Initial import of Calc 2.02f.

1 files changed, 1699 insertions, 0 deletions

diff --git a/lisp/calc/calc-alg.el b/lisp/calc/calc-alg.el
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+;; Calculator for GNU Emacs, part II [calc-alg.el]
+;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
+;; Written by Dave Gillespie, [email protected].
+
+;; This file is part of GNU Emacs.
+
+;; GNU Emacs is distributed in the hope that it will be useful,
+;; but WITHOUT ANY WARRANTY.  No author or distributor
+;; accepts responsibility to anyone for the consequences of using it
+;; or for whether it serves any particular purpose or works at all,
+;; unless he says so in writing.  Refer to the GNU Emacs General Public
+;; License for full details.
+
+;; Everyone is granted permission to copy, modify and redistribute
+;; GNU Emacs, but only under the conditions described in the
+;; GNU Emacs General Public License.   A copy of this license is
+;; supposed to have been given to you along with GNU Emacs so you
+;; can know your rights and responsibilities.  It should be in a
+;; file named COPYING.  Among other things, the copyright notice
+;; and this notice must be preserved on all copies.
+
+
+
+;; This file is autoloaded from calc-ext.el.
+(require 'calc-ext)
+
+(require 'calc-macs)
+
+(defun calc-Need-calc-alg () nil)
+
+
+;;; Algebra commands.
+
+(defun calc-alg-evaluate (arg)
+  (interactive "p")
+  (calc-slow-wrapper
+   (calc-with-default-simplification
+    (let ((math-simplify-only nil))
+      (calc-modify-simplify-mode arg)
+      (calc-enter-result 1 "dsmp" (calc-top 1)))))
+)
+
+(defun calc-modify-simplify-mode (arg)
+  (if (= (math-abs arg) 2)
+      (setq calc-simplify-mode 'alg)
+    (if (>= (math-abs arg) 3)
+	(setq calc-simplify-mode 'ext)))
+  (if (< arg 0)
+      (setq calc-simplify-mode (list calc-simplify-mode)))
+)
+
+(defun calc-simplify ()
+  (interactive)
+  (calc-slow-wrapper
+   (calc-with-default-simplification
+    (calc-enter-result 1 "simp" (math-simplify (calc-top-n 1)))))
+)
+
+(defun calc-simplify-extended ()
+  (interactive)
+  (calc-slow-wrapper
+   (calc-with-default-simplification
+    (calc-enter-result 1 "esmp" (math-simplify-extended (calc-top-n 1)))))
+)
+
+(defun calc-expand-formula (arg)
+  (interactive "p")
+  (calc-slow-wrapper
+   (calc-with-default-simplification
+    (let ((math-simplify-only nil))
+      (calc-modify-simplify-mode arg)
+      (calc-enter-result 1 "expf" 
+			 (if (> arg 0)
+			     (let ((math-expand-formulas t))
+			       (calc-top-n 1))
+			   (let ((top (calc-top-n 1)))
+			     (or (math-expand-formula top)
+				 top)))))))
+)
+
+(defun calc-factor (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (calc-unary-op "fctr" (if (calc-is-hyperbolic)
+			     'calcFunc-factors 'calcFunc-factor)
+		  arg))
+)
+
+(defun calc-expand (n)
+  (interactive "P")
+  (calc-slow-wrapper
+   (calc-enter-result 1 "expa"
+		      (append (list 'calcFunc-expand
+				    (calc-top-n 1))
+			      (and n (list (prefix-numeric-value n))))))
+)
+
+(defun calc-collect (&optional var)
+  (interactive "sCollect terms involving: ")
+  (calc-slow-wrapper
+   (if (or (equal var "") (equal var "$") (null var))
+       (calc-enter-result 2 "clct" (cons 'calcFunc-collect
+					 (calc-top-list-n 2)))
+     (let ((var (math-read-expr var)))
+       (if (eq (car-safe var) 'error)
+	   (error "Bad format in expression: %s" (nth 1 var)))
+       (calc-enter-result 1 "clct" (list 'calcFunc-collect
+					 (calc-top-n 1)
+					 var)))))
+)
+
+(defun calc-apart (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (calc-unary-op "aprt" 'calcFunc-apart arg))
+)
+
+(defun calc-normalize-rat (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (calc-unary-op "nrat" 'calcFunc-nrat arg))
