cdr (cdr expr)) (nth 2 (nth 1 expr)))
! (setcar expr (car (nth 1 expr)))
! (setcar (cdr (cdr (nth 1 expr))) x)
! (setcar (nth 1 expr) op)))
! ((and (eq (car expr) '+)
! (Math-numberp (nth 1 expr))
! (not (Math-numberp (nth 2 expr))))
! (let ((x (nth 2 expr)))
! (setcar (cdr (cdr expr)) (nth 1 expr))
! (setcar (cdr expr) x))))
! (let ((aa expr)
aaa temp)
(while (memq (car-safe (setq aaa (nth 1 aa))) '(+ -))
! (if (setq temp (math-combine-sum (nth 2 aaa) (nth 2 expr)
! (eq (car aaa) '-) (eq (car expr) '-) t))
(progn
! (setcar (cdr (cdr expr)) temp)
! (setcar expr '+)
(setcar (cdr (cdr aaa)) 0)))
(setq aa (nth 1 aa)))
! (if (setq temp (math-combine-sum aaa (nth 2 expr)
! nil (eq (car expr) '-) t))
(progn
! (setcar (cdr (cdr expr)) temp)
! (setcar expr '+)
(setcar (cdr aa) 0)))
! expr))
(math-defsimplify *
(math-simplify-times))
(defun math-simplify-times ()
! (if (eq (car-safe (nth 2 expr)) '*)
! (and (math-beforep (nth 1 (nth 2 expr)) (nth 1 expr))
! (or (math-known-scalarp (nth 1 expr) t)
! (math-known-scalarp (nth 1 (nth 2 expr)) t))
! (let ((x (nth 1 expr)))
! (setcar (cdr expr) (nth 1 (nth 2 expr)))
! (setcar (cdr (nth 2 expr)) x)))
! (and (math-beforep (nth 2 expr) (nth 1 expr))
! (or (math-known-scalarp (nth 1 expr) t)
! (math-known-scalarp (nth 2 expr) t))
! (let ((x (nth 2 expr)))
! (setcar (cdr (cdr expr)) (nth 1 expr))
! (setcar (cdr expr) x))))
! (let ((aa expr)
aaa temp
! (safe t) (scalar (math-known-scalarp (nth 1 expr))))
! (if (and (Math-ratp (nth 1 expr))
! (setq temp (math-common-constant-factor (nth 2 expr))))
(progn
! (setcar (cdr (cdr expr))
! (math-cancel-common-factor (nth 2 expr) temp))
! (setcar (cdr expr) (math-mul (nth 1 expr) temp))))
(while (and (eq (car-safe (setq aaa (nth 2 aa))) '*)
safe)
! (if (setq temp (math-combine-prod (nth 1 expr) (nth 1 aaa) nil nil t))
(progn
! (setcar (cdr expr) temp)
(setcar (cdr aaa) 1)))
(setq safe (or scalar (math-known-scalarp (nth 1 aaa) t))
aa (nth 2 aa)))
! (if (and (setq temp (math-combine-prod aaa (nth 1 expr) nil nil t))
safe)
(progn
! (setcar (cdr expr) temp)
(setcar (cdr (cdr aa)) 1)))
! (if (and (eq (car-safe (nth 1 expr)) 'frac)
! (memq (nth 1 (nth 1 expr)) '(1 -1)))
! (math-div (math-mul (nth 2 expr) (nth 1 (nth 1 expr)))
! (nth 2 (nth 1 expr)))
! expr)))
(math-defsimplify /
(math-simplify-divide))
(defun math-simplify-divide ()
! (let ((np (cdr expr))
(nover nil)
! (nn (and (or (eq (car expr) '/) (not (Math-realp (nth 2 expr))))
! (math-common-constant-factor (nth 2 expr))))
n op)
(if nn
(progn
! (setq n (and (or (eq (car expr) '/) (not (Math-realp (nth 1 expr))))
! (math-common-constant-factor (nth 1 expr))))
(if (and (eq (car-safe nn) 'frac) (eq (nth 1 nn) 1) (not n))
(progn
! (setcar (cdr expr) (math-mul (nth 2 nn) (nth 1 expr)))
! (setcar (cdr (cdr expr))
! (math-cancel-common-factor (nth 2 expr) nn))
(if (and (math-negp nn)
! (setq op (assq (car expr) calc-tweak-eqn-table)))
! (setcar expr (nth 1 op))))
(if (and n (not (eq (setq n (math-frac-gcd n nn)) 1)))
(progn
! (setcar (cdr expr)
! (math-cancel-common-factor (nth 1 expr) n))
! (setcar (cdr (cdr expr))
! (math-cancel-common-factor (nth 2 expr) n))
(if (and (math-negp n)
! (setq op (assq (car expr) calc-tweak-eqn-table)))
! (setcar expr (nth 1 op))))))))
(if (and (eq (car-safe (car np)) '/)
! (math-known-scalarp (nth 2 expr) t))
(progn
! (setq np (cdr (nth 1 expr)))
(while (eq (car-safe (setq n (car np))) '*)
(and (math-known-scalarp (nth 2 n) t)
! (math-simplify-divisor (cdr n) (cdr (cdr expr)) nil t))
(setq np (cdr (cdr n))))
! (math-simplify-divisor np (cdr (cdr expr)) nil t)
(setq nover t
! np (cdr (cdr (nth 1 expr))))))
(while (eq (car-safe (setq n (car np))) '*)
(and (math-known-scalarp (nth 2 n) t)
! (math-simplify-divisor (cdr n) (cdr (cdr expr)) nover t))
(setq np (cdr (cdr n))))
! (math-simplify-divisor np (cdr (cdr expr)) nover t)
! expr))
! (defun math-simplify-divisor (np dp nover dover)
(cond ((eq (car-safe (car dp)) '/)
! (math-simplify-divisor np (cdr (car dp)) nover dover)
(and (math-known-scalarp (nth 1 (car dp)) t)
(math-simplify-divisor np (cdr (cdr (car dp)))
! nover (not dover))))
! ((or (or (eq (car expr) '/)
(let ((signs (math-possible-signs (car np))))
(or (memq signs '(1 4))
! (and (memq (car expr) '(calcFunc-eq calcFunc-neq))
(eq signs 5))
math-living-dangerously)))
(math-numberp (car np)))
! (let ((n (car np))
! d dd temp op
! (safe t) (scalar (math-known-scalarp n)))
(while (and (eq (car-safe (setq d (car dp))) '*)
safe)
(math-simplify-one-divisor np (cdr d))
--- 337,509 ----
(defun math-need-std-simps ()
nil)
+ ;; The function created by math-defsimplify uses the variable
+ ;; math-simplify-expr, and so is used by functions in math-defsimplify
+ (defvar math-simplify-expr)
+
(math-defsimplify (+ -)
(math-simplify-plus))
(defun math-simplify-plus ()
! (cond ((and (memq (car-safe (nth 1 math-simplify-expr)) '(+ -))
! (Math-numberp (nth 2 (nth 1 math-simplify-expr)))
! (not (Math-numberp (nth 2 math-simplify-expr))))
! (let ((x (nth 2 math-simplify-expr))
! (op (car math-simplify-expr)))
! (setcar (cdr (cdr math-simplify-expr)) (nth 2 (nth 1
math-simplify-expr)))
! (setcar math-simplify-expr (car (nth 1 math-simplify-expr)))
