[Emacs-diffs] Changes to emacs/lisp/calc/calc-poly.el

[Colin Walters]

Index: emacs/lisp/calc/calc-poly.el
diff -u emacs/lisp/calc/calc-poly.el:1.1 emacs/lisp/calc/calc-poly.el:1.2
--- emacs/lisp/calc/calc-poly.el:1.1    Tue Nov  6 13:59:06 2001
+++ emacs/lisp/calc/calc-poly.el        Wed Nov 14 04:06:36 2001
@@ -1,5 +1,5 @@
 ;; Calculator for GNU Emacs, part II [calc-poly.el]
-;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
+;; Copyright (C) 1990, 1991, 1992, 1993, 2001 Free Software Foundation, Inc.
 ;; Written by Dave Gillespie, address@hidden
 
 ;; This file is part of GNU Emacs.
@@ -65,23 +65,20 @@
                   (math-neg (math-poly-gcd cont c2))
                 (math-poly-gcd cont c2))))))
        (var expr)
-       (t 1))
-)
+       (t 1)))
 
 (defun calcFunc-pprim (expr &optional var)
   (let ((cont (calcFunc-pcont expr var)))
     (if (math-equal-int cont 1)
        expr
-      (math-poly-div-exact expr cont var)))
-)
+      (math-poly-div-exact expr cont var))))
 
 (defun math-div-poly-const (expr c)
   (cond ((memq (car-safe expr) '(+ -))
         (list (car expr)
               (math-div-poly-const (nth 1 expr) c)
               (math-div-poly-const (nth 2 expr) c)))
-       (t (math-div expr c)))
-)
+       (t (math-div expr c))))
 
 (defun calcFunc-pdeg (expr &optional var)
   (if (Math-zerop expr)
@@ -89,8 +86,7 @@
     (if var
        (or (math-polynomial-p expr var)
            (math-reject-arg expr "Expected a polynomial"))
-      (math-poly-degree expr)))
-)
+      (math-poly-degree expr))))
 
 (defun math-poly-degree (expr)
   (cond ((Math-primp expr)
@@ -108,8 +104,7 @@
        ((memq (car expr) '(+ -))
         (max (math-poly-degree (nth 1 expr))
              (math-poly-degree (nth 2 expr))))
-       (t 1))
-)
+       (t 1)))
 
 (defun calcFunc-plead (expr var)
   (cond ((eq (car-safe expr) '*)
@@ -128,8 +123,7 @@
         (let ((p (math-is-polynomial expr var)))
           (if (cdr p)
               (nth (1- (length p)) p)
-            1))))
-)
+            1)))))
 
 
 
@@ -149,8 +143,7 @@
       (math-reject-arg pd "Coefficients must be rational"))
   (let ((calc-prefer-frac t)
        (math-poly-modulus (math-poly-modulus pn pd)))
-    (math-poly-gcd pn pd))
-)
+    (math-poly-gcd pn pd)))
 
 ;;; Return only quotient to top of stack (nil if zero)
 (defun calcFunc-pdiv (pn pd &optional base)
@@ -158,29 +151,25 @@
         (math-poly-modulus (math-poly-modulus pn pd))
         (res (math-poly-div pn pd base)))
     (setq calc-poly-div-remainder (cdr res))
-    (car res))
-)
+    (car res)))
 
 ;;; Return only remainder to top of stack
 (defun calcFunc-prem (pn pd &optional base)
   (let ((calc-prefer-frac t)
        (math-poly-modulus (math-poly-modulus pn pd)))
-    (cdr (math-poly-div pn pd base)))
-)
+    (cdr (math-poly-div pn pd base))))
 
 (defun calcFunc-pdivrem (pn pd &optional base)
   (let* ((calc-prefer-frac t)
         (math-poly-modulus (math-poly-modulus pn pd))
         (res (math-poly-div pn pd base)))
-    (list 'vec (car res) (cdr res)))
-)
+    (list 'vec (car res) (cdr res))))
 
 (defun calcFunc-pdivide (pn pd &optional base)
   (let* ((calc-prefer-frac t)
         (math-poly-modulus (math-poly-modulus pn pd))
         (res (math-poly-div pn pd base)))
-    (math-add (car res) (math-div (cdr res) pd)))
-)
+    (math-add (car res) (math-div (cdr res) pd))))
 
