diff options
Diffstat (limited to 'lisp/calc/calc-alg.el')
| -rw-r--r-- | lisp/calc/calc-alg.el | 932 |
1 files changed, 462 insertions, 470 deletions
diff --git a/lisp/calc/calc-alg.el b/lisp/calc/calc-alg.el index 7a448d20ec2..2f23399841e 100644 --- a/lisp/calc/calc-alg.el +++ b/lisp/calc/calc-alg.el @@ -1,4 +1,4 @@ -;;; calc-alg.el --- algebraic functions for Calc +;;; calc-alg.el --- algebraic functions for Calc -*- lexical-binding:t -*- ;; Copyright (C) 1990-1993, 2001-2018 Free Software Foundation, Inc. @@ -308,7 +308,7 @@ (let ((math-living-dangerously t)) (math-simplify a))) -(defalias 'calcFunc-esimplify 'math-simplify-extended) +(defalias 'calcFunc-esimplify #'math-simplify-extended) ;;; Rewrite the trig functions in a form easier to simplify. (defun math-trig-rewrite (fn) @@ -329,7 +329,7 @@ (list '/ (cons 'calcFunc-cos newfn) (cons 'calcFunc-sin newfn)))) (t - (mapcar 'math-trig-rewrite fn)))) + (mapcar #'math-trig-rewrite fn)))) (defun math-hyperbolic-trig-rewrite (fn) "Rewrite hyperbolic functions in terms of sinhs and coshs." @@ -349,7 +349,7 @@ (list '/ (cons 'calcFunc-cosh newfn) (cons 'calcFunc-sinh newfn)))) (t - (mapcar 'math-hyperbolic-trig-rewrite fn)))) + (mapcar #'math-hyperbolic-trig-rewrite fn)))) ;; math-top-only is local to math-simplify, but is used by ;; math-simplify-step, which is called by math-simplify. @@ -402,11 +402,11 @@ (setq top-expr res))))) top-expr) -(defalias 'calcFunc-simplify 'math-simplify) +(defalias 'calcFunc-simplify #'math-simplify) -;;; The following has a "bug" in that if any recursive simplifications -;;; occur only the first handler will be tried; this doesn't really -;;; matter, since math-simplify-step is iterated to a fixed point anyway. +;; The following has a "bug" in that if any recursive simplifications +;; occur only the first handler will be tried; this doesn't really +;; matter, since math-simplify-step is iterated to a fixed point anyway. (defun math-simplify-step (a) (if (Math-primp a) a @@ -414,7 +414,7 @@ (memq (car a) '(calcFunc-quote calcFunc-condition calcFunc-evalto))) a - (cons (car a) (mapcar 'math-simplify-step (cdr a)))))) + (cons (car a) (mapcar #'math-simplify-step (cdr a)))))) (and (symbolp (car aa)) (let ((handler (get (car aa) 'math-simplify))) (and handler @@ -427,159 +427,155 @@ (defmacro math-defsimplify (funcs &rest code) + "Define the simplification code for functions FUNCS. +Code can refer to the expression to simplify via lexical variable `expr' +and should return the simplified expression to use (or nil)." + (declare (indent 1) (debug (sexp body))) (cons 'progn (mapcar #'(lambda (func) `(put ',func 'math-simplify (nconc (get ',func 'math-simplify) (list - #'(lambda (math-simplify-expr) ,@code))))) + #'(lambda (expr) ,@code))))) (if (symbolp funcs) (list funcs) funcs)))) -(put 'math-defsimplify 'lisp-indent-hook 1) - -;; 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) + (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 math-simplify-expr) + (if (setq temp (math-combine-sum (nth 2 aaa) (nth 2 expr) (eq (car aaa) '-) - (eq (car math-simplify-expr) '-) t)) + (eq (car expr) '-) t)) (progn - (setcar (cdr (cdr math-simplify-expr)) temp) - (setcar math-simplify-expr '+) + (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 math-simplify-expr) - nil (eq (car math-simplify-expr) '-) t)) + (if (setq temp (math-combine-sum aaa (nth 2 expr) + nil (eq (car expr) '-) t)) (progn - (setcar (cdr (cdr math-simplify-expr)) temp) - (setcar math-simplify-expr '+) + (setcar (cdr (cdr expr)) temp) + (setcar expr '+) (setcar (cdr aa) 0))) - math-simplify-expr)) + 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) + (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 math-simplify-expr)))) - (if (and (Math-ratp (nth 1 math-simplify-expr)) - (setq temp (math-common-constant-factor (nth 2 math-simplify-expr)))) + (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 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)))) + (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 