;;; Code:
;; This file is autoloaded from calc-ext.el.
-(require 'calc-ext)
+(require 'calc-ext)
(require 'calc-macs)
-(defun calc-Need-calc-poly () nil)
-
-
(defun calcFunc-pcont (expr &optional var)
(cond ((Math-primp expr)
(cond ((Math-zerop expr) 1)
;;; 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)
(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))
(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))
(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)))
(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)
(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)))))))
(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)
(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)
(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))))
(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.
(defun calcFunc-expandpow (x n)
(math-normalize (math-expand-power x n)))
+(provide 'calc-poly)
+
;;; arch-tag: d2566c51-2ccc-45f1-8c50-f3462c2953ff
;;; calc-poly.el ends here