+)
+
+(defun calc-poly-gcd (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (calc-binary-op "pgcd" 'calcFunc-pgcd arg))
+)
+
+(defun calc-poly-div (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (setq calc-poly-div-remainder nil)
+   (calc-binary-op "pdiv" 'calcFunc-pdiv arg)
+   (if (and calc-poly-div-remainder (null arg))
+       (progn
+	 (calc-clear-command-flag 'clear-message)
+	 (calc-record calc-poly-div-remainder "prem")
+	 (if (not (Math-zerop calc-poly-div-remainder))
+	     (message "(Remainder was %s)"
+		      (math-format-flat-expr calc-poly-div-remainder 0))
+	   (message "(No remainder)")))))
+)
+
+(defun calc-poly-rem (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (calc-binary-op "prem" 'calcFunc-prem arg))
+)
+
+(defun calc-poly-div-rem (arg)
+  (interactive "P")
+  (calc-slow-wrapper
+   (if (calc-is-hyperbolic)
+       (calc-binary-op "pdvr" 'calcFunc-pdivide arg)
+     (calc-binary-op "pdvr" 'calcFunc-pdivrem arg)))
+)
+
+(defun calc-substitute (&optional oldname newname)
+  (interactive "sSubstitute old: ")
+  (calc-slow-wrapper
+   (let (old new (num 1) expr)
+     (if (or (equal oldname "") (equal oldname "$") (null oldname))
+	 (setq new (calc-top-n 1)
+	       old (calc-top-n 2)
+	       expr (calc-top-n 3)
+	       num 3)
+       (or newname
+	   (progn (calc-unread-command ?\C-a)
+		  (setq newname (read-string (concat "Substitute old: "
+						     oldname
+						     ", new: ")
+					     oldname))))
+       (if (or (equal newname "") (equal newname "$") (null newname))
+	   (setq new (calc-top-n 1)
+		 expr (calc-top-n 2)
+		 num 2)
+	 (setq new (if (stringp newname) (math-read-expr newname) newname))
+	 (if (eq (car-safe new) 'error)
+	     (error "Bad format in expression: %s" (nth 1 new)))
+	 (setq expr (calc-top-n 1)))
+       (setq old (if (stringp oldname) (math-read-expr oldname) oldname))
+       (if (eq (car-safe old) 'error)
+	   (error "Bad format in expression: %s" (nth 1 old)))
+       (or (math-expr-contains expr old)
+	   (error "No occurrences found.")))
+     (calc-enter-result num "sbst" (math-expr-subst expr old new))))
+)
+
+
+(defun calc-has-rules (name)
+  (setq name (calc-var-value name))
+  (and (consp name)
+       (memq (car name) '(vec calcFunc-assign calcFunc-condition))
+       name)
+)
+
+(defun math-recompile-eval-rules ()
+  (setq math-eval-rules-cache (and (calc-has-rules 'var-EvalRules)
+				   (math-compile-rewrites
+				    '(var EvalRules var-EvalRules)))
+	math-eval-rules-cache-other (assq nil math-eval-rules-cache)
+	math-eval-rules-cache-tag (calc-var-value 'var-EvalRules))
+)
+
+
+;;; Try to expand a formula according to its definition.
+(defun math-expand-formula (expr)
+  (and (consp expr)
+       (symbolp (car expr))
+       (or (get (car expr) 'calc-user-defn)
+	   (get (car expr) 'math-expandable))
+       (let ((res (let ((math-expand-formulas t))
+		    (apply (car expr) (cdr expr)))))
+	 (and (not (eq (car-safe res) (car expr)))
+	      res)))
+)
+
+
+
+
+;;; True if A comes before B in a canonical ordering of expressions.  [P X X]
+(defun math-beforep (a b)   ; [Public]
+  (cond ((and (Math-realp a) (Math-realp b))
+	 (let ((comp (math-compare a b)))
+	   (or (eq comp -1)
+	       (and (eq comp 0)
+		    (not (equal a b))
+		    (> (length (memq (car-safe a)
+				     '(bigneg nil bigpos frac float)))
+		       (length (memq (car-safe b)
+				     '(bigneg nil bigpos frac float))))))))
+	((equal b '(neg (var inf var-inf))) nil)
+	((equal a '(neg (var inf var-inf))) t)
+	((equal a '(var inf var-inf)) nil)
+	((equal b '(var inf var-inf)) t)
+	((Math-realp a)
+	 (if (and (eq (car-safe b) 'intv) (math-intv-constp b))
+	     (if (or (math-beforep a (nth 2 b)) (Math-equal a (nth 2 b)))
+		 t
+	       nil)