math-simplify-expr) + (if (setq temp (math-combine-prod (nth 1 expr) (nth 1 aaa) nil nil t)) (progn - (setcar (cdr math-simplify-expr) temp) + (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 math-simplify-expr) nil nil t)) + (if (and (setq temp (math-combine-prod aaa (nth 1 expr) nil nil t)) safe) (progn - (setcar (cdr math-simplify-expr) temp) + (setcar (cdr 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))) + (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)) + (math-simplify-divide expr)) -(defun math-simplify-divide () - (let ((np (cdr math-simplify-expr)) +(defvar math--simplify-divide-expr) + +(defun math-simplify-divide (expr) + (let ((np (cdr 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)))) + (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 math-simplify-expr) '/) - (not (Math-realp (nth 1 math-simplify-expr)))) - (math-common-constant-factor (nth 1 math-simplify-expr)))) + (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)) - (unless (and (eq (car-safe math-simplify-expr) 'calcFunc-eq) - (eq (car-safe (nth 1 math-simplify-expr)) 'var) - (not (math-expr-contains (nth 2 math-simplify-expr) - (nth 1 math-simplify-expr)))) - (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)) + (unless (and (eq (car-safe expr) 'calcFunc-eq) + (eq (car-safe (nth 1 expr)) 'var) + (not (math-expr-contains (nth 2 expr) + (nth 1 expr)))) + (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 math-simplify-expr) calc-tweak-eqn-table))) - (setcar math-simplify-expr (nth 1 op)))) + (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 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)) + (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 math-simplify-expr) + (setq op (assq (car 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)) + (setcar expr (nth 1 op)))))))) + (let ((math--simplify-divide-expr expr)) ;For use in math-simplify-divisor + (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))) ;; The variables math-simplify-divisor-nover and math-simplify-divisor-dover ;; are local variables for math-simplify-divisor, but are used by @@ -587,25 +583,25 @@ (defvar math-simplify-divisor-nover) (defvar math-simplify-divisor-dover) -(defun math-simplify-divisor (np dp math-simplify-divisor-nover - math-simplify-divisor-dover) +(defun math-simplify-divisor (np dp nover dover) (cond ((eq (car-safe (car dp)) '/) (math-simplify-divisor np (cdr (car dp)) - math-simplify-divisor-nover - math-simplify-divisor-dover) + nover 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) '/) + nover (not dover)))) + ((or (or (eq (car math--simplify-divide-expr) '/) (let ((signs (math-possible-signs (car np)))) (or (memq signs '(1 4)) - (and (memq (car math-simplify-expr) '(calcFunc-eq calcFunc-neq)) + (and (memq (car math--simplify-divide-expr) + '(calcFunc-eq calcFunc-neq)) (eq signs 5)) math-living-dangerously))) (math-numberp (car np))) (let (d (safe t) + (math-simplify-divisor-nover nover) + (math-simplify-divisor-dover dover) (scalar (math-known-scalarp (car np)))) (while (and (eq (car-safe (setq d (car dp))) '*) safe) @@ -621,14 +617,16 @@ op) (if temp (progn - (and (not (memq (car math-simplify-expr) '(/ calcFunc-eq calcFunc-neq))) + (and (not (memq (car math--simplify-divide-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))) + (setq op (assq (car math--simplify-divide-expr) + calc-tweak-eqn-table)) + (setcar math--simplify-divide-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 math--simplify-divide-expr) '/) (eq (car-safe (car dp)) 'calcFunc-sqrt) (Math-integerp (nth 1 (car dp))) (progn @@ -680,26 +678,23 @@ (math-gcd (nth 2 a) (nth 2 b))))))) (math-defsimplify % - (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) + (and (Math-realp (nth 2 expr)) + (Math-posp (nth 2 expr)) + (let ((lin (math-is-linear (nth 1 expr))) + t1) (or (and lin (or (math-negp (car lin)) - (not (Math-lessp (car lin) (nth 2 math-simplify-expr)))) + (not (Math-lessp (car lin) (nth 2 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))) + (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 math-simplify-expr)) - (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2 math-simplify-expr))) + (math-num-integerp (nth 2 expr)) + (setq t1 (calcFunc-gcd (nth 1 lin) (nth 2 expr))) (not (math-equal-int t1 1)) (list '* t1 @@ -709,53 +704,53 @@ (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-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 math-simplify-expr))) + (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 math-simplify-expr) 3) - (math-simplify-ineq))) + (if (= (length expr) 3) + (math-simplify-ineq expr))) -(defun math-simplify-ineq () - (let ((np (cdr math-simplify-expr)) +(defun math-simplify-ineq (expr) + (let ((np (cdr expr)) n) (while (memq (car-safe (setq n (car np))) '(+ -)) - (math-simplify-add-term (cdr (cdr n)) (cdr (cdr math-simplify-expr)) + (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 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) + (math-simplify-add-term np (cdr (cdr expr)) nil + (eq np (cdr expr))) + (math-simplify-divide expr) + (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 math-simplify-expr) 'calcFunc-neq) + ((eq (car expr) 'calcFunc-neq) (or (and (eq signs 2) 0) (and (memq signs '(1 4 5)) 1))) - ((eq (car math-simplify-expr) 'calcFunc-lt) + ((eq (car expr) 'calcFunc-lt) (or (and (eq signs 1) 1) (and (memq signs '(2 4 6)) 0))) - ((eq (car math-simplify-expr) 'calcFunc-gt) + ((eq (car expr) 'calcFunc-gt) (or (and (eq signs 4) 1) (and (memq signs '(1 2 3)) 0))) - ((eq (car math-simplify-expr) 'calcFunc-leq) + ((eq (car expr) 'calcFunc-leq) (or (and (eq signs 4) 0) (and (memq signs '(1 2 3)) 1))) - ((eq (car math-simplify-expr) 'calcFunc-geq) + ((eq (car expr) 'calcFunc-geq) (or (and (eq signs 1) 0) (and (memq signs '(2 4 6)) 1)))) - math-simplify-expr)))) + expr)))) (defun math-simplify-add-term (np dp minus lplain) (or (math-vectorp (car np)) (let ((rplain t) - n d dd temp) + n d temp) (while (memq (car-safe (setq n (car np) d (car dp))) '(+ -)) (setq rplain nil) (if (setq temp (math-combine-sum n (nth 2 d) @@ -782,27 +777,27 @@ (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))))) + (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 math-simplify-expr) '(var pi var-pi)))) + (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 math-simplify-expr)))) + (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 math-simplify-expr)) 'calcFunc-arccos) + (and (eq (car-safe (nth 1 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)) + (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 math-simplify-expr))))))) - (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) + (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 '+ @@ -812,27 +807,27 @@ (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)))) + (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 math-simplify-expr) '(var pi var-pi)))) + (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 math-simplify-expr)))) + (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 math-simplify-expr)) 'calcFunc-arcsin) + (and (eq (car-safe (nth 1 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-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 math-simplify-expr))))))) - (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) + (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 '- @@ -842,53 +837,53 @@ (list 'calcFunc-sin a)))))))) (math-defsimplify calcFunc-sec - (or (and (math-looks-negp (nth 1 math-simplify-expr)) - (list 'calcFunc-sec (math-neg (nth 1 math-simplify-expr)))) + (or (and (math-looks-negp (nth 1 expr)) + (list 'calcFunc-sec (math-neg (nth 1 expr)))) (and (eq calc-angle-mode 'rad) - (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) + (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi)))) (and n (math-div 1 (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)))) + (let ((n (math-integer-plus (nth 1 expr)))) (and n (math-div 1 (math-known-sin (car n) (nth 1 n) '(frac 2 3) 300))))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin) (math-div 1 (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-sub 1 (math-sqr (nth 1 (nth 1 expr))))))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos) (math-div 1 - (nth 1 (nth 1 math-simplify-expr)))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctan) + (nth 1 (nth 1 expr)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan) (list 'calcFunc-sqrt (math-add 1 - (math-sqr (nth 1 (nth 1 math-simplify-expr)))))))) + (math-sqr (nth 1 (nth 1 expr)))))))) (math-defsimplify calcFunc-csc - (or (and (math-looks-negp (nth 1 math-simplify-expr)) - (math-neg (list 'calcFunc-csc (math-neg (nth 1 math-simplify-expr))))) + (or (and (math-looks-negp (nth 1 expr)) + (math-neg (list 'calcFunc-csc (math-neg (nth 1 expr))))) (and (eq calc-angle-mode 'rad) - (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) + (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi)))) (and n (math-div 1 (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)))) + (let ((n (math-integer-plus (nth 1 expr)))) (and n (math-div 1 (math-known-sin (car n) (nth 1 n) '(frac 2 3) 0))))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) - (math-div 1 (nth 1 (nth 1 math-simplify-expr)))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin) + (math-div 1 (nth 1 (nth 1 expr)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos) (math-div 1 (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) + (nth 1 (nth 1 expr))))))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan) (math-div (list 'calcFunc-sqrt (math-add 1 (math-sqr - (nth 1 (nth 1 math-simplify-expr))))) - (nth 1 (nth 1 math-simplify-expr)))))) + (nth 1 (nth 1 expr))))) + (nth 1 (nth 1 expr)))))) (defun math-should-expand-trig (x &optional hyperbolic) (let ((m (math-is-multiple x))) @@ -943,55 +938,55 @@ (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))))) + (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 math-simplify-expr) '(var pi var-pi)))) + (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 math-simplify-expr)))) + (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 math-simplify-expr)) 'calcFunc-arcsin) - (math-div (nth 1 (nth 1 math-simplify-expr)) + (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 math-simplify-expr))))))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) + (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 math-simplify-expr))))) - (nth 1 (nth 1 math-simplify-expr)))) - (let ((m (math-should-expand-trig (nth 1 math-simplify-expr)))) + (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 math-simplify-expr)) - (list 'calcFunc-cos (nth 1 math-simplify-expr)))))))) + (math-div (list 'calcFunc-sin (nth 1 expr)) + (list 'calcFunc-cos (nth 1 expr)))))))) (math-defsimplify calcFunc-cot - (or (and (math-looks-negp (nth 1 math-simplify-expr)) - (math-neg (list 'calcFunc-cot (math-neg (nth 1 math-simplify-expr))))) + (or (and (math-looks-negp (nth 1 expr)) + (math-neg (list 'calcFunc-cot (math-neg (nth 1 expr))))) (and (eq calc-angle-mode 'rad) - (let ((n (math-linear-in (nth 1 math-simplify-expr) '(var pi var-pi)))) + (let ((n (math-linear-in (nth 1 expr) '(var pi var-pi)))) (and n (math-div 1 (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)))) + (let ((n (math-integer-plus (nth 1 expr)))) (and n (math-div 1 (math-known-tan (car n) (nth 1 n) '(frac 2 3)))))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsin) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsin) (math-div (list 'calcFunc-sqrt - (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))) - (nth 1 (nth 1 math-simplify-expr)))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccos) - (math-div (nth 1 (nth 1 math-simplify-expr)) + (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))) + (nth 1 (nth 1 expr)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccos) + (math-div (nth 1 (nth 1 