! (setcar (cdr (cdr (nth 1 math-simplify-expr))) x)
! (setcar (nth 1 math-simplify-expr) op)))
! ((and (eq (car math-simplify-expr) '+)
! (Math-numberp (nth 1 math-simplify-expr))
! (not (Math-numberp (nth 2 math-simplify-expr))))
! (let ((x (nth 2 math-simplify-expr)))
! (setcar (cdr (cdr math-simplify-expr)) (nth 1 math-simplify-expr))
! (setcar (cdr math-simplify-expr) x))))
! (let ((aa math-simplify-expr)
aaa temp)
(while (memq (car-safe (setq aaa (nth 1 aa))) '(+ -))
! (if (setq temp (math-combine-sum (nth 2 aaa) (nth 2 math-simplify-expr)
! (eq (car aaa) '-)
! (eq (car math-simplify-expr) '-) t))
(progn
! (setcar (cdr (cdr math-simplify-expr)) temp)
! (setcar math-simplify-expr '+)
(setcar (cdr (cdr aaa)) 0)))
(setq aa (nth 1 aa)))
! (if (setq temp (math-combine-sum aaa (nth 2 math-simplify-expr)
! nil (eq (car math-simplify-expr) '-) t))
(progn
! (setcar (cdr (cdr math-simplify-expr)) temp)
! (setcar math-simplify-expr '+)
(setcar (cdr aa) 0)))
! math-simplify-expr))
(math-defsimplify *
(math-simplify-times))
(defun math-simplify-times ()
! (if (eq (car-safe (nth 2 math-simplify-expr)) '*)
! (and (math-beforep (nth 1 (nth 2 math-simplify-expr)) (nth 1
math-simplify-expr))
! (or (math-known-scalarp (nth 1 math-simplify-expr) t)
! (math-known-scalarp (nth 1 (nth 2 math-simplify-expr)) t))
! (let ((x (nth 1 math-simplify-expr)))
! (setcar (cdr math-simplify-expr) (nth 1 (nth 2
math-simplify-expr)))
! (setcar (cdr (nth 2 math-simplify-expr)) x)))
! (and (math-beforep (nth 2 math-simplify-expr) (nth 1 math-simplify-expr))
! (or (math-known-scalarp (nth 1 math-simplify-expr) t)
! (math-known-scalarp (nth 2 math-simplify-expr) t))
! (let ((x (nth 2 math-simplify-expr)))
! (setcar (cdr (cdr math-simplify-expr)) (nth 1 math-simplify-expr))
! (setcar (cdr math-simplify-expr) x))))
! (let ((aa math-simplify-expr)
aaa temp
! (safe t) (scalar (math-known-scalarp (nth 1 math-simplify-expr))))
! (if (and (Math-ratp (nth 1 math-simplify-expr))
! (setq temp (math-common-constant-factor (nth 2
math-simplify-expr))))
(progn
! (setcar (cdr (cdr math-simplify-expr))
! (math-cancel-common-factor (nth 2 math-simplify-expr) temp))
! (setcar (cdr math-simplify-expr) (math-mul (nth 1 math-simplify-expr)
temp))))
(while (and (eq (car-safe (setq aaa (nth 2 aa))) '*)
safe)
! (if (setq temp (math-combine-prod (nth 1 math-simplify-expr)
! (nth 1 aaa) nil nil t))
(progn
! (setcar (cdr math-simplify-expr) temp)
(setcar (cdr aaa) 1)))
(setq safe (or scalar (math-known-scalarp (nth 1 aaa) t))
aa (nth 2 aa)))
! (if (and (setq temp (math-combine-prod aaa (nth 1 math-simplify-expr) nil
nil t))
safe)
(progn
! (setcar (cdr math-simplify-expr) temp)
(setcar (cdr (cdr aa)) 1)))
! (if (and (eq (car-safe (nth 1 math-simplify-expr)) 'frac)
! (memq (nth 1 (nth 1 math-simplify-expr)) '(1 -1)))
! (math-div (math-mul (nth 2 math-simplify-expr)
! (nth 1 (nth 1 math-simplify-expr)))
! (nth 2 (nth 1 math-simplify-expr)))
! math-simplify-expr)))
(math-defsimplify /
(math-simplify-divide))
(defun math-simplify-divide ()
! (let ((np (cdr math-simplify-expr))
(nover nil)
! (nn (and (or (eq (car math-simplify-expr) '/)
! (not (Math-realp (nth 2 math-simplify-expr))))
! (math-common-constant-factor (nth 2 math-simplify-expr))))
n op)
(if nn
(progn
! (setq n (and (or (eq (car math-simplify-expr) '/)
! (not (Math-realp (nth 1 math-simplify-expr))))
! (math-common-constant-factor (nth 1
math-simplify-expr))))
(if (and (eq (car-safe nn) 'frac) (eq (nth 1 nn) 1) (not n))
(progn
! (setcar (cdr math-simplify-expr)
! (math-mul (nth 2 nn) (nth 1 math-simplify-expr)))
! (setcar (cdr (cdr math-simplify-expr))
! (math-cancel-common-factor (nth 2 math-simplify-expr)
nn))
(if (and (math-negp nn)
! (setq op (assq (car math-simplify-expr)
calc-tweak-eqn-table)))
! (setcar math-simplify-expr (nth 1 op))))
(if (and n (not (eq (setq n (math-frac-gcd n nn)) 1)))
(progn
! (setcar (cdr math-simplify-expr)
! (math-cancel-common-factor (nth 1 math-simplify-expr)
n))
! (setcar (cdr (cdr math-simplify-expr))
! (math-cancel-common-factor (nth 2 math-simplify-expr)
n))
(if (and (math-negp n)
! (setq op (assq (car math-simplify-expr)
! calc-tweak-eqn-table)))
! (setcar math-simplify-expr (nth 1 op))))))))
(if (and (eq (car-safe (car np)) '/)
! (math-known-scalarp (nth 2 math-simplify-expr) t))
(progn
! (setq np (cdr (nth 1 math-simplify-expr)))
(while (eq (car-safe (setq n (car np))) '*)
(and (math-known-scalarp (nth 2 n) t)
! (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr))
nil t))
(setq np (cdr (cdr n))))
! (math-simplify-divisor np (cdr (cdr math-simplify-expr)) nil t)
(setq nover t
! np (cdr (cdr (nth 1 math-simplify-expr))))))
(while (eq (car-safe (setq n (car np))) '*)
(and (math-known-scalarp (nth 2 n) t)
! (math-simplify-divisor (cdr n) (cdr (cdr math-simplify-expr)) nover
t))
(setq np (cdr (cdr n))))
! (math-simplify-divisor np (cdr (cdr math-simplify-expr)) nover t)
! math-simplify-expr))
! ;; The variables math-simplify-divisor-nover and math-simplify-divisor-dover
! ;; are local variables for math-simplify-divisor, but are used by
! ;; math-simplify-one-divisor.
! (defvar math-simplify-divisor-nover)
! (defvar math-simplify-divisor-dover)
!