+	   t))
+	((Math-realp b)
+	 (if (and (eq (car-safe a) 'intv) (math-intv-constp a))
+	     (if (math-beforep (nth 2 a) b)
+		 t
+	       nil)
+	   nil))
+	((and (eq (car a) 'intv) (eq (car b) 'intv)
+	      (math-intv-constp a) (math-intv-constp b))
+	 (let ((comp (math-compare (nth 2 a) (nth 2 b))))
+	   (cond ((eq comp -1) t)
+		 ((eq comp 1) nil)
+		 ((and (memq (nth 1 a) '(2 3)) (memq (nth 1 b) '(0 1))) t)
+		 ((and (memq (nth 1 a) '(0 1)) (memq (nth 1 b) '(2 3))) nil)
+		 ((eq (setq comp (math-compare (nth 3 a) (nth 3 b))) -1) t)
+		 ((eq comp 1) nil)
+		 ((and (memq (nth 1 a) '(0 2)) (memq (nth 1 b) '(1 3))) t)
+		 (t nil))))
+	((not (eq (not (Math-objectp a)) (not (Math-objectp b))))
+	 (Math-objectp a))
+	((eq (car a) 'var)
+	 (if (eq (car b) 'var)
+	     (string-lessp (symbol-name (nth 1 a)) (symbol-name (nth 1 b)))
+	   (not (Math-numberp b))))
+	((eq (car b) 'var) (Math-numberp a))
+	((eq (car a) (car b))
+	 (while (and (setq a (cdr a) b (cdr b)) a
+		     (equal (car a) (car b))))
+	 (and b
+	      (or (null a)
+		  (math-beforep (car a) (car b)))))
+	(t (string-lessp (symbol-name (car a)) (symbol-name (car b)))))
+)
+
+
+(defun math-simplify-extended (a)
+  (let ((math-living-dangerously t))
+    (math-simplify a))
+)
+(fset 'calcFunc-esimplify (symbol-function '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
+				 (calc-has-rules 'var-ExtSimpRules)
+				 '((var ExtSimpRules var-ExtSimpRules)))
+			    (and math-simplifying-units
+				 (calc-has-rules 'var-UnitSimpRules)
+				 '((var UnitSimpRules var-UnitSimpRules)))
+			    (and math-integrating
+				 (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)
+		top-expr (math-normalize res))
+	  (while r
+	    (setq top-expr (math-rewrite top-expr (car r)
+					 '(neg (var inf var-inf)))
+		  r (cdr r))))
+      (calc-with-default-simplification
+       (while (let ((r simp-rules))
+		(setq res (math-normalize top-expr))
+		(while r
+		  (setq res (math-rewrite res (car r))
+			r (cdr r)))
+		(not (equal top-expr (setq res (math-simplify-step res)))))
+	 (setq top-expr res)))))
+  top-expr
+)
+(fset 'calcFunc-simplify (symbol-function '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.
+(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
+		(cons (car a) (mapcar 'math-simplify-step (cdr a))))))
+      (and (symbolp (car aa))
+	   (let ((handler (get (car aa) 'math-simplify)))
+	     (and handler
+		  (while (and handler
+			      (equal (setq aa (or (funcall (car handler) aa)
+						  aa))
+				     a))
+		    (setq handler (cdr handler))))))
+      aa))
+)
+
+
+(defun math-need-std-simps ()
+  ;; Placeholder, to synchronize autoloading.
+)
+
+(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))
+	     (setq safe (or scalar (math-known-scalarp (nth 1 d) t))
+		   dp (cdr (cdr d))))
+	   (if safe
+	       (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)
+      (if (Math-ratp expr)
+	  (and (not (memq expr '(0 1 -1)))
+	       (math-abs expr))
+	(if (math-ratp (setq expr (math-to-simple-fraction expr)))
+	    (math-common-constant-factor expr)))
+    (if (memq (car expr) '(+ - cplx sdev))
+	(let ((f1 (math-common-constant-factor (nth 1 expr)))
+	      (f2 (math-common-constant-factor (nth 2 expr))))
+	  (and f1 f2
+	       (not (eq (setq f1 (math-frac-gcd f1 f2)) 1))
+	       f1))
+      (if (memq (car expr) '(* polar))
+	  (math-common-constant-factor (nth 1 expr))
+	(if (eq (car expr) '/)
+	    (or (math-common-constant-factor (nth 1 expr))
+		(and (Math-integerp (nth 2 expr))
+		     (list 'frac 1 (math-abs (nth 2 expr)))))))))
+)
+
+(defun math-cancel-common-factor (expr val)
+  (if (memq (car-safe expr) '(+ - cplx sdev))
+      (progn
+	(setcar (cdr expr) (math-cancel-common-factor (nth 1 expr) val))