 
 ;;; Multiply two terms, expanding out products of sums.
@@ -193,16 +182,14 @@
        (list (car rhs)
              (math-mul-thru lhs (nth 1 rhs))
              (math-mul-thru lhs (nth 2 rhs)))
-      (math-mul lhs rhs)))
-)
+      (math-mul lhs rhs))))
 
 (defun math-div-thru (num den)
   (if (memq (car-safe num) '(+ -))
       (list (car num)
            (math-div-thru (nth 1 num) den)
            (math-div-thru (nth 2 num) den))
-    (math-div num den))
-)
+    (math-div num den)))
 
 
 ;;; Sort the terms of a sum into canonical order.
@@ -211,8 +198,7 @@
       (math-list-to-sum
        (sort (math-sum-to-list expr)
             (function (lambda (a b) (math-beforep (car a) (car b))))))
-    expr)
-)
+    expr))
 
 (defun math-list-to-sum (lst)
   (if (cdr lst)
@@ -221,8 +207,7 @@
            (car (car lst)))
     (if (cdr (car lst))
        (math-neg (car (car lst)))
-      (car (car lst))))
-)
+      (car (car lst)))))
 
 (defun math-sum-to-list (tree &optional neg)
   (cond ((eq (car-safe tree) '+)
@@ -231,39 +216,34 @@
        ((eq (car-safe tree) '-)
         (nconc (math-sum-to-list (nth 1 tree) neg)
                (math-sum-to-list (nth 2 tree) (not neg))))
-       (t (list (cons tree neg))))
-)
+       (t (list (cons tree neg)))))
 
 ;;; Check if the polynomial coefficients are modulo forms.
 (defun math-poly-modulus (expr &optional expr2)
   (or (math-poly-modulus-rec expr)
       (and expr2 (math-poly-modulus-rec expr2))
-      1)
-)
+      1))
 
 (defun math-poly-modulus-rec (expr)
   (if (and (eq (car-safe expr) 'mod) (Math-natnump (nth 2 expr)))
       (list 'mod 1 (nth 2 expr))
     (and (memq (car-safe expr) '(+ - * /))
         (or (math-poly-modulus-rec (nth 1 expr))
-            (math-poly-modulus-rec (nth 2 expr)))))
-)
+            (math-poly-modulus-rec (nth 2 expr))))))
 
 
 ;;; Divide two polynomials.  Return (quotient . remainder).
 (defun math-poly-div (u v &optional math-poly-div-base)
   (if math-poly-div-base
       (math-do-poly-div u v)
-    (math-do-poly-div (calcFunc-expand u) (calcFunc-expand v)))
-)
+    (math-do-poly-div (calcFunc-expand u) (calcFunc-expand v))))
 (setq math-poly-div-base nil)
 
 (defun math-poly-div-exact (u v &optional base)
   (let ((res (math-poly-div u v base)))
     (if (eq (cdr res) 0)
        (car res)
-      (math-reject-arg (list 'vec u v) "Argument is not a polynomial")))
-)
+      (math-reject-arg (list 'vec u v) "Argument is not a polynomial"))))
 
 (defun math-do-poly-div (u v)
   (cond ((math-constp u)
@@ -293,8 +273,7 @@
             (setq up (math-is-polynomial u base nil 'gen)
                   res (math-poly-div-coefs up vp))
             (cons (math-build-polynomial-expr (car res) base)
-                  (math-build-polynomial-expr (cdr res) base))))))
-)
+                  (math-build-polynomial-expr (cdr res) base)))))))
 
 (defun math-poly-div-rec (u v)
   (cond ((math-constp u)
@@ -322,8 +301,7 @@
                   res (math-poly-div-coefs up vp))
             (math-add (math-build-polynomial-expr (car res) base)
                       (math-div (math-build-polynomial-expr (cdr res) base)
-                                v))))))
-)
+                                v)))))))
 
 ;;; Divide two polynomials in coefficient-list form.  Return (quot . rem).
 (defun math-poly-div-coefs (u v)
@@ -349,8 +327,7 @@
           (cons q (nreverse (mapcar 'math-simplify urev)))))
        (t
         (cons (list (math-poly-div-rec (car u) (car v)))
-              nil)))
-)
+              nil))))
 