! (defun math-simplify-divisor (np dp math-simplify-divisor-nover
! math-simplify-divisor-dover)
(cond ((eq (car-safe (car dp)) '/)
! (math-simplify-divisor np (cdr (car dp))
! math-simplify-divisor-nover
! math-simplify-divisor-dover)
(and (math-known-scalarp (nth 1 (car dp)) t)
(math-simplify-divisor np (cdr (cdr (car dp)))
! math-simplify-divisor-nover
! (not math-simplify-divisor-dover))))
! ((or (or (eq (car math-simplify-expr) '/)
(let ((signs (math-possible-signs (car np))))
(or (memq signs '(1 4))
! (and (memq (car math-simplify-expr) '(calcFunc-eq
calcFunc-neq))
(eq signs 5))
math-living-dangerously)))
(math-numberp (car np)))
! (let (d
! (safe t)
! (scalar (math-known-scalarp (car np))))
(while (and (eq (car-safe (setq d (car dp))) '*)
safe)
(math-simplify-one-divisor np (cdr d))
***************
*** 483,503 ****
(math-simplify-one-divisor np dp))))))
(defun math-simplify-one-divisor (np dp)
! (if (setq temp (math-combine-prod (car np) (car dp) nover dover t))
! (progn
! (and (not (memq (car expr) '(/ calcFunc-eq calcFunc-neq)))
! (math-known-negp (car dp))
! (setq op (assq (car expr) calc-tweak-eqn-table))
! (setcar expr (nth 1 op)))
! (setcar np (if nover (math-div 1 temp) temp))
! (setcar dp 1))
! (and dover (not nover) (eq (car expr) '/)
! (eq (car-safe (car dp)) 'calcFunc-sqrt)
! (Math-integerp (nth 1 (car dp)))
! (progn
! (setcar np (math-mul (car np)
! (list 'calcFunc-sqrt (nth 1 (car dp)))))
! (setcar dp (nth 1 (car dp)))))))
(defun math-common-constant-factor (expr)
(if (Math-realp expr)
--- 513,537 ----
(math-simplify-one-divisor np dp))))))
(defun math-simplify-one-divisor (np dp)
! (let ((temp (math-combine-prod (car np) (car dp)
math-simplify-divisor-nover
! math-simplify-divisor-dover t))
! op)
! (if temp
! (progn
! (and (not (memq (car math-simplify-expr) '(/ calcFunc-eq
calcFunc-neq)))
! (math-known-negp (car dp))
! (setq op (assq (car math-simplify-expr) calc-tweak-eqn-table))
! (setcar math-simplify-expr (nth 1 op)))
! (setcar np (if math-simplify-divisor-nover (math-div 1 temp) temp))
! (setcar dp 1))
! (and math-simplify-divisor-dover (not math-simplify-divisor-nover)
! (eq (car math-simplify-expr) '/)
! (eq (car-safe (car dp)) 'calcFunc-sqrt)
! (Math-integerp (nth 1 (car dp)))
! (progn
! (setcar np (math-mul (car np)
! (list 'calcFunc-sqrt (nth 1 (car dp)))))
! (setcar dp (nth 1 (car dp))))))))
(defun math-common-constant-factor (expr)
(if (Math-realp expr)
***************
*** 546,568 ****
(math-simplify-mod))
(defun math-simplify-mod ()
! (and (Math-realp (nth 2 expr))
! (Math-posp (nth 2 expr))
! (let ((lin (math-is-linear (nth 1 expr)))
t1 t2 t3)
(or (and lin
(or (math-negp (car lin))
! (not (Math-lessp (car lin) (nth 2 expr))))
(list '%
(list '+
(math-mul (nth 1 lin) (nth 2 lin))
! (math-mod (car lin) (nth 2 expr)))
! (nth 2 expr)))
(and lin
(not (math-equal-int (nth 1 lin) 1))
(math-num-integerp (nth 1 lin))
! (math-num-integerp (nth 2 expr))
! (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2 expr)))
(not (math-equal-int t1 1))
(list '*
t1
--- 580,602 ----
(math-simplify-mod))
(defun math-simplify-mod ()
! (and (Math-realp (nth 2 math-simplify-expr))
! (Math-posp (nth 2 math-simplify-expr))
! (let ((lin (math-is-linear (nth 1 math-simplify-expr)))
t1 t2 t3)
(or (and lin
(or (math-negp (car lin))
! (not (Math-lessp (car lin) (nth 2 math-simplify-expr))))
(list '%
(list '+
(math-mul (nth 1 lin) (nth 2 lin))
! (math-mod (car lin) (nth 2 math-simplify-expr)))
! (nth 2 math-simplify-expr)))
(and lin
(not (math-equal-int (nth 1 lin) 1))
(math-num-integerp (nth 1 lin))
! (math-num-integerp (nth 2 math-simplify-expr))
! (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2
math-simplify-expr)))
(not (math-equal-int t1 1))
(list '*
t1
***************
*** 572,618 ****
(nth 2 lin))
(let ((calc-prefer-frac t))
(math-div (car lin) t1)))
! (math-div (nth 2 expr) t1))))
! (and (math-equal-int (nth 2 expr) 1)
(math-known-integerp (if lin
(math-mul (nth 1 lin) (nth 2 lin))
! (nth 1 expr)))
(if lin (math-mod (car lin) 1) 0))))))
(math-defsimplify (calcFunc-eq calcFunc-neq calcFunc-lt
calcFunc-gt calcFunc-leq calcFunc-geq)
! (if (= (length expr) 3)
(math-simplify-ineq)))
(defun math-simplify-ineq ()
! (let ((np (cdr expr))
n)
(while (memq (car-safe (setq n (car np))) '(+ -))
! (math-simplify-add-term (cdr (cdr n)) (cdr (cdr expr))
(eq (car n) '-) nil)
(setq np (cdr n)))
! (math-simplify-add-term np (cdr (cdr expr)) nil (eq np (cdr expr)))
(math-simplify-divide)
! (let ((signs (math-possible-signs (cons '- (cdr expr)))))
! (or (cond ((eq (car expr) 'calcFunc-eq)
(or (and (eq signs 2) 1)
(and (memq signs '(1 4 5)) 0)))
! ((eq (car expr) 'calcFunc-neq)
(or (and (eq signs 2) 0)
(and (memq signs '(1 4 5)) 1)))
! ((eq (car expr) 'calcFunc-lt)
(or (and (eq signs 1) 1)
(and (memq signs '(2 4 6)) 0)))
! ((eq (car expr) 'calcFunc-gt)
(or (and (eq signs 4) 1)
(and (memq signs '(1 2 3)) 0)))
! ((eq (car expr) 'calcFunc-leq)
(or (and (eq signs 4) 0)
(and (memq signs '(1 2 3)) 1)))
! ((eq (car expr) 'calcFunc-geq)
(or (and (eq signs 1) 0)
(and (memq signs '(2 4 6)) 1))))
! expr))))
(defun math-simplify-add-term (np dp minus lplain)
(or (math-vectorp (car np))
--- 606,653 ----
(nth 2 lin))
(let ((calc-prefer-frac t))
(math-div (car lin) t1)))
! (math-div (nth 2 math-simplify-expr) t1))))
! (and (math-equal-int (nth 2 math-simplify-expr) 1)
(math-known-integerp (if lin
(math-mul (nth 1 lin) (nth 2 lin))
! (nth 1 math-simplify-expr)))
(if lin (math-mod (car lin) 1) 0))))))
(math-defsimplify (calcFunc-eq calcFunc-neq calcFunc-lt
calcFunc-gt calcFunc-leq calcFunc-geq)
! (if (= (length math-simplify-expr) 3)
(math-simplify-ineq)))
(defun math-simplify-ineq ()
! (let ((np (cdr math-simplify-expr))
n)
(while (memq (car-safe (setq n (car np))) '(+ -))
! (math-simplify-add-term (cdr (cdr n)) (cdr (cdr math-simplify-expr))
(eq (car n) '-) nil)
(setq np (cdr n)))
! (math-simplify-add-term np (cdr (cdr math-simplify-expr)) nil
! (eq np (cdr math-simplify-expr)))
(math-simplify-divide)
! (let ((signs (math-possible-signs (cons '- (cdr math-simplify-expr)))))
! (or (cond ((eq (car math-simplify-expr) 'calcFunc-eq)
(or (and (eq signs 2) 1)
(and (memq signs '(1 4 5)) 0)))
! ((eq (car math-simplify-expr) 'calcFunc-neq)
(or (and (eq signs 2) 0)
(and (memq signs '(1 4 5)) 1)))
! ((eq (car math-simplify-expr) 'calcFunc-lt)
(or (and (eq signs 1) 1)
(and (memq signs '(2 4 6)) 0)))
! ((eq (car math-simplify-expr) 'calcFunc-gt)
(or (and (eq signs 4) 1)
(and (memq signs '(1 2 3)) 0)))
! ((eq (car math-simplify-expr) 'calcFunc-leq)
(or (and (eq signs 4) 0)
(and (memq signs '(1 2 3)) 1)))
! ((eq (car math-simplify-expr) 'calcFunc-geq)
(or (and (eq signs 1) 0)
(and (memq signs '(2 4 6)) 1))))
! math-simplify-expr))))
(defun math-simplify-add-term (np dp minus lplain)
(or (math-vectorp (car np))
***************
*** 644,668 ****
(setcar dp (setq n (math-neg temp)))))))))
(math-defsimplify calcFunc-sin
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin)
! (nth 1 (nth 1 expr)))