+	(setcar (cdr (cdr expr)) (math-cancel-common-factor (nth 2 expr) val))
+	expr)
+    (if (eq (car-safe expr) '*)
+	(math-mul (math-cancel-common-factor (nth 1 expr) val) (nth 2 expr))
+      (math-div expr val)))
+)
+
+(defun math-frac-gcd (a b)
+  (if (Math-zerop a)
+      b
+    (if (Math-zerop b)
+	a
+      (if (and (Math-integerp a)
+	       (Math-integerp b))
+	  (math-gcd a b)
+	(and (Math-integerp a) (setq a (list 'frac a 1)))
+	(and (Math-integerp b) (setq b (list 'frac b 1)))
+	(math-make-frac (math-gcd (nth 1 a) (nth 1 b))
+			(math-gcd (nth 2 a) (nth 2 b))))))
+)
+
+(math-defsimplify %
+  (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
+			(list '%
+			      (list '+
+				    (math-mul (math-div (nth 1 lin) t1)
+					      (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))
+      (let ((rplain t)
+	    n d dd 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)
+					   minus (eq (car d) '+) t))
+	      (if (or lplain (eq (math-looks-negp temp) minus))
+		  (progn
+		    (setcar np (setq n (if minus (math-neg temp) temp)))
+		    (setcar (cdr (cdr d)) 0))
+		(progn
+		  (setcar np 0)
+		  (setcar (cdr (cdr d)) (setq n (if (eq (car d) '+)
+						    (math-neg temp)
+						  temp))))))
+	  (setq dp (cdr d)))
+	(if (setq temp (math-combine-sum n d minus t t))
+	    (if (or lplain
+		    (and (not rplain)
+			 (eq (math-looks-negp temp) minus)))
+		(progn
+		  (setcar np (setq n (if minus (math-neg temp) temp)))
+		  (setcar dp 0))
+	      (progn
+		(setcar np 0)
+		(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 '+
+		     (list '* (list 'calcFunc-sin (list '* (1- n) a))
+			   (list 'calcFunc-cos a))
+		     (list '* (list 'calcFunc-cos (list '* (1- n) a))
+			   (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 '-
+		     (list '* (list 'calcFunc-cos (list '* (1- n) a))
+			   (list 'calcFunc-cos a))
+		     (list '* (list 'calcFunc-sin (list '* (1- n) a))
+			   (list 'calcFunc-sin a)))))))
+)
+
+(defun math-should-expand-trig (x &optional hyperbolic)
+  (let ((m (math-is-multiple x)))
+    (and math-living-dangerously
+	 m (or (and (integerp (car m)) (> (car m) 1))
+	       (equal (car m) '(frac 1 2)))
+	 (or math-integrating
+	     (memq (car-safe (nth 1 m))
+		   (if hyperbolic
+		       '(calcFunc-arcsinh calcFunc-arccosh calcFunc-arctanh)
+		     '(calcFunc-arcsin calcFunc-arccos calcFunc-arctan)))
+	     (and (eq (car-safe (nth 1 m)) 'calcFunc-ln)
+		  (eq hyperbolic 'exp)))
+	 m))
+)
+
+(defun math-known-sin (plus n mul off)
+  (setq n (math-mul n mul))
+  (and (math-num-integerp n)
+       (setq n (math-mod (math-add (math-trunc n) off) 240))
+       (if (>= n 120)
+	   (and (setq n (math-known-sin plus (- n 120) 1 0))
+		(math-neg n))
+	 (if (> n 60)
+	     (setq n (- 120 n)))
+	 (if (math-zerop plus)
+	     (and (or calc-symbolic-mode
+		      (memq n '(0 20 60)))
+		  (cdr (assq n
+			     '( (0 . 0)
+				(10 . (/ (calcFunc-sqrt
+					  (- 2 (calcFunc-sqrt 3))) 2))
+				(12 . (/ (- (calcFunc-sqrt 5) 1) 4))
+				(15 . (/ (calcFunc-sqrt
+					  (- 2 (calcFunc-sqrt 2))) 2))
+				(20 . (/ 1 2))
+				(24 . (* (^ (/ 1 2) (/ 3 2))
+					 (calcFunc-sqrt
+					  (- 5 (calcFunc-sqrt 5)))))
+				(30 . (/ (calcFunc-sqrt 2) 2))
+				(36 . (/ (+ (calcFunc-sqrt 5) 1) 4))
+				(40 . (/ (calcFunc-sqrt 3) 2))
+				(45 . (/ (calcFunc-sqrt
+					  (+ 2 (calcFunc-sqrt 2))) 2))
+				(48 . (* (^ (/ 1 2) (/ 3 2))
+					 (calcFunc-sqrt
+					  (+ 5 (calcFunc-sqrt 5)))))
+				(50 . (/ (calcFunc-sqrt
+					  (+ 2 (calcFunc-sqrt 3))) 2))
+				(60 . 1)))))
+	   (cond ((eq n 0) (math-normalize (list 'calcFunc-sin plus)))
+		 ((eq n 60) (math-normalize (list 'calcFunc-cos plus)))
+		 (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))
+  (and (math-num-integerp n)