 ;;; Perform a pseudo-division of polynomials.  (See Knuth section 4.6.1.)
 ;;; This returns only the remainder from the pseudo-division.
@@ -375,8 +352,7 @@
           (while (and urev (Math-zerop (car urev)))
             (setq urev (cdr urev)))
           (nreverse (mapcar 'math-simplify urev))))
-       (t nil))
-)
+       (t nil)))
 
 ;;; Compute the GCD of two multivariate polynomials.
 (defun math-poly-gcd (u v)
@@ -398,16 +374,14 @@
                  (math-poly-gcd-coefs (math-is-polynomial u base nil 'gen)
                                       (math-is-polynomial v base nil 'gen))
                  base)))
-            (calcFunc-gcd (calcFunc-pcont u) (calcFunc-pcont u))))))
-)
+            (calcFunc-gcd (calcFunc-pcont u) (calcFunc-pcont u)))))))
 
 (defun math-poly-div-list (lst a)
   (if (eq a 1)
       lst
     (if (eq a -1)
        (math-mul-list lst a)
-      (mapcar (function (lambda (x) (math-poly-div-exact x a))) lst)))
-)
+      (mapcar (function (lambda (x) (math-poly-div-exact x a))) lst))))
 
 (defun math-mul-list (lst a)
   (if (eq a 1)
@@ -415,8 +389,7 @@
     (if (eq a -1)
        (mapcar 'math-neg lst)
       (and (not (eq a 0))
-          (mapcar (function (lambda (x) (math-mul x a))) lst))))
-)
+          (mapcar (function (lambda (x) (math-mul x a))) lst)))))
 
 ;;; Run GCD on all elements in a list.
 (defun math-poly-gcd-list (lst)
@@ -427,8 +400,7 @@
        (or (eq (car lst) 0)
            (setq gcd (math-poly-gcd gcd (car lst)))))
       (if lst (setq lst (math-poly-gcd-frac-list lst)))
-      gcd))
-)
+      gcd)))
 
 (defun math-poly-gcd-frac-list (lst)
   (while (and lst (not (eq (car-safe (car lst)) 'frac)))
@@ -439,8 +411,7 @@
          (if (eq (car-safe (car lst)) 'frac)
              (setq denom (calcFunc-lcm denom (nth 2 (car lst))))))
        (list 'frac 1 denom))
-    1)
-)
+    1))
 
 ;;; Compute the GCD of two monovariate polynomial lists.
 ;;; Knuth section 4.6.1, algorithm C.
@@ -473,8 +444,7 @@
        (setq v (math-mul-list v -1)))
     (while (>= (setq z (1- z)) 0)
       (setq v (cons 0 v)))
-    v)
-)
+    v))
 
 
 ;;; Return true if is a factor containing no sums or quotients.
@@ -486,8 +456,7 @@
         nil)
        ((memq (car-safe expr) '(^ neg))
         (math-atomic-factorp (nth 1 expr)))
-       (t t))
-)
+       (t t)))
 
 ;;; Find a suitable base for dividing a by b.
 ;;; The base must exist in both expressions.
@@ -506,8 +475,7 @@
               (if maybe
                   (if (>= (nth 1 (car a-base)) (nth 1 maybe))
                       (throw 'return (car (car a-base))))))
-            (setq a-base (cdr a-base))))))
-)
+            (setq a-base (cdr a-base)))))))
 
 ;;; Same as above but for gcd algorithm.
 ;;; Here there is no requirement that degree(a) > degree(b).
@@ -526,16 +494,14 @@
                   (setq a-base (cdr a-base)))
               (if (assoc (car (car b-base)) a-base)
                   (throw 'return (car (car b-base)))
-                (setq b-base (cdr b-base))))))))
-)
+                (setq b-base (cdr b-base)))))))))
 
 ;;; Sort a list of polynomial bases.
 (defun math-sort-poly-base-list (lst)
   (sort lst (function (lambda (a b)
                        (or (> (nth 1 a) (nth 1 b))
                            (and (= (nth 1 a) (nth 1 b))
-                                (math-beforep (car a) (car b)))))))
-)
+                                (math-beforep (car a) (car b))))))))
 
 ;;; Given an expression find all variables that are polynomial bases.
 ;;; Return list in the form '( (var1 degree1) (var2 degree2) ... ).
@@ -543,8 +509,7 @@
 (defun math-total-polynomial-base (expr)
   (let ((mpb-total-base nil))
     (math-polynomial-base expr 'math-polynomial-p1)
-    (math-sort-poly-base-list mpb-total-base))
-)
+    (math-sort-poly-base-list mpb-total-base)))
 