! (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-sin (math-neg (nth 1 expr)))))
(and (eq calc-angle-mode 'rad)
! (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi))))
(and n
(math-known-sin (car n) (nth 1 n) 120 0))))
(and (eq calc-angle-mode 'deg)
! (let ((n (math-integer-plus (nth 1 expr))))
(and n
(math-known-sin (car n) (nth 1 n) '(frac 2 3) 0))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos)
! (list 'calcFunc-sqrt (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan)
! (math-div (nth 1 (nth 1 expr))
(list 'calcFunc-sqrt
! (math-add 1 (math-sqr (nth 1 (nth 1 expr)))))))
! (let ((m (math-should-expand-trig (nth 1 expr))))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(list '+
--- 679,705 ----
(setcar dp (setq n (math-neg temp)))))))))
(math-defsimplify calcFunc-sin
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin)
! (nth 1 (nth 1 math-simplify-expr)))
! (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-sin (math-neg (nth 1
math-simplify-expr)))))
(and (eq calc-angle-mode 'rad)
! (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi
var-pi))))
(and n
(math-known-sin (car n) (nth 1 n) 120 0))))
(and (eq calc-angle-mode 'deg)
! (let ((n (math-integer-plus (nth 1 math-simplify-expr))))
(and n
(math-known-sin (car n) (nth 1 n) '(frac 2 3) 0))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos)
! (list 'calcFunc-sqrt (math-sub 1 (math-sqr
! (nth 1 (nth 1
math-simplify-expr))))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan)
! (math-div (nth 1 (nth 1 math-simplify-expr))
(list 'calcFunc-sqrt
! (math-add 1 (math-sqr
! (nth 1 (nth 1
math-simplify-expr)))))))
! (let ((m (math-should-expand-trig (nth 1 math-simplify-expr))))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(list '+
***************
*** 672,696 ****
(list 'calcFunc-sin a))))))))
(math-defsimplify calcFunc-cos
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos)
! (nth 1 (nth 1 expr)))
! (and (math-looks-negp (nth 1 expr))
! (list 'calcFunc-cos (math-neg (nth 1 expr))))
(and (eq calc-angle-mode 'rad)
! (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi))))
(and n
(math-known-sin (car n) (nth 1 n) 120 300))))
(and (eq calc-angle-mode 'deg)
! (let ((n (math-integer-plus (nth 1 expr))))
(and n
(math-known-sin (car n) (nth 1 n) '(frac 2 3) 300))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin)
! (list 'calcFunc-sqrt (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan)
(math-div 1
(list 'calcFunc-sqrt
! (math-add 1 (math-sqr (nth 1 (nth 1 expr)))))))
! (let ((m (math-should-expand-trig (nth 1 expr))))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(list '-
--- 709,735 ----
(list 'calcFunc-sin a))))))))
(math-defsimplify calcFunc-cos
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos)
! (nth 1 (nth 1 math-simplify-expr)))
! (and (math-looks-negp (nth 1 math-simplify-expr))
! (list 'calcFunc-cos (math-neg (nth 1 math-simplify-expr))))
(and (eq calc-angle-mode 'rad)
! (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi
var-pi))))
(and n
(math-known-sin (car n) (nth 1 n) 120 300))))
(and (eq calc-angle-mode 'deg)
! (let ((n (math-integer-plus (nth 1 math-simplify-expr))))
(and n
(math-known-sin (car n) (nth 1 n) '(frac 2 3) 300))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin)
! (list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan)
(math-div 1
(list 'calcFunc-sqrt
! (math-add 1
! (math-sqr (nth 1 (nth 1
math-simplify-expr)))))))
! (let ((m (math-should-expand-trig (nth 1 math-simplify-expr))))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(list '-
***************
*** 752,784 ****
(t nil))))))
(math-defsimplify calcFunc-tan
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan)
! (nth 1 (nth 1 expr)))
! (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-tan (math-neg (nth 1 expr)))))
(and (eq calc-angle-mode 'rad)
! (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi))))
(and n
(math-known-tan (car n) (nth 1 n) 120))))
(and (eq calc-angle-mode 'deg)
! (let ((n (math-integer-plus (nth 1 expr))))
(and n
(math-known-tan (car n) (nth 1 n) '(frac 2 3)))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin)
! (math-div (nth 1 (nth 1 expr))
(list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1 expr)))))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos)
(math-div (list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1 expr)))))
! (nth 1 (nth 1 expr))))
! (let ((m (math-should-expand-trig (nth 1 expr))))
(and m
(if (equal (car m) '(frac 1 2))
(math-div (math-sub 1 (list 'calcFunc-cos (nth 1 m)))
(list 'calcFunc-sin (nth 1 m)))
! (math-div (list 'calcFunc-sin (nth 1 expr))
! (list 'calcFunc-cos (nth 1 expr))))))))
(defun math-known-tan (plus n mul)
(setq n (math-mul n mul))
--- 791,823 ----
(t nil))))))
(math-defsimplify calcFunc-tan
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan)
! (nth 1 (nth 1 math-simplify-expr)))
! (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-tan (math-neg (nth 1
math-simplify-expr)))))
(and (eq calc-angle-mode 'rad)
! (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi
var-pi))))
(and n
(math-known-tan (car n) (nth 1 n) 120))))
(and (eq calc-angle-mode 'deg)
! (let ((n (math-integer-plus (nth 1 math-simplify-expr))))
(and n
(math-known-tan (car n) (nth 1 n) '(frac 2 3)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin)
! (math-div (nth 1 (nth 1 math-simplify-expr))
(list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1
math-simplify-expr)))))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos)
(math-div (list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1
math-simplify-expr)))))
! (nth 1 (nth 1 math-simplify-expr))))
! (let ((m (math-should-expand-trig (nth 1 math-simplify-expr))))
(and m
(if (equal (car m) '(frac 1 2))
(math-div (math-sub 1 (list 'calcFunc-cos (nth 1 m)))
(list 'calcFunc-sin (nth 1 m)))
! (math-div (list 'calcFunc-sin (nth 1 math-simplify-expr))
! (list 'calcFunc-cos (nth 1 math-simplify-expr))))))))
(defun math-known-tan (plus n mul)
(setq n (math-mul n mul))
***************
*** 813,831 ****
(t nil))))))
(math-defsimplify calcFunc-sinh
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh)
! (nth 1 (nth 1 expr)))
! (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-sinh (math-neg (nth 1 expr)))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh)
math-living-dangerously
! (list 'calcFunc-sqrt (math-sub (math-sqr (nth 1 (nth 1 expr))) 1)))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh)
math-living-dangerously
! (math-div (nth 1 (nth 1 expr))
(list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1 expr)))))))
! (let ((m (math-should-expand-trig (nth 1 expr) t)))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(if (> n 1)
--- 852,871 ----
(t nil))))))
(math-defsimplify calcFunc-sinh
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh)
! (nth 1 (nth 1 math-simplify-expr)))
! (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-sinh (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh)
math-living-dangerously
! (list 'calcFunc-sqrt