+       (setq n (math-mod (math-trunc n) 120))
+       (if (> n 60)
+	   (and (setq n (math-known-tan plus (- 120 n) 1))
+		(math-neg n))
+	 (if (math-zerop plus)
+	     (and (or calc-symbolic-mode
+		      (memq n '(0 30 60)))
+		  (cdr (assq n '( (0 . 0)
+				  (10 . (- 2 (calcFunc-sqrt 3)))
+				  (12 . (calcFunc-sqrt
+					 (- 1 (* (/ 2 5) (calcFunc-sqrt 5)))))
+				  (15 . (- (calcFunc-sqrt 2) 1))
+				  (20 . (/ (calcFunc-sqrt 3) 3))
+				  (24 . (calcFunc-sqrt
+					 (- 5 (* 2 (calcFunc-sqrt 5)))))
+				  (30 . 1)
+				  (36 . (calcFunc-sqrt
+					 (+ 1 (* (/ 2 5) (calcFunc-sqrt 5)))))
+				  (40 . (calcFunc-sqrt 3))
+				  (45 . (+ (calcFunc-sqrt 2) 1))
+				  (48 . (calcFunc-sqrt
+					 (+ 5 (* 2 (calcFunc-sqrt 5)))))
+				  (50 . (+ 2 (calcFunc-sqrt 3)))
+				  (60 . (var uinf var-uinf))))))
+	   (cond ((eq n 0) (math-normalize (list 'calcFunc-tan plus)))
+		 ((eq n 60) (math-normalize (list '/ -1
+						  (list 'calcFunc-tan plus))))
+		 (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)
+		   (list '+
+			 (list '* (list 'calcFunc-sinh (list '* (1- n) a))
+			       (list 'calcFunc-cosh a))
+			 (list '* (list 'calcFunc-cosh (list '* (1- n) a))
+			       (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)
+		   (list '+
+			 (list '* (list 'calcFunc-cosh (list '* (1- n) a))
+			       (list 'calcFunc-cosh a))
+			 (list '* (list 'calcFunc-sinh (list '* (1- n) a))
+			       (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)
+			   (or (and (eq (car-safe (nth 1 a)) 'calcFunc-sinh)
+				    (list 'calcFunc-cosh (nth 1 (nth 1 a))))
+			       (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))
+			   (let ((out 1) (rest 1) (sums 1) fac pow)
+			     (while (setq f (cdr f))
+			       (setq fac (nth 1 (car f))
+				     pow (nth 2 (car f)))
+			       (if (> pow 1)
+				   (setq out (math-mul out (math-pow
+							    fac (/ pow 2)))
+					 pow (% pow 2)))
+			       (if (> pow 0)
+				   (if (memq (car-safe fac) '(+ -))
+				       (setq sums (math-mul-thru sums fac))
+				     (setq rest (math-mul rest fac)))))
+			     (and (not (and (eq out 1) (memq rest '(1 -1))))
+				  (math-mul
+				   out
+				   (list 'calcFunc-sqrt
+					 (math-mul sums rest)))))))))))
+)
+
+;;; Rather than factoring x into primes, just check for the first ten primes.
+(defun math-squared-factor (x)
+  (if (Math-integerp x)
+      (let ((prsqr '(4 9 25 49 121 169 289 361 529 841))
+	    (fac 1)
+	    res)
+	(while prsqr
+	  (if (eq (cdr (setq res (math-idivmod x (car prsqr)))) 0)
+	      (setq x (car res)
+		    fac (math-mul fac (car prsqr)))
+	    (setq prsqr (cdr prsqr))))
+	fac))
+)
+
+(math-defsimplify calcFunc-exp
+  (math-simplify-exp (nth 1 expr))
+)
+
+(defun math-simplify-exp (x)
+  (or (and (eq (car-safe x) 'calcFunc-ln)
+	   (nth 1 x))
+      (and math-living-dangerously
+	   (or (and (eq (car-safe x) 'calcFunc-arcsinh)
+		    (math-add (nth 1 x)
+			      (list 'calcFunc-sqrt
+				    (math-add (math-sqr (nth 1 x)) 1))))
+	       (and (eq (car-safe x) 'calcFunc-arccosh)
+		    (math-add (nth 1 x)
+			      (list 'calcFunc-sqrt
+				    (math-sub (math-sqr (nth 1 x)) 1))))
+	       (and (eq (car-safe x) 'calcFunc-arctanh)
+		    (math-div (list 'calcFunc-sqrt (math-add 1 (nth 1 x)))
+			      (list 'calcFunc-sqrt (math-sub 1 (nth 1 x)))))
+	       (let ((m (math-should-expand-trig x 'exp)))
+		 (and m (integerp (car m))
+		      (list '^ (list 'calcFunc-exp (nth 1 m)) (car m))))))
+      (and calc-symbolic-mode
+	   (math-known-imagp x)
+	   (let* ((ip (calcFunc-im x))
+		  (n (math-linear-in ip '(var pi var-pi)))
+		  s c)
+	     (and n
+		  (setq s (math-known-sin (car n) (nth 1 n) 120 0))
+		  (setq c (math-known-sin (car n) (nth 1 n) 120 300))
+		  (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)))
