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

(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.

1 files changed, 74 insertions, 45 deletions

diff --git a/lisp/calc/calc-poly.el b/lisp/calc/calc-poly.el
index 8a4b2571d20..28958efaab7 100644
--- a/lisp/calc/calc-poly.el
+++ b/lisp/calc/calc-poly.el
@@ -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.