! (math-sub (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh)
math-living-dangerously
! (math-div (nth 1 (nth 1 math-simplify-expr))
(list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1
math-simplify-expr)))))))
! (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t)))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(if (> n 1)
***************
*** 836,854 ****
(list 'calcFunc-sinh a)))))))))
(math-defsimplify calcFunc-cosh
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh)
! (nth 1 (nth 1 expr)))
! (and (math-looks-negp (nth 1 expr))
! (list 'calcFunc-cosh (math-neg (nth 1 expr))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh)
math-living-dangerously
! (list 'calcFunc-sqrt (math-add (math-sqr (nth 1 (nth 1 expr))) 1)))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh)
math-living-dangerously
(math-div 1
(list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1 expr)))))))
! (let ((m (math-should-expand-trig (nth 1 expr) t)))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(if (> n 1)
--- 876,895 ----
(list 'calcFunc-sinh a)))))))))
(math-defsimplify calcFunc-cosh
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh)
! (nth 1 (nth 1 math-simplify-expr)))
! (and (math-looks-negp (nth 1 math-simplify-expr))
! (list 'calcFunc-cosh (math-neg (nth 1 math-simplify-expr))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh)
math-living-dangerously
! (list 'calcFunc-sqrt
! (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh)
math-living-dangerously
(math-div 1
(list 'calcFunc-sqrt
! (math-sub 1 (math-sqr (nth 1 (nth 1
math-simplify-expr)))))))
! (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t)))
(and m (integerp (car m))
(let ((n (car m)) (a (nth 1 m)))
(if (> n 1)
***************
*** 859,991 ****
(list 'calcFunc-sinh a)))))))))
(math-defsimplify calcFunc-tanh
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh)
! (nth 1 (nth 1 expr)))
! (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-tanh (math-neg (nth 1 expr)))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh)
math-living-dangerously
! (math-div (nth 1 (nth 1 expr))
(list 'calcFunc-sqrt
! (math-add (math-sqr (nth 1 (nth 1 expr))) 1))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh)
math-living-dangerously
(math-div (list 'calcFunc-sqrt
! (math-sub (math-sqr (nth 1 (nth 1 expr))) 1))
! (nth 1 (nth 1 expr))))
! (let ((m (math-should-expand-trig (nth 1 expr) t)))
(and m
(if (equal (car m) '(frac 1 2))
(math-div (math-sub (list 'calcFunc-cosh (nth 1 m)) 1)
(list 'calcFunc-sinh (nth 1 m)))
! (math-div (list 'calcFunc-sinh (nth 1 expr))
! (list 'calcFunc-cosh (nth 1 expr))))))))
(math-defsimplify calcFunc-arcsin
! (or (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-arcsin (math-neg (nth 1 expr)))))
! (and (eq (nth 1 expr) 1)
(math-quarter-circle t))
! (and (equal (nth 1 expr) '(frac 1 2))
(math-div (math-half-circle t) 6))
(and math-living-dangerously
! (eq (car-safe (nth 1 expr)) 'calcFunc-sin)
! (nth 1 (nth 1 expr)))
(and math-living-dangerously
! (eq (car-safe (nth 1 expr)) 'calcFunc-cos)
(math-sub (math-quarter-circle t)
! (nth 1 (nth 1 expr))))))
(math-defsimplify calcFunc-arccos
! (or (and (eq (nth 1 expr) 0)
(math-quarter-circle t))
! (and (eq (nth 1 expr) -1)
(math-half-circle t))
! (and (equal (nth 1 expr) '(frac 1 2))
(math-div (math-half-circle t) 3))
! (and (equal (nth 1 expr) '(frac -1 2))
(math-div (math-mul (math-half-circle t) 2) 3))
(and math-living-dangerously
! (eq (car-safe (nth 1 expr)) 'calcFunc-cos)
! (nth 1 (nth 1 expr)))
(and math-living-dangerously
! (eq (car-safe (nth 1 expr)) 'calcFunc-sin)
(math-sub (math-quarter-circle t)
! (nth 1 (nth 1 expr))))))
(math-defsimplify calcFunc-arctan
! (or (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-arctan (math-neg (nth 1 expr)))))
! (and (eq (nth 1 expr) 1)
(math-div (math-half-circle t) 4))
(and math-living-dangerously
! (eq (car-safe (nth 1 expr)) 'calcFunc-tan)
! (nth 1 (nth 1 expr)))))
(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)))))
(math-defsimplify calcFunc-arccosh
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-cosh)
(or math-living-dangerously
! (math-known-realp (nth 1 (nth 1 expr))))
! (nth 1 (nth 1 expr))))
(math-defsimplify calcFunc-arctanh
! (or (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-arctanh (math-neg (nth 1 expr)))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-tanh)
(or math-living-dangerously
! (math-known-realp (nth 1 (nth 1 expr))))
! (nth 1 (nth 1 expr)))))
(math-defsimplify calcFunc-sqrt
(math-simplify-sqrt))
(defun math-simplify-sqrt ()
! (or (and (eq (car-safe (nth 1 expr)) 'frac)
! (math-div (list 'calcFunc-sqrt (math-mul (nth 1 (nth 1 expr))
! (nth 2 (nth 1 expr))))
! (nth 2 (nth 1 expr))))
! (let ((fac (if (math-objectp (nth 1 expr))
! (math-squared-factor (nth 1 expr))
! (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))))))
(and math-living-dangerously
! (or (and (eq (car-safe (nth 1 expr)) '-)
! (math-equal-int (nth 1 (nth 1 expr)) 1)
! (eq (car-safe (nth 2 (nth 1 expr))) '^)
! (math-equal-int (nth 2 (nth 2 (nth 1 expr))) 2)
! (or (and (eq (car-safe (nth 1 (nth 2 (nth 1 expr))))
'calcFunc-sin)
(list 'calcFunc-cos
! (nth 1 (nth 1 (nth 2 (nth 1 expr))))))
! (and (eq (car-safe (nth 1 (nth 2 (nth 1 expr))))
'calcFunc-cos)
(list 'calcFunc-sin
! (nth 1 (nth 1 (nth 2 (nth 1 expr))))))))
! (and (eq (car-safe (nth 1 expr)) '-)
! (math-equal-int (nth 2 (nth 1 expr)) 1)
! (eq (car-safe (nth 1 (nth 1 expr))) '^)
! (math-equal-int (nth 2 (nth 1 (nth 1 expr))) 2)
! (and (eq (car-safe (nth 1 (nth 1 (nth 1 expr))))
'calcFunc-cosh)
(list 'calcFunc-sinh
! (nth 1 (nth 1 (nth 1 (nth 1 expr)))))))
! (and (eq (car-safe (nth 1 expr)) '+)
! (let ((a (nth 1 (nth 1 expr)))
! (b (nth 2 (nth 1 expr))))
(and (or (and (math-equal-int a 1)
! (setq a b b (nth 1 (nth 1 expr))))
(math-equal-int b 1))
(eq (car-safe a) '^)
(math-equal-int (nth 2 a) 2)
--- 900,1035 ----
(list 'calcFunc-sinh a)))))))))
(math-defsimplify calcFunc-tanh
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh)
! (nth 1 (nth 1 math-simplify-expr)))
! (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-tanh (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh)
math-living-dangerously
! (math-div (nth 1 (nth 1 math-simplify-expr))
(list 'calcFunc-sqrt
! (math-add (math-sqr (nth 1 (nth 1
math-simplify-expr))) 1))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh)
math-living-dangerously
(math-div (list 'calcFunc-sqrt
! (math-sub (math-sqr (nth 1 (nth 1
math-simplify-expr))) 1))
! (nth 1 (nth 1 math-simplify-expr))))
! (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t)))
(and m
(if (equal (car m) '(frac 1 2))
(math-div (math-sub (list 'calcFunc-cosh (nth 1 m)) 1)
(list 'calcFunc-sinh (nth 1 m)))
! (math-div (list 'calcFunc-sinh (nth 1 math-simplify-expr))
! (list 'calcFunc-cosh (nth 1 math-simplify-expr))))))))
(math-defsimplify calcFunc-arcsin
! (or (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-arcsin (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (nth 1 math-simplify-expr) 1)