+      (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)
+				'(/ (* (var pi var-pi) (var i var-i)) 2)))
+		 (and (memq ips '(1 3))
+		      (math-sub (list 'calcFunc-ln (math-neg ip))
+				'(/ (* (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 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)
+  (if (math-expr-contains expr term)
+      (let* ((calc-prefer-frac t)
+	     (p (math-is-polynomial expr term 1)))
+	(and (cdr p)
+	     p))
+    (and always (list expr 0)))
+)
+
+(defun math-multiple-of (expr term)
+  (let ((p (math-linear-in expr term)))
+    (and p
+	 (math-zerop (car p))
+	 (nth 1 p)))
+)
+
+(defun math-integer-plus (expr)
+  (cond ((Math-integerp expr)
+	 (list 0 expr))
+	((and (memq (car expr) '(+ -))
+	      (Math-integerp (nth 1 expr)))
+	 (list (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr)))
+	       (nth 1 expr)))
+	((and (memq (car expr) '(+ -))
+	      (Math-integerp (nth 2 expr)))
+	 (list (nth 1 expr)
+	       (if (eq (car expr) '+) (nth 2 expr) (math-neg (nth 2 expr)))))
+	(t nil))   ; not perfect, but it'll do
+)
+
+(defun math-is-linear (expr &optional always)
+  (let ((offset nil)
+	(coef nil))
+    (if (eq (car-safe expr) '+)
+	(if (Math-objectp (nth 1 expr))
+	    (setq offset (nth 1 expr)
+		  expr (nth 2 expr))
+	  (if (Math-objectp (nth 2 expr))
+	      (setq offset (nth 2 expr)
+		    expr (nth 1 expr))))
+      (if (eq (car-safe expr) '-)
+	  (if (Math-objectp (nth 1 expr))
+	      (setq offset (nth 1 expr)
+		    expr (math-neg (nth 2 expr)))
+	    (if (Math-objectp (nth 2 expr))
+		(setq offset (math-neg (nth 2 expr))
+		      expr (nth 1 expr))))))
+    (setq coef (math-is-multiple expr always))
+    (if offset
+	(list offset (or (car coef) 1) (or (nth 1 coef) expr))
+      (if coef
+	  (cons 0 coef))))
+)
+
+(defun math-is-multiple (expr &optional always)
+  (or (if (eq (car-safe expr) '*)
+	  (if (Math-objectp (nth 1 expr))
+	      (list (nth 1 expr) (nth 2 expr)))
+	(if (eq (car-safe expr) '/)
+	    (if (and (Math-objectp (nth 1 expr))
+		     (not (math-equal-int (nth 1 expr) 1)))
+		(list (nth 1 expr) (math-div 1 (nth 2 expr)))
+	      (if (Math-objectp (nth 2 expr))
+		  (list (math-div 1 (nth 2 expr)) (nth 1 expr))
+		(let ((res (math-is-multiple (nth 1 expr))))
+		  (if res
+		      (list (car res)
+			    (math-div (nth 2 (nth 1 expr)) (nth 2 expr)))
+		    (setq res (math-is-multiple (nth 2 expr)))
+		    (if res
+			(list (math-div 1 (car res))
+			      (math-div (nth 1 expr)
+					(nth 2 (nth 2 expr)))))))))
+	  (if (eq (car-safe expr) 'neg)
+	      (list -1 (nth 1 expr)))))
+      (if (Math-objvecp expr)
+	  (and (eq always 1)
+	       (list expr 1))
+	(and always 
+	     (list 1 expr))))
+)
+
+(defun calcFunc-lin (expr &optional var)
+  (if var
+      (let ((res (math-linear-in expr var t)))
+	(or res (math-reject-arg expr "Linear term expected"))
+	(list 'vec (car res) (nth 1 res) var))
+    (let ((res (math-is-linear expr t)))
+      (or res (math-reject-arg expr "Linear term expected"))
+      (cons 'vec res)))
+)
+
+(defun calcFunc-linnt (expr &optional var)
+  (if var
+      (let ((res (math-linear-in expr var)))
+	(or res (math-reject-arg expr "Linear term expected"))
+	(list 'vec (car res) (nth 1 res) var))
+    (let ((res (math-is-linear expr)))
+      (or res (math-reject-arg expr "Linear term expected"))
+      (cons 'vec res)))
+)
+
+(defun calcFunc-islin (expr &optional var)
+  (if (and (Math-objvecp expr) (not var))
+      0
+    (calcFunc-lin expr var)
+    1)
+)
+
+(defun calcFunc-islinnt (expr &optional var)
+  (if (Math-objvecp expr)
+      0
+    (calcFunc-linnt expr var)
+    1)
+)
+
+
+
+
+;;; Simple operations on expressions.
+
+;;; Return number of ocurrences of thing in expr, or nil if none.