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-arctan) - (math-div 1 (nth 1 (nth 1 math-simplify-expr)))))) + (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctan) + (math-div 1 (nth 1 (nth 1 expr)))))) (defun math-known-tan (plus n mul) (setq n (math-mul n mul)) @@ -1026,20 +1021,20 @@ (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) + (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 math-simplify-expr))) 1))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) + (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 math-simplify-expr)) + (math-div (nth 1 (nth 1 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))) + (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) @@ -1050,20 +1045,20 @@ (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) + (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 math-simplify-expr))) 1))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) + (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 math-simplify-expr))))))) - (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) + (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) @@ -1074,188 +1069,188 @@ (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) + (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 math-simplify-expr)) + (math-div (nth 1 (nth 1 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-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 math-simplify-expr))) 1)) - (nth 1 (nth 1 math-simplify-expr)))) - (let ((m (math-should-expand-trig (nth 1 math-simplify-expr) t))) + (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 math-simplify-expr)) - (list 'calcFunc-cosh (nth 1 math-simplify-expr)))))))) + (math-div (list 'calcFunc-sinh (nth 1 expr)) + (list 'calcFunc-cosh (nth 1 expr)))))))) (math-defsimplify calcFunc-sech - (or (and (math-looks-negp (nth 1 math-simplify-expr)) - (list 'calcFunc-sech (math-neg (nth 1 math-simplify-expr)))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) + (or (and (math-looks-negp (nth 1 expr)) + (list 'calcFunc-sech (math-neg (nth 1 expr)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh) math-living-dangerously (math-div 1 (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-add (math-sqr (nth 1 (nth 1 expr))) 1)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh) math-living-dangerously - (math-div 1 (nth 1 (nth 1 math-simplify-expr))) 1) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arctanh) + (math-div 1 (nth 1 (nth 1 expr))) 1) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh) math-living-dangerously (list 'calcFunc-sqrt - (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr)))))))) + (math-sub 1 (math-sqr (nth 1 (nth 1 expr)))))))) (math-defsimplify calcFunc-csch - (or (and (math-looks-negp (nth 1 math-simplify-expr)) - (math-neg (list 'calcFunc-csch (math-neg (nth 1 math-simplify-expr))))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) + (or (and (math-looks-negp (nth 1 expr)) + (math-neg (list 'calcFunc-csch (math-neg (nth 1 expr))))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh) math-living-dangerously - (math-div 1 (nth 1 (nth 1 math-simplify-expr)))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) + (math-div 1 (nth 1 (nth 1 expr)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh) math-living-dangerously (math-div 1 (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-sub (math-sqr (nth 1 (nth 1 expr))) 1)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh) math-living-dangerously (math-div (list 'calcFunc-sqrt - (math-sub 1 (math-sqr (nth 1 (nth 1 math-simplify-expr))))) - (nth 1 (nth 1 math-simplify-expr)))))) + (math-sub 1 (math-sqr (nth 1 (nth 1 expr))))) + (nth 1 (nth 1 expr)))))) (math-defsimplify calcFunc-coth - (or (and (math-looks-negp (nth 1 math-simplify-expr)) - (math-neg (list 'calcFunc-coth (math-neg (nth 1 math-simplify-expr))))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arcsinh) + (or (and (math-looks-negp (nth 1 expr)) + (math-neg (list 'calcFunc-coth (math-neg (nth 1 expr))))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arcsinh) math-living-dangerously (math-div (list 'calcFunc-sqrt - (math-add (math-sqr (nth 1 (nth 1 math-simplify-expr))) 1)) - (nth 1 (nth 1 math-simplify-expr)))) - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-arccosh) + (math-add (math-sqr (nth 1 (nth 1 expr))) 1)) + (nth 1 (nth 1 expr)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arccosh) math-living-dangerously - (math-div (nth 1 (nth 1 math-simplify-expr)) + (math-div (nth 1 (nth 1 expr)) (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-sub (math-sqr (nth 1 (nth 1 expr))) 1)))) + (and (eq (car-safe (nth 1 expr)) 'calcFunc-arctanh) math-living-dangerously - (math-div 1 (nth 1 (nth 1 math-simplify-expr)))))) + (math-div 1 (nth 1 (nth 1 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) + (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 math-simplify-expr) '(frac 1 2)) + (and (equal (nth 1 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))) + (eq (car-safe (nth 1 expr)) 'calcFunc-sin) + (nth 1 (nth 1 expr))) (and math-living-dangerously - (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cos) + (eq (car-safe (nth 1 expr)) 'calcFunc-cos) (math-sub (math-quarter-circle t) - (nth 1 (nth 1 math-simplify-expr)))))) + (nth 1 (nth 1 expr)))))) (math-defsimplify calcFunc-arccos - (or (and (eq (nth 1 math-simplify-expr) 0) + (or (and (eq (nth 1 expr) 0) (math-quarter-circle t)) - (and (eq (nth 1 math-simplify-expr) -1) + (and (eq (nth 1 expr) -1) (math-half-circle t)) - (and (equal (nth 1 math-simplify-expr) '(frac 1 2)) + (and (equal (nth 1 expr) '(frac 1 2)) (math-div (math-half-circle t) 3)) - (and (equal (nth 1 math-simplify-expr) '(frac -1 2)) + (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 math-simplify-expr)) 'calcFunc-cos) - (nth 1 (nth 1 math-simplify-expr))) + (eq (car-safe (nth 1 expr)) 'calcFunc-cos) + (nth 1 (nth 1 expr))) (and math-living-dangerously - (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-sin) + (eq (car-safe (nth 1 expr)) 'calcFunc-sin) (math-sub (math-quarter-circle t) - (nth 1 (nth 1 math-simplify-expr)))))) + (nth 1 (nth 1 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) + (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 math-simplify-expr)) 'calcFunc-tan) - (nth 1 (nth 1 math-simplify-expr))))) + (eq (car-safe (nth 1 expr)) 'calcFunc-tan) + (nth 1 (nth 1 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 (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 math-simplify-expr)))) - (nth 1 (nth 1 math-simplify-expr))))) + (math-known-realp (nth 1 (nth 1 expr)))) + (nth 1 (nth 1 expr))))) (math-defsimplify calcFunc-arccosh - (and (eq (car-safe (nth 1 math-simplify-expr)) 'calcFunc-cosh) + (and (eq (car-safe (nth 1 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-known-realp (nth 1 (nth 1 expr)))) + (nth 1 (nth 1 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 (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 math-simplify-expr)))) - (nth 1 (nth 1 math-simplify-expr))))) + (math-known-realp (nth 1 (nth 1 expr)))) + (nth 1 (nth 1 expr))))) (math-defsimplify calcFunc-sqrt - (math-simplify-sqrt)) + (math-simplify-sqrt expr)) -(defun math-simplify-sqrt () - (or (and (eq (car-safe (nth 1 math-simplify-expr)) 'frac) +(defun math-simplify-sqrt (expr) + (or (and (eq (car-safe (nth 1 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))))) + (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 math-simplify-expr) fac)))))) + (nth 1 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)))) + (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 math-simplify-expr)))))) - (and (eq (car-safe (nth 1 (nth 2 (nth 1 math-simplify-expr)))) + (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 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)))) + (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 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)))) + (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 