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(math-poly-base-top-expr): New variable.

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(math-polynomial-p1): Replace variable mpb-top-expr by declared
variable.
(math-poly-base-total-base): New variable.
(math-total-polynomial-base, math-polynomial-p1): Replace variable
mpb-total-base by declared variable.
(math-factored-vars, math-to-list): Declare it.
(math-fact-expr): New variable.
(calcFunc-factors, calcFunc-factor, math-factor-expr,
math-factor-expr-try, math-factor-expr-part): Replace variable expr by
declared variable.
(math-fet-x): New variable.
(math-factor-expr-try, math-factor-poly-coefs): Replace variable x by
declared variable.
(math-factor-poly-coefs): Make temp a local variable.
This commit is contained in:
Jay Belanger 2004-11-25 05:52:38 +00:00
parent 885e6671fc
commit 4fd1fc35b1
1 changed files with 74 additions and 45 deletions
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119
lisp/calc/calc-poly.el
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@ -516,48 +516,72 @@
;;; Given an expression find all variables that are polynomial bases.
;;; Return list in the form '( (var1 degree1) (var2 degree2) ... ).
;;; Note dynamic scope of mpb-total-base.
;; The variable math-poly-base-total-base is local to
;; math-total-polynomial-base, but is used by math-polynomial-p1,
;; which is called by math-total-polynomial-base.
(defvar math-poly-base-total-base)
(defun math-total-polynomial-base (expr)
(let ((mpb-total-base nil))
(let ((math-poly-base-total-base nil))
(math-polynomial-base expr 'math-polynomial-p1)
(math-sort-poly-base-list mpb-total-base)))
(math-sort-poly-base-list math-poly-base-total-base)))
;; The variable math-poly-base-top-expr is local to math-polynomial-base
;; in calc-alg.el, but is used by math-polynomial-p1 which is called
;; by math-polynomial-base.
(defvar math-poly-base-top-expr)
(defun math-polynomial-p1 (subexpr)
(or (assoc subexpr mpb-total-base)
(or (assoc subexpr math-poly-base-total-base)
(memq (car subexpr) '(+ - * / neg))
(and (eq (car subexpr) '^) (natnump (nth 2 subexpr)))
(let* ((math-poly-base-variable subexpr)
(exponent (math-polynomial-p mpb-top-expr subexpr)))
(exponent (math-polynomial-p math-poly-base-top-expr subexpr)))
(if exponent
(setq mpb-total-base (cons (list subexpr exponent)
mpb-total-base)))))
(setq math-poly-base-total-base (cons (list subexpr exponent)
math-poly-base-total-base)))))
nil)
;; The variable math-factored-vars is local to calcFunc-factors and
;; calcFunc-factor, but is used by math-factor-expr and
;; math-factor-expr-part, which are called (directly and indirectly) by
;; calcFunc-factor and calcFunc-factors.
(defvar math-factored-vars)
;; The variable math-fact-expr is local to calcFunc-factors,
;; calcFunc-factor and math-factor-expr, but is used by math-factor-expr-try
;; and math-factor-expr-part, which are called (directly and indirectly) by
;; calcFunc-factor, calcFunc-factors and math-factor-expr.
(defvar math-fact-expr)
;; The variable math-to-list is local to calcFunc-factors and
;; calcFunc-factor, but is used by math-accum-factors, which is
;; called (indirectly) by calcFunc-factors and calcFunc-factor.
(defvar math-to-list)
(defun calcFunc-factors (expr &optional var)
(defun calcFunc-factors (math-fact-expr &optional var)
(let ((math-factored-vars (if var t nil))
(math-to-list t)
(calc-prefer-frac t))
(or var
(setq var (math-polynomial-base expr)))
(setq var (math-polynomial-base math-fact-expr)))
(let ((res (math-factor-finish
(or (catch 'factor (math-factor-expr-try var))
expr))))
math-fact-expr))))
(math-simplify (if (math-vectorp res)
res
(list 'vec (list 'vec res 1)))))))
(defun calcFunc-factor (expr &optional var)
(defun calcFunc-factor (math-fact-expr &optional var)
(let ((math-factored-vars nil)
(math-to-list nil)
(calc-prefer-frac t))
(math-simplify (math-factor-finish
(if var
(let ((math-factored-vars t))
(or (catch 'factor (math-factor-expr-try var)) expr))
(math-factor-expr expr))))))
(or (catch 'factor (math-factor-expr-try var)) math-fact-expr))
(math-factor-expr math-fact-expr))))))
(defun math-factor-finish (x)
(if (Math-primp x)
@ -571,18 +595,18 @@
(list 'calcFunc-Fac-Prot x)
x))
(defun math-factor-expr (expr)
(cond ((eq math-factored-vars t) expr)
((or (memq (car-safe expr) '(* / ^ neg))
(assq (car-safe expr) calc-tweak-eqn-table))
(cons (car expr) (mapcar 'math-factor-expr (cdr expr))))
((memq (car-safe expr) '(+ -))
(defun math-factor-expr (math-fact-expr)
(cond ((eq math-factored-vars t) math-fact-expr)
((or (memq (car-safe math-fact-expr) '(* / ^ neg))
(assq (car-safe math-fact-expr) calc-tweak-eqn-table))
(cons (car math-fact-expr) (mapcar 'math-factor-expr (cdr math-fact-expr))))
((memq (car-safe math-fact-expr) '(+ -))
(let* ((math-factored-vars math-factored-vars)
(y (catch 'factor (math-factor-expr-part expr))))
(y (catch 'factor (math-factor-expr-part math-fact-expr))))
(if y
(math-factor-expr y)
expr)))
(t expr)))
math-fact-expr)))
(t math-fact-expr)))
(defun math-factor-expr-part (x) ; uses "expr"
(if (memq (car-safe x) '(+ - * / ^ neg))
@ -590,21 +614,25 @@
(math-factor-expr-part (car x)))
(and (not (Math-objvecp x))
(not (assoc x math-factored-vars))
(> (math-factor-contains expr x) 1)
(> (math-factor-contains math-fact-expr x) 1)
(setq math-factored-vars (cons (list x) math-factored-vars))
(math-factor-expr-try x))))
(defun math-factor-expr-try (x)
(if (eq (car-safe expr) '*)
(let ((res1 (catch 'factor (let ((expr (nth 1 expr)))
(math-factor-expr-try x))))
(res2 (catch 'factor (let ((expr (nth 2 expr)))
(math-factor-expr-try x)))))
;; The variable math-fet-x is local to math-factor-expr-try, but is
;; used by math-factor-poly-coefs, which is called by math-factor-expr-try.