(math-quarter-circle t))
! (and (equal (nth 1 math-simplify-expr) '(frac 1 2))
(math-div (math-half-circle t) 6))
(and math-living-dangerously
! (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin)
! (nth 1 (nth 1 math-simplify-expr)))
(and math-living-dangerously
! (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos)
(math-sub (math-quarter-circle t)
! (nth 1 (nth 1 math-simplify-expr))))))
(math-defsimplify calcFunc-arccos
! (or (and (eq (nth 1 math-simplify-expr) 0)
(math-quarter-circle t))
! (and (eq (nth 1 math-simplify-expr) -1)
(math-half-circle t))
! (and (equal (nth 1 math-simplify-expr) '(frac 1 2))
(math-div (math-half-circle t) 3))
! (and (equal (nth 1 math-simplify-expr) '(frac -1 2))
(math-div (math-mul (math-half-circle t) 2) 3))
(and math-living-dangerously
! (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos)
! (nth 1 (nth 1 math-simplify-expr)))
(and math-living-dangerously
! (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin)
(math-sub (math-quarter-circle t)
! (nth 1 (nth 1 math-simplify-expr))))))
(math-defsimplify calcFunc-arctan
! (or (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-arctan (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (nth 1 math-simplify-expr) 1)
(math-div (math-half-circle t) 4))
(and math-living-dangerously
! (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-tan)
! (nth 1 (nth 1 math-simplify-expr)))))
(math-defsimplify calcFunc-arcsinh
! (or (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-arcsinh (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sinh)
(or math-living-dangerously
! (math-known-realp (nth 1 (nth 1 math-simplify-expr))))
! (nth 1 (nth 1 math-simplify-expr)))))
(math-defsimplify calcFunc-arccosh
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh)
(or math-living-dangerously
! (math-known-realp (nth 1 (nth 1 math-simplify-expr))))
! (nth 1 (nth 1 math-simplify-expr))))
(math-defsimplify calcFunc-arctanh
! (or (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-arctanh (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-tanh)
(or math-living-dangerously
! (math-known-realp (nth 1 (nth 1 math-simplify-expr))))
! (nth 1 (nth 1 math-simplify-expr)))))
(math-defsimplify calcFunc-sqrt
(math-simplify-sqrt))
(defun math-simplify-sqrt ()
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'frac)
! (math-div (list 'calcFunc-sqrt
! (math-mul (nth 1 (nth 1 math-simplify-expr))
! (nth 2 (nth 1 math-simplify-expr))))
! (nth 2 (nth 1 math-simplify-expr))))
! (let ((fac (if (math-objectp (nth 1 math-simplify-expr))
! (math-squared-factor (nth 1 math-simplify-expr))
! (math-common-constant-factor (nth 1 math-simplify-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 math-simplify-expr) fac))))))
(and math-living-dangerously
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) '-)
! (math-equal-int (nth 1 (nth 1 math-simplify-expr)) 1)
! (eq (car-safe (nth 2 (nth 1 math-simplify-expr))) '^)
! (math-equal-int (nth 2 (nth 2 (nth 1 math-simplify-expr)))
2)
! (or (and (eq (car-safe (nth 1 (nth 2 (nth 1
math-simplify-expr))))
'calcFunc-sin)
(list 'calcFunc-cos
! (nth 1 (nth 1 (nth 2 (nth 1
math-simplify-expr))))))
! (and (eq (car-safe (nth 1 (nth 2 (nth 1
math-simplify-expr))))
'calcFunc-cos)
(list 'calcFunc-sin
! (nth 1 (nth 1 (nth 2
! (nth 1
math-simplify-expr))))))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) '-)
! (math-equal-int (nth 2 (nth 1 math-simplify-expr)) 1)
! (eq (car-safe (nth 1 (nth 1 math-simplify-expr))) '^)
! (math-equal-int (nth 2 (nth 1 (nth 1 math-simplify-expr)))
2)
! (and (eq (car-safe (nth 1 (nth 1 (nth 1
math-simplify-expr))))
'calcFunc-cosh)
(list 'calcFunc-sinh
! (nth 1 (nth 1 (nth 1 (nth 1
math-simplify-expr)))))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) '+)
! (let ((a (nth 1 (nth 1 math-simplify-expr)))
! (b (nth 2 (nth 1 math-simplify-expr))))
(and (or (and (math-equal-int a 1)
! (setq a b b (nth 1 (nth 1
math-simplify-expr))))
(math-equal-int b 1))
(eq (car-safe a) '^)
(math-equal-int (nth 2 a) 2)
***************
*** 994,1013 ****
(and (eq (car-safe (nth 1 a)) 'calcFunc-tan)
(list '/ 1 (list 'calcFunc-cos
(nth 1 (nth 1 a)))))))))
! (and (eq (car-safe (nth 1 expr)) '^)
(list '^
! (nth 1 (nth 1 expr))
! (math-div (nth 2 (nth 1 expr)) 2)))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-sqrt)
! (list '^ (nth 1 (nth 1 expr)) (math-div 1 4)))
! (and (memq (car-safe (nth 1 expr)) '(* /))
! (list (car (nth 1 expr))
! (list 'calcFunc-sqrt (nth 1 (nth 1 expr)))
! (list 'calcFunc-sqrt (nth 2 (nth 1 expr)))))
! (and (memq (car-safe (nth 1 expr)) '(+ -))
! (not (math-any-floats (nth 1 expr)))
(let ((f (calcFunc-factors (calcFunc-expand
! (nth 1 expr)))))
(and (math-vectorp f)
(or (> (length f) 2)
(> (nth 2 (nth 1 f)) 1))
--- 1038,1057 ----
(and (eq (car-safe (nth 1 a)) 'calcFunc-tan)
(list '/ 1 (list 'calcFunc-cos
(nth 1 (nth 1 a)))))))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) '^)
(list '^
! (nth 1 (nth 1 math-simplify-expr))
! (math-div (nth 2 (nth 1 math-simplify-expr)) 2)))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sqrt)
! (list '^ (nth 1 (nth 1 math-simplify-expr)) (math-div 1 4)))
! (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
! (list (car (nth 1 math-simplify-expr))
! (list 'calcFunc-sqrt (nth 1 (nth 1
math-simplify-expr)))
! (list 'calcFunc-sqrt (nth 2 (nth 1
math-simplify-expr)))))
! (and (memq (car-safe (nth 1 math-simplify-expr)) '(+ -))
! (not (math-any-floats (nth 1 math-simplify-expr)))
(let ((f (calcFunc-factors (calcFunc-expand
! (nth 1 math-simplify-expr)))))
(and (math-vectorp f)
(or (> (length f) 2)
(> (nth 2 (nth 1 f)) 1))
***************
*** 1043,1049 ****
fac)))
(math-defsimplify calcFunc-exp
! (math-simplify-exp (nth 1 expr)))
(defun math-simplify-exp (x)
(or (and (eq (car-safe x) 'calcFunc-ln)
--- 1087,1093 ----
fac)))
(math-defsimplify calcFunc-exp
! (math-simplify-exp (nth 1 math-simplify-expr)))
(defun math-simplify-exp (x)
(or (and (eq (car-safe x) 'calcFunc-ln)
***************
*** 1074,1095 ****
(list '+ c (list '* s '(var i var-i))))))))
(math-defsimplify calcFunc-ln
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-exp)
(or math-living-dangerously
! (math-known-realp (nth 1 (nth 1 expr))))
! (nth 1 (nth 1 expr)))
! (and (eq (car-safe (nth 1 expr)) '^)
! (equal (nth 1 (nth 1 expr)) '(var e var-e))
(or math-living-dangerously
! (math-known-realp (nth 2 (nth 1 expr))))
! (nth 2 (nth 1 expr)))
(and calc-symbolic-mode
! (math-known-negp (nth 1 expr))
! (math-add (list 'calcFunc-ln (math-neg (nth 1 expr)))
'(* (var pi var-pi) (var i var-i))))
(and calc-symbolic-mode
! (math-known-imagp (nth 1 expr))
! (let* ((ip (calcFunc-im (nth 1 expr)))
(ips (math-possible-signs ip)))
(or (and (memq ips '(4 6))
(math-add (list 'calcFunc-ln ip)
--- 1118,1139 ----
(list '+ c (list '* s '(var i var-i))))))))
(math-defsimplify calcFunc-ln
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-exp)
(or math-living-dangerously
! (math-known-realp (nth 1 (nth 1 math-simplify-expr))))
! (nth 1 (nth 1 math-simplify-expr)))