math-simplify-expr)))) + (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) @@ -1269,20 +1264,20 @@ (and (eq (car-safe (nth 1 a)) 'calcFunc-cot) (list '/ 1 (list 'calcFunc-sin (nth 1 (nth 1 a))))))))) - (and (eq (car-safe (nth 1 math-simplify-expr)) '^) + (and (eq (car-safe (nth 1 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))) + (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 math-simplify-expr))))) + (nth 1 expr))))) (and (math-vectorp f) (or (> (length f) 2) (> (nth 2 (nth 1 f)) 1)) @@ -1318,7 +1313,7 @@ fac))) (math-defsimplify calcFunc-exp - (math-simplify-exp (nth 1 math-simplify-expr))) + (math-simplify-exp (nth 1 expr))) (defun math-simplify-exp (x) (or (and (eq (car-safe x) 'calcFunc-ln) @@ -1349,22 +1344,22 @@ (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 (and (eq (car-safe (nth 1 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)) + (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 math-simplify-expr)))) - (nth 2 (nth 1 math-simplify-expr))) + (math-known-realp (nth 2 (nth 1 expr)))) + (nth 2 (nth 1 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))) + (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 math-simplify-expr)) - (let* ((ip (calcFunc-im (nth 1 math-simplify-expr))) + (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) @@ -1374,95 +1369,92 @@ '(/ (* (var pi var-pi) (var i var-i)) 2)))))))) (math-defsimplify ^ - (math-simplify-pow)) - -(defun math-simplify-pow () (or (and math-living-dangerously - (or (and (eq (car-safe (nth 1 math-simplify-expr)) '^) + (or (and (eq (car-safe (nth 1 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) + (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 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) + (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 math-simplify-expr)) - (nth 2 math-simplify-expr)))) - (and (equal (nth 1 math-simplify-expr) '(var i var-i)) + (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 math-simplify-expr)) - (let ((x (math-mod (math-trunc (nth 2 math-simplify-expr)) 4))) + (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 math-simplify-expr)) + ((eq x 1) (nth 1 expr)) ((eq x 2) -1) - ((eq x 3) (math-neg (nth 1 math-simplify-expr)))))) + ((eq x 3) (math-neg (nth 1 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)) + (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 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)) + (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 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)))) + (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 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))) + (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 expr))) (and temp - (list '^ temp (math-mul (nth 2 math-simplify-expr) 2))))))) + (list '^ temp (math-mul (nth 2 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) + (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 math-simplify-expr)))) - (nth 2 (nth 1 math-simplify-expr)))) + (math-known-realp (nth 2 (nth 1 expr)))) + (nth 2 (nth 1 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) + (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 math-simplify-expr))))))) + (list 'calcFunc-erf (nth 1 (nth 1 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) + (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 math-simplify-expr))))))) + (list 'calcFunc-erfc (nth 1 (nth 1 expr))))))) (defun math-linear-in (expr term &optional always) @@ -1614,10 +1606,12 @@ (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)) +(defun math-expr-subst (expr old new) + (let ((math-expr-subst-old old) + (math-expr-subst-new new)) + (math-expr-subst-rec expr))) -(defalias 'calcFunc-subst 'math-expr-subst) +(defalias 'calcFunc-subst #'math-expr-subst) (defun math-expr-subst-rec (expr) (cond ((equal expr math-expr-subst-old) math-expr-subst-new) @@ -1632,7 +1626,7 @@ (math-expr-subst-rec (nth 2 expr))))) (t (cons (car expr) - (mapcar 'math-expr-subst-rec (cdr expr)))))) + (mapcar #'math-expr-subst-rec (cdr expr)))))) ;;; Various measures of the size of an expression. (defun math-expr-weight (expr) @@ -1659,7 +1653,7 @@ (defun calcFunc-collect (expr base) (let ((p (math-is-polynomial expr base 50 t))) (if (cdr p) - (math-build-polynomial-expr (mapcar 'math-normalize p) base) + (math-build-polynomial-expr (mapcar #'math-normalize p) base) (car p)))) ;;; If expr is of the form "a + bx + cx^2 + ...", return the list (a b c ...), @@ -1672,13 +1666,16 @@ (defvar math-is-poly-loose) (defvar math-var) -(defun math-is-polynomial (expr math-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) math-var '(var XXX XXX)) +(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)) + (math-var var) + (math-is-poly-loose loose) + (math-is-poly-degree degree) (poly (math-is-poly-rec expr math-poly-neg-powers))) - (and (or (null math-is-poly-degree) - (<= (length poly) (1+ math-is-poly-degree))) + (and (or (null degree) + (<= (length poly) (1+ degree))) poly))) (defun math-is-poly-rec (expr negpow) @@ -1749,7 +1746,7 @@ (math-poly-mix p1 1 p2 (if (eq (car expr) '+) 1 -1))))))) ((eq (car expr) 'neg) - (mapcar 'math-neg (math-is-poly-rec (nth 1 expr) negpow))) + (mapcar #'math-neg (math-is-poly-rec (nth 1 expr) negpow))) ((eq (car expr) '*) (let ((p1 (math-is-poly-rec (nth 1 expr) negpow))) (and p1 @@ -1812,24 +1809,20 @@ (math-expr-contains expr math-poly-base-variable) (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) -;; The variable math-poly-base-top-expr is local to math-polynomial-base, -;; but is used by math-polynomial-p1 in calc-poly.el, which is called -;; by math-polynomial-base. - -(defun math-polynomial-base (math-poly-base-top-expr &optional math-poly-base-pred) - (or math-poly-base-pred - (setq math-poly-base-pred (function (lambda (base) (math-polynomial-p - math-poly-base-top-expr base))))) +(defun math-polynomial-base (top-expr &optional pred) + "Find the variable (or sub-expression) which is the base of polynomial expr." + (let ((math-poly-base-pred + (or pred (function (lambda (base) (math-polynomial-p + top-expr base)))))) (or (let ((math-poly-base-const-ok nil)) - (math-polynomial-base-rec math-poly-base-top-expr)) + (math-polynomial-base-rec top-expr)) (let ((math-poly-base-const-ok t)) - (math-polynomial-base-rec math-poly-base-top-expr)))) + (math-polynomial-base-rec top-expr))))) (defun math-polynomial-base-rec (mpb-expr) (and (not (Math-objvecp mpb-expr)) @@ -1846,8 +1839,8 @@ (funcall math-poly-base-pred mpb-expr) mpb-expr)))) -;;; Return non-nil if expr refers to any variables. (defun math-expr-contains-vars (expr) + "Return non-nil if expr refers to any variables." (or (eq (car-safe expr) 'var) (and (not (Math-primp expr)) (progn @@ -1855,9 +1848,9 @@ (not (math-expr-contains-vars (car expr))))) expr)))) -;;; Simplify a polynomial in list form by stripping off high-end zeros. -;;; This always leaves the constant part, i.e., nil->nil and non-nil->non-nil. (defun math-poly-simplify (p) + "Simplify a polynomial in list form by stripping off high-end zeros. +This always leaves the constant part, i.e., nil->nil and non-nil->non-nil." (and p (if (Math-zerop (nth (1- (length p)) p)) (let ((pp (copy-sequence p))) @@ -1879,14 +1872,14 @@ (or (null a) (and (null (cdr a)) (Math-zerop (car a))))) -;;; Multiply two polynomials in list form. (defun math-poly-mul (a b) + "Multiply two polynomials in list form." (and a b (math-poly-mix b (car a) (math-poly-mul (cdr a) (cons 0 b)) 1))) -;;; Build an expression from a polynomial list. (defun math-build-polynomial-expr (p var) + "Build an expression from a polynomial list." (if p (if (Math-numberp var) (math-with-extra-prec 1 @@ -1897,8 +1890,7 @@ accum)) (let* ((rp (reverse p)) (n (1- (length rp))) - (accum (math-mul (car rp) (math-pow var n))) - term) + (accum (math-mul (car rp) (math-pow var n)))) (while (setq rp (cdr rp)) (setq n (1- n)) (or (math-zerop (car rp)) |