(defvar math-fet-x)
(defun math-factor-expr-try (math-fet-x)
(if (eq (car-safe math-fact-expr) '*)
(let ((res1 (catch 'factor (let ((math-fact-expr (nth 1 math-fact-expr)))
(math-factor-expr-try math-fet-x))))
(res2 (catch 'factor (let ((math-fact-expr (nth 2 math-fact-expr)))
(math-factor-expr-try math-fet-x)))))
(and (or res1 res2)
(throw 'factor (math-accum-factors (or res1 (nth 1 expr)) 1
(or res2 (nth 2 expr))))))
(let* ((p (math-is-polynomial expr x 30 'gen))
(math-poly-modulus (math-poly-modulus expr))
(throw 'factor (math-accum-factors (or res1 (nth 1 math-fact-expr)) 1
(or res2 (nth 2 math-fact-expr))))))
(let* ((p (math-is-polynomial math-fact-expr math-fet-x 30 'gen))
(math-poly-modulus (math-poly-modulus math-fact-expr))
res)
(and (cdr p)
(setq res (math-factor-poly-coefs p))
@ -642,11 +670,11 @@
(math-mul (math-pow fac pow) facs)))
(defun math-factor-poly-coefs (p &optional square-free) ; uses "x"
(let (t1 t2)
(let (t1 t2 temp)
(cond ((not (cdr p))
(or (car p) 0))
;; Strip off multiples of x.
;; Strip off multiples of math-fet-x.
((Math-zerop (car p))
(let ((z 0))
(while (and p (Math-zerop (car p)))
@ -654,7 +682,7 @@
(if (cdr p)
(setq p (math-factor-poly-coefs p square-free))
(setq p (math-sort-terms (math-factor-expr (car p)))))
(math-accum-factors x z (math-factor-protect p))))
(math-accum-factors math-fet-x z (math-factor-protect p))))
;; Factor out content.
((and (not square-free)
@ -665,12 +693,12 @@
(math-accum-factors t1 1 (math-factor-poly-coefs
(math-poly-div-list p t1) 'cont)))
;; Check if linear in x.
;; Check if linear in math-fet-x.
((not (cdr (cdr p)))
(math-add (math-factor-protect
(math-sort-terms
(math-factor-expr (car p))))
(math-mul x (math-factor-protect
(math-mul math-fet-x (math-factor-protect
(math-sort-terms
(math-factor-expr (nth 1 p)))))))
@ -683,7 +711,7 @@
(setq pp (cdr pp)))
pp)
(let ((res (math-rewrite
(list 'calcFunc-thecoefs x (cons 'vec p))
(list 'calcFunc-thecoefs math-fet-x (cons 'vec p))
'(var FactorRules var-FactorRules))))
(or (and (eq (car-safe res) 'calcFunc-thefactors)
(= (length res) 3)
@ -693,7 +721,7 @@
(while (setq vec (cdr vec))
(setq facs (math-accum-factors (car vec) 1 facs)))
facs))
(math-build-polynomial-expr p x))))
(math-build-polynomial-expr p math-fet-x))))
;; Check if rational coefficients (i.e., not modulo a prime).
((eq math-poly-modulus 1)
@ -724,12 +752,13 @@
(setq scale (math-div scale den))
(math-add
(math-add
(math-mul den (math-pow x 2))
(math-mul (math-mul coef1 den) x))
(math-mul den (math-pow math-fet-x 2))
(math-mul (math-mul coef1 den)
math-fet-x))
(math-mul coef0 den)))
(let ((den (math-lcm-denoms coef0)))
(setq scale (math-div scale den))
(math-add (math-mul den x)
(math-add (math-mul den math-fet-x)
(math-mul coef0 den))))
1 expr)
roots (cdr roots))))
@ -738,8 +767,8 @@
(math-mul csign
(math-build-polynomial-expr
(math-mul-list (nth 1 t1) scale)
x)))))
(math-build-polynomial-expr p x)) ; can't factor it.
math-fet-x)))))
(math-build-polynomial-expr p math-fet-x)) ; can't factor it.
;; Separate out the squared terms (Knuth exercise 4.6.2-34).
;; This step also divides out the content of the polynomial.