! (and (eq (car-safe (nth 1 math-simplify-expr)) '^)
! (equal (nth 1 (nth 1 math-simplify-expr)) '(var e var-e))
(or math-living-dangerously
! (math-known-realp (nth 2 (nth 1 math-simplify-expr))))
! (nth 2 (nth 1 math-simplify-expr)))
(and calc-symbolic-mode
! (math-known-negp (nth 1 math-simplify-expr))
! (math-add (list 'calcFunc-ln (math-neg (nth 1 math-simplify-expr)))
'(* (var pi var-pi) (var i var-i))))
(and calc-symbolic-mode
! (math-known-imagp (nth 1 math-simplify-expr))
! (let* ((ip (calcFunc-im (nth 1 math-simplify-expr)))
(ips (math-possible-signs ip)))
(or (and (memq ips '(4 6))
(math-add (list 'calcFunc-ln ip)
***************
*** 1103,1185 ****
(defun math-simplify-pow ()
(or (and math-living-dangerously
! (or (and (eq (car-safe (nth 1 expr)) '^)
(list '^
! (nth 1 (nth 1 expr))
! (math-mul (nth 2 expr) (nth 2 (nth 1 expr)))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-sqrt)
(list '^
! (nth 1 (nth 1 expr))
! (math-div (nth 2 expr) 2)))
! (and (memq (car-safe (nth 1 expr)) '(* /))
! (list (car (nth 1 expr))
! (list '^ (nth 1 (nth 1 expr)) (nth 2 expr))
! (list '^ (nth 2 (nth 1 expr)) (nth 2 expr))))))
! (and (math-equal-int (nth 1 expr) 10)
! (eq (car-safe (nth 2 expr)) 'calcFunc-log10)
! (nth 1 (nth 2 expr)))
! (and (equal (nth 1 expr) '(var e var-e))
! (math-simplify-exp (nth 2 expr)))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-exp)
(not math-integrating)
! (list 'calcFunc-exp (math-mul (nth 1 (nth 1 expr)) (nth 2 expr))))
! (and (equal (nth 1 expr) '(var i var-i))
(math-imaginary-i)
! (math-num-integerp (nth 2 expr))
! (let ((x (math-mod (math-trunc (nth 2 expr)) 4)))
(cond ((eq x 0) 1)
! ((eq x 1) (nth 1 expr))
((eq x 2) -1)
! ((eq x 3) (math-neg (nth 1 expr))))))
(and math-integrating
! (integerp (nth 2 expr))
! (>= (nth 2 expr) 2)
! (or (and (eq (car-safe (nth 1 expr)) 'calcFunc-cos)
! (math-mul (math-pow (nth 1 expr) (- (nth 2 expr) 2))
(math-sub 1
(math-sqr
(list 'calcFunc-sin
! (nth 1 (nth 1 expr)))))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-cosh)
! (math-mul (math-pow (nth 1 expr) (- (nth 2 expr) 2))
(math-add 1
(math-sqr
(list 'calcFunc-sinh
! (nth 1 (nth 1 expr)))))))))
! (and (eq (car-safe (nth 2 expr)) 'frac)
! (Math-ratp (nth 1 expr))
! (Math-posp (nth 1 expr))
! (if (equal (nth 2 expr) '(frac 1 2))
! (list 'calcFunc-sqrt (nth 1 expr))
! (let ((flr (math-floor (nth 2 expr))))
(and (not (Math-zerop flr))
! (list '* (list '^ (nth 1 expr) flr)
! (list '^ (nth 1 expr)
! (math-sub (nth 2 expr) flr)))))))
! (and (eq (math-quarter-integer (nth 2 expr)) 2)
(let ((temp (math-simplify-sqrt)))
(and temp
! (list '^ temp (math-mul (nth 2 expr) 2)))))))
(math-defsimplify calcFunc-log10
! (and (eq (car-safe (nth 1 expr)) '^)
! (math-equal-int (nth 1 (nth 1 expr)) 10)
(or math-living-dangerously
! (math-known-realp (nth 2 (nth 1 expr))))
! (nth 2 (nth 1 expr))))
(math-defsimplify calcFunc-erf
! (or (and (math-looks-negp (nth 1 expr))
! (math-neg (list 'calcFunc-erf (math-neg (nth 1 expr)))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-conj)
! (list 'calcFunc-conj (list 'calcFunc-erf (nth 1 (nth 1 expr)))))))
(math-defsimplify calcFunc-erfc
! (or (and (math-looks-negp (nth 1 expr))
! (math-sub 2 (list 'calcFunc-erfc (math-neg (nth 1 expr)))))
! (and (eq (car-safe (nth 1 expr)) 'calcFunc-conj)
! (list 'calcFunc-conj (list 'calcFunc-erfc (nth 1 (nth 1 expr)))))))
(defun math-linear-in (expr term &optional always)
--- 1147,1237 ----
(defun math-simplify-pow ()
(or (and math-living-dangerously
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) '^)
(list '^
! (nth 1 (nth 1 math-simplify-expr))
! (math-mul (nth 2 math-simplify-expr)
! (nth 2 (nth 1 math-simplify-expr)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sqrt)
(list '^
! (nth 1 (nth 1 math-simplify-expr))
! (math-div (nth 2 math-simplify-expr) 2)))
! (and (memq (car-safe (nth 1 math-simplify-expr)) '(* /))
! (list (car (nth 1 math-simplify-expr))
! (list '^ (nth 1 (nth 1 math-simplify-expr))
! (nth 2 math-simplify-expr))
! (list '^ (nth 2 (nth 1 math-simplify-expr))
! (nth 2 math-simplify-expr))))))
! (and (math-equal-int (nth 1 math-simplify-expr) 10)
! (eq (car-safe (nth 2 math-simplify-expr)) 'calcFunc-log10)
! (nth 1 (nth 2 math-simplify-expr)))
! (and (equal (nth 1 math-simplify-expr) '(var e var-e))
! (math-simplify-exp (nth 2 math-simplify-expr)))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-exp)
(not math-integrating)
! (list 'calcFunc-exp (math-mul (nth 1 (nth 1 math-simplify-expr))
! (nth 2 math-simplify-expr))))
! (and (equal (nth 1 math-simplify-expr) '(var i var-i))
(math-imaginary-i)
! (math-num-integerp (nth 2 math-simplify-expr))
! (let ((x (math-mod (math-trunc (nth 2 math-simplify-expr)) 4)))
(cond ((eq x 0) 1)
! ((eq x 1) (nth 1 math-simplify-expr))
((eq x 2) -1)
! ((eq x 3) (math-neg (nth 1 math-simplify-expr))))))
(and math-integrating
! (integerp (nth 2 math-simplify-expr))
! (>= (nth 2 math-simplify-expr) 2)
! (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos)
! (math-mul (math-pow (nth 1 math-simplify-expr)
! (- (nth 2 math-simplify-expr) 2))
(math-sub 1
(math-sqr
(list 'calcFunc-sin
! (nth 1 (nth 1
math-simplify-expr)))))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh)
! (math-mul (math-pow (nth 1 math-simplify-expr)
! (- (nth 2 math-simplify-expr) 2))
(math-add 1
(math-sqr
(list 'calcFunc-sinh
! (nth 1 (nth 1
math-simplify-expr)))))))))
! (and (eq (car-safe (nth 2 math-simplify-expr)) 'frac)
! (Math-ratp (nth 1 math-simplify-expr))
! (Math-posp (nth 1 math-simplify-expr))
! (if (equal (nth 2 math-simplify-expr) '(frac 1 2))
! (list 'calcFunc-sqrt (nth 1 math-simplify-expr))
! (let ((flr (math-floor (nth 2 math-simplify-expr))))
(and (not (Math-zerop flr))
! (list '* (list '^ (nth 1 math-simplify-expr) flr)
! (list '^ (nth 1 math-simplify-expr)
! (math-sub (nth 2 math-simplify-expr) flr)))))))
! (and (eq (math-quarter-integer (nth 2 math-simplify-expr)) 2)
(let ((temp (math-simplify-sqrt)))
(and temp
! (list '^ temp (math-mul (nth 2 math-simplify-expr) 2)))))))
(math-defsimplify calcFunc-log10
! (and (eq (car-safe (nth 1 math-simplify-expr)) '^)
! (math-equal-int (nth 1 (nth 1 math-simplify-expr)) 10)
(or math-living-dangerously
! (math-known-realp (nth 2 (nth 1 math-simplify-expr))))
! (nth 2 (nth 1 math-simplify-expr))))
(math-defsimplify calcFunc-erf
! (or (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-neg (list 'calcFunc-erf (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-conj)
! (list 'calcFunc-conj
! (list 'calcFunc-erf (nth 1 (nth 1 math-simplify-expr)))))))
(math-defsimplify calcFunc-erfc
! (or (and (math-looks-negp (nth 1 math-simplify-expr))
! (math-sub 2 (list 'calcFunc-erfc (math-neg (nth 1
math-simplify-expr)))))
! (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-conj)
! (list 'calcFunc-conj
! (list 'calcFunc-erfc (nth 1 (nth 1 math-simplify-expr)))))))
(defun math-linear-in (expr term &optional always)
***************
*** 1325,1343 ****
thing))
;;; Substitute all occurrences of old for new in expr (non-destructive).