+(defun math-expr-contains-count (expr thing)
+  (cond ((equal expr thing) 1)
+	((Math-primp expr) nil)
+	(t
+	 (let ((num 0))
+	   (while (setq expr (cdr expr))
+	     (setq num (+ num (or (math-expr-contains-count
+				   (car expr) thing) 0))))
+	   (and (> num 0)
+		num))))
+)
+
+(defun math-expr-contains (expr thing)
+  (cond ((equal expr thing) 1)
+	((Math-primp expr) nil)
+	(t
+	 (while (and (setq expr (cdr expr))
+		     (not (math-expr-contains (car expr) thing))))
+	 expr))
+)
+
+;;; Return non-nil if any variable of thing occurs in expr.
+(defun math-expr-depends (expr thing)
+  (if (Math-primp thing)
+      (and (eq (car-safe thing) 'var)
+	   (math-expr-contains expr thing))
+    (while (and (setq thing (cdr thing))
+		(not (math-expr-depends expr (car thing)))))
+    thing)
+)
+
+;;; Substitute all occurrences of old for new in expr (non-destructive).
+(defun math-expr-subst (expr old new)
+  (math-expr-subst-rec expr)
+)
+(fset 'calcFunc-subst (symbol-function '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)))))
+	(t
+	 (cons (car expr)
+	       (mapcar 'math-expr-subst-rec (cdr expr)))))
+)
+
+;;; Various measures of the size of an expression.
+(defun math-expr-weight (expr)
+  (if (Math-primp expr)
+      1
+    (let ((w 1))
+      (while (setq expr (cdr expr))
+	(setq w (+ w (math-expr-weight (car expr)))))
+      w))
+)
+
+(defun math-expr-height (expr)
+  (if (Math-primp expr)
+      0
+    (let ((h 0))
+      (while (setq expr (cdr expr))
+	(setq h (max h (math-expr-height (car expr)))))
+      (1+ h)))
+)
+
+
+
+
+;;; Polynomial operations (to support the integrator and solve-for).
+
+(defun calcFunc-collect (expr base)
+  (let ((p (math-is-polynomial expr base 50 t)))
+    (if (cdr p)
+	(math-normalize   ; fix selection bug
+	 (math-build-polynomial-expr p base))
+      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)
+  (math-poly-simplify
+   (or (cond ((or (equal expr var)
+		  (eq (car-safe expr) '^))
+	      (let ((pow 1)
+		    (expr expr))
+		(or (equal expr var)
+		    (setq pow (nth 2 expr)
+			  expr (nth 1 expr)))
+		(or (eq math-poly-mult-powers 1)
+		    (setq pow (let ((m (math-is-multiple pow 1)))
+				(and (eq (car-safe (car m)) 'cplx)
+				     (Math-zerop (nth 1 (car m)))
+				     (setq m (list (nth 2 (car m))
+						   (math-mul (nth 1 m)
+							     '(var i var-i)))))
+				(and (if math-poly-mult-powers
+					 (equal math-poly-mult-powers
+						(nth 1 m))
+				       (setq math-poly-mult-powers (nth 1 m)))
+				     (or (equal expr var)
+					 (eq math-poly-mult-powers 1))
+				     (car m)))))
+		(if (consp pow)
+		    (progn
+		      (setq pow (math-to-simple-fraction pow))
+		      (and (eq (car-safe pow) 'frac)
+			   math-poly-frac-powers
+			   (equal expr var)
+			   (setq math-poly-frac-powers
+				 (calcFunc-lcm math-poly-frac-powers
+					       (nth 2 pow))))))
+		(or (memq math-poly-frac-powers '(1 nil))
+		    (setq pow (math-mul pow math-poly-frac-powers)))
+		(if (integerp pow)
+		    (if (and (= pow 1)
+			     (equal expr var))
+			(list 0 1)
+		      (if (natnump pow)
+			  (let ((p1 (if (equal expr var)
+					(list 0 1)
+				      (math-is-poly-rec expr nil)))
+				(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)
+					   n (1- n)))
+				   accum)))
+			(and negpow
+			     (math-is-poly-rec expr nil)
+			     (setq math-poly-neg-powers
+				   (cons (math-pow expr (- pow))
+					 math-poly-neg-powers))
+			     (list (list '^ expr pow))))))))
+	     ((Math-objectp expr)
+	      (list expr))
+	     ((memq (car expr) '(+ -))
+	      (let ((p1 (math-is-poly-rec (nth 1 expr) negpow)))
+		(and p1
+		     (let ((p2 (math-is-poly-rec (nth 2 expr) negpow)))
+		       (and p2
+			    (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)))
+	     ((eq (car expr) '*)
+	      (let ((p1 (math-is-poly-rec (nth 1 expr) negpow)))
+		(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))
+		       (and negpow
+			    (math-is-poly-rec (nth 2 expr) nil)
+			    (setq math-poly-neg-powers
+				  (cons (nth 2 expr) math-poly-neg-powers))))
+		   (not (Math-zerop (nth 2 expr)))
+		   (let ((p1 (math-is-poly-rec (nth 1 expr) negpow)))
+		     (mapcar (function (lambda (x) (math-div x (nth 2 expr))))
+			     p1))))
+	     ((and (eq (car expr) 'calcFunc-exp)
+		   (equal var '(var e var-e)))
+	      (math-is-poly-rec (list '^ var (nth 1 expr)) negpow))
+	     ((and (eq (car expr) 'calcFunc-sqrt)
+		   math-poly-frac-powers)
+	      (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))))
+)
+
+;;; Check if expr is a polynomial in var; if so, return its degree.