! (defun math-expr-subst (expr old new)
(math-expr-subst-rec expr))
(defalias 'calcFunc-subst 'math-expr-subst)
(defun math-expr-subst-rec (expr)
! (cond ((equal expr old) new)
((Math-primp expr) expr)
((memq (car expr) '(calcFunc-deriv
calcFunc-tderiv))
(if (= (length expr) 2)
! (if (equal (nth 1 expr) old)
! (append expr (list new))
expr)
(list (car expr) (nth 1 expr)
(math-expr-subst-rec (nth 2 expr)))))
--- 1377,1401 ----
thing))
;;; Substitute all occurrences of old for new in expr (non-destructive).
!
! ;; The variables math-expr-subst-old and math-expr-subst-new are local
! ;; for math-expr-subst, but used by math-expr-subst-rec.
! (defvar math-expr-subst-old)
! (defvar math-expr-subst-new)
!
! (defun math-expr-subst (expr math-expr-subst-old math-expr-subst-new)
(math-expr-subst-rec expr))
(defalias 'calcFunc-subst 'math-expr-subst)
(defun math-expr-subst-rec (expr)
! (cond ((equal expr math-expr-subst-old) math-expr-subst-new)
((Math-primp expr) expr)
((memq (car expr) '(calcFunc-deriv
calcFunc-tderiv))
(if (= (length expr) 2)
! (if (equal (nth 1 expr) math-expr-subst-old)
! (append expr (list math-expr-subst-new))
expr)
(list (car expr) (nth 1 expr)
(math-expr-subst-rec (nth 2 expr)))))
***************
*** 1375,1389 ****
expr)))
;;; If expr is of the form "a + bx + cx^2 + ...", return the list (a b c ...),
! ;;; else return nil if not in polynomial form. If "loose", coefficients
! ;;; may contain x, e.g., sin(x) + cos(x) x^2 is a loose polynomial in x.
! (defun math-is-polynomial (expr var &optional degree loose)
! (let* ((math-poly-base-variable (if loose
! (if (eq loose 'gen) var '(var XXX XXX))
math-poly-base-variable))
(poly (math-is-poly-rec expr math-poly-neg-powers)))
! (and (or (null degree)
! (<= (length poly) (1+ degree)))
poly)))
(defun math-is-poly-rec (expr negpow)
--- 1433,1453 ----
expr)))
;;; If expr is of the form "a + bx + cx^2 + ...", return the list (a b c ...),
! ;;; else return nil if not in polynomial form. If "loose"
(math-is-poly-loose),
! ;;; coefficients may contain x, e.g., sin(x) + cos(x) x^2 is a loose
polynomial in x.
!
! ;; The variables math-is-poly-degree and math-is-poly-loose are local to
! ;; math-is-polynomial, but are used by math-is-poly-rec
! (defvar math-is-poly-degree)
! (defvar math-is-poly-loose)
!
! (defun math-is-polynomial (expr var &optional math-is-poly-degree
math-is-poly-loose)
! (let* ((math-poly-base-variable (if math-is-poly-loose
! (if (eq math-is-poly-loose 'gen) var
'(var XXX XXX))
math-poly-base-variable))
(poly (math-is-poly-rec expr math-poly-neg-powers)))
! (and (or (null math-is-poly-degree)
! (<= (length poly) (1+ math-is-poly-degree)))
poly)))
(defun math-is-poly-rec (expr negpow)
***************
*** 1431,1438 ****
(n pow)
(accum (list 1)))
(and p1
! (or (null degree)
! (<= (* (1- (length p1)) n) degree))
(progn
(while (>= n 1)
(setq accum (math-poly-mul accum p1)
--- 1495,1502 ----
(n pow)
(accum (list 1)))
(and p1
! (or (null math-is-poly-degree)
! (<= (* (1- (length p1)) n)
math-is-poly-degree))
(progn
(while (>= n 1)
(setq accum (math-poly-mul accum p1)
***************
*** 1460,1467 ****
(and p1
(let ((p2 (math-is-poly-rec (nth 2 expr) negpow)))
(and p2
! (or (null degree)
! (<= (- (+ (length p1) (length p2)) 2) degree))
(math-poly-mul p1 p2))))))
((eq (car expr) '/)
(and (or (not (math-poly-depends (nth 2 expr) var))
--- 1524,1532 ----
(and p1
(let ((p2 (math-is-poly-rec (nth 2 expr) negpow)))
(and p2
! (or (null math-is-poly-degree)
! (<= (- (+ (length p1) (length p2)) 2)
! math-is-poly-degree))
(math-poly-mul p1 p2))))))
((eq (car expr) '/)
(and (or (not (math-poly-depends (nth 2 expr) var))
***************
*** 1481,1487 ****
(math-is-poly-rec (list '^ (nth 1 expr) '(frac 1 2)) negpow))
(t nil))
(and (or (not (math-poly-depends expr var))
! loose)
(not (eq (car expr) 'vec))
(list expr)))))
--- 1546,1552 ----
(math-is-poly-rec (list '^ (nth 1 expr) '(frac 1 2)) negpow))
(t nil))
(and (or (not (math-poly-depends expr var))
! math-is-poly-loose)
(not (eq (car expr) 'vec))
(list expr)))))
***************
*** 1517,1529 ****
(math-expr-depends expr var)))
;;; Find the variable (or sub-expression) which is the base of polynomial
expr.
! (defun math-polynomial-base (mpb-top-expr &optional mpb-pred)
! (or mpb-pred
! (setq mpb-pred (function (lambda (base) (math-polynomial-p
mpb-top-expr base)))))
! (or (let ((const-ok nil))
(math-polynomial-base-rec mpb-top-expr))
! (let ((const-ok t))
(math-polynomial-base-rec mpb-top-expr))))
(defun math-polynomial-base-rec (mpb-expr)
--- 1582,1599 ----
(math-expr-depends expr var)))
;;; Find the variable (or sub-expression) which is the base of polynomial
expr.
! ;; The variables math-poly-base-const-ok and math-poly-base-pred are
! ;; local to math-polynomial-base, but are used by math-polynomial-base-rec.
! (defvar math-poly-base-const-ok)
! (defvar math-poly-base-pred)
!
! (defun math-polynomial-base (mpb-top-expr &optional math-poly-base-pred)
! (or math-poly-base-pred
! (setq math-poly-base-pred (function (lambda (base) (math-polynomial-p
mpb-top-expr base)))))
! (or (let ((math-poly-base-const-ok nil))
(math-polynomial-base-rec mpb-top-expr))
! (let ((math-poly-base-const-ok t))
(math-polynomial-base-rec mpb-top-expr))))
(defun math-polynomial-base-rec (mpb-expr)
***************
*** 1537,1544 ****
(math-polynomial-base-rec (nth 1 mpb-expr)))
(and (eq (car mpb-expr) 'calcFunc-exp)
(math-polynomial-base-rec '(var e var-e)))
! (and (or const-ok (math-expr-contains-vars mpb-expr))
! (funcall mpb-pred mpb-expr)
mpb-expr))))
;;; Return non-nil if expr refers to any variables.
--- 1607,1614 ----
(math-polynomial-base-rec (nth 1 mpb-expr)))
(and (eq (car mpb-expr) 'calcFunc-exp)
(math-polynomial-base-rec '(var e var-e)))
! (and (or math-poly-base-const-ok (math-expr-contains-vars mpb-expr))
! (funcall math-poly-base-pred mpb-expr)
mpb-expr))))
;;; Return non-nil if expr refers to any variables.
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