+(defun math-polynomial-p (expr var)
+  (cond ((equal expr var) 1)
+	((Math-primp expr) 0)
+	((memq (car expr) '(+ -))
+	 (let ((p1 (math-polynomial-p (nth 1 expr) var))
+	       p2)
+	   (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var))
+		(max p1 p2))))
+	((eq (car expr) '*)
+	 (let ((p1 (math-polynomial-p (nth 1 expr) var))
+	       p2)
+	   (and p1 (setq p2 (math-polynomial-p (nth 2 expr) var))
+		(+ p1 p2))))
+	((eq (car expr) 'neg)
+	 (math-polynomial-p (nth 1 expr) var))
+	((and (eq (car expr) '/)
+	      (not (math-poly-depends (nth 2 expr) var)))
+	 (math-polynomial-p (nth 1 expr) var))
+	((and (eq (car expr) '^)
+	      (natnump (nth 2 expr)))
+	 (let ((p1 (math-polynomial-p (nth 1 expr) var)))
+	   (and p1 (* p1 (nth 2 expr)))))
+	((math-poly-depends expr var) nil)
+	(t 0))
+)
+
+(defun math-poly-depends (expr var)
+  (if math-poly-base-variable
+      (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.
+(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)
+  (and (not (Math-objvecp mpb-expr))
+       (or (and (memq (car mpb-expr) '(+ - *))
+		(or (math-polynomial-base-rec (nth 1 mpb-expr))
+		    (math-polynomial-base-rec (nth 2 mpb-expr))))
+	   (and (memq (car mpb-expr) '(/ neg))
+		(math-polynomial-base-rec (nth 1 mpb-expr)))
+	   (and (eq (car mpb-expr) '^)
+		(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.
+(defun math-expr-contains-vars (expr)
+  (or (eq (car-safe expr) 'var)
+      (and (not (Math-primp expr))
+	   (progn
+	     (while (and (setq expr (cdr expr))
+			 (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 nonnil->nonnil.
+(defun math-poly-simplify (p)
+  (and p
+       (if (Math-zerop (nth (1- (length p)) p))
+	   (let ((pp (copy-sequence p)))
+	     (while (and (cdr pp)
+			 (Math-zerop (nth (1- (length pp)) pp)))
+	       (setcdr (nthcdr (- (length pp) 2) pp) nil))
+	     pp)
+	 p))
+)
+
+;;; Compute ac*a + bc*b for polynomials in list form a, b and
+;;; coefficients ac, bc.  Result may be unsimplified.
+(defun math-poly-mix (a ac b bc)
+  (and (or a b)
+       (cons (math-add (math-mul (or (car a) 0) ac)
+		       (math-mul (or (car b) 0) bc))
+	     (math-poly-mix (cdr a) ac (cdr b) bc)))
+)
+
+(defun math-poly-zerop (a)
+  (or (null a)
+      (and (null (cdr a)) (Math-zerop (car a))))
+)
+
+;;; Multiply two polynomials in list form.
+(defun math-poly-mul (a b)
+  (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)
+  (if p
+      (if (Math-numberp var)
+	  (math-with-extra-prec 1
+	    (let* ((rp (reverse p))
+		   (accum (car rp)))
+	      (while (setq rp (cdr rp))
+		(setq accum (math-add (car rp) (math-mul accum var))))
+	      accum))
+	(let* ((rp (reverse p))
+	       (n (1- (length rp)))
+	       (accum (math-mul (car rp) (math-pow var n)))
+	       term)
+	  (while (setq rp (cdr rp))
+	    (setq n (1- n))
+	    (or (math-zerop (car rp))
+		(setq accum (list (if (math-looks-negp (car rp)) '- '+)
+				  accum
+				  (math-mul (if (math-looks-negp (car rp))
+						(math-neg (car rp))
+					      (car rp))
+					    (math-pow var n))))))
+	  accum))
+    0)
+)
+
+
+(defun math-to-simple-fraction (f)
+  (or (and (eq (car-safe f) 'float)
+	   (or (and (>= (nth 2 f) 0)
+		    (math-scale-int (nth 1 f) (nth 2 f)))
+	       (and (integerp (nth 1 f))
+		    (> (nth 1 f) -1000)
+		    (< (nth 1 f) 1000)
+		    (math-make-frac (nth 1 f)
+				    (math-scale-int 1 (- (nth 2 f)))))))
+      f)
+)
+