 (defun math-polynomial-p1 (subexpr)
   (or (assoc subexpr mpb-total-base)
@@ -555,8 +520,7 @@
        (if exponent
            (setq mpb-total-base (cons (list subexpr exponent)
                                       mpb-total-base)))))
-  nil
-)
+  nil)
 
 
 
@@ -572,8 +536,7 @@
                    expr))))
       (math-simplify (if (math-vectorp res)
                         res
-                      (list 'vec (list 'vec res 1))))))
-)
+                      (list 'vec (list 'vec res 1)))))))
 
 (defun calcFunc-factor (expr &optional var)
   (let ((math-factored-vars nil)
@@ -583,22 +546,19 @@
                    (if var
                        (let ((math-factored-vars t))
                          (or (catch 'factor (math-factor-expr-try var)) expr))
-                     (math-factor-expr expr)))))
-)
+                     (math-factor-expr expr))))))
 
 (defun math-factor-finish (x)
   (if (Math-primp x)
       x
     (if (eq (car x) 'calcFunc-Fac-Prot)
        (math-factor-finish (nth 1 x))
-      (cons (car x) (mapcar 'math-factor-finish (cdr x)))))
-)
+      (cons (car x) (mapcar 'math-factor-finish (cdr x))))))
 
 (defun math-factor-protect (x)
   (if (memq (car-safe x) '(+ -))
       (list 'calcFunc-Fac-Prot x)
-    x)
-)
+    x))
 
 (defun math-factor-expr (expr)
   (cond ((eq math-factored-vars t) expr)
@@ -611,8 +571,7 @@
           (if y
               (math-factor-expr y)
             expr)))
-       (t expr))
-)
+       (t expr)))
 
 (defun math-factor-expr-part (x)    ; uses "expr"
   (if (memq (car-safe x) '(+ - * / ^ neg))
@@ -622,8 +581,7 @@
         (not (assoc x math-factored-vars))
         (> (math-factor-contains expr x) 1)
         (setq math-factored-vars (cons (list x) math-factored-vars))
-        (math-factor-expr-try x)))
-)
+        (math-factor-expr-try x))))
 
 (defun math-factor-expr-try (x)
   (if (eq (car-safe expr) '*)
@@ -639,8 +597,7 @@
           res)
       (and (cdr p)
           (setq res (math-factor-poly-coefs p))
-          (throw 'factor res))))
-)
+          (throw 'factor res)))))
 
 (defun math-accum-factors (fac pow facs)
   (if math-to-list
@@ -671,8 +628,7 @@
                  (cons 'vec (cons (nth 1 facs) (cons (list 'vec fac pow)
                                                      (cdr (cdr facs)))))
                (cons 'vec (cons (list 'vec fac pow) (cdr facs))))))))
-    (math-mul (math-pow fac pow) facs))
-)
+    (math-mul (math-pow fac pow) facs)))
 
 (defun math-factor-poly-coefs (p &optional square-free)    ; uses "x"
   (let (t1 t2)
@@ -813,8 +769,7 @@
           (and (setq temp (math-factor-poly-coefs p))
                (math-pow temp (nth 2 math-poly-modulus))))
          (t
-          (math-reject-arg nil "*Modulo factorization not yet implemented"))))
-)
+          (math-reject-arg nil "*Modulo factorization not yet implemented")))))
 
 (defun math-poly-deriv-coefs (p)
   (let ((n 1)
@@ -822,8 +777,7 @@
     (while (setq p (cdr p))
       (setq dp (cons (math-mul (car p) n) dp)
            n (1+ n)))
-    (nreverse dp))
-)
+    (nreverse dp)))
 
 (defun math-factor-contains (x a)
   (if (equal x a)
@@ -836,8 +790,7 @@
       (if (and (eq (car-safe x) '^)
               (natnump (nth 2 x)))
          (* (math-factor-contains (nth 1 x) a) (nth 2 x))
-       0)))
-)
+       0))))
 
 
 
@@ -860,14 +813,12 @@
                (den2 (math-poly-div den g)))
            (and (eq (cdr num2) 0) (eq (cdr den2) 0)
                 (setq num (car num2) den (car den2)))))
-      (math-simplify (math-div num den))))
-)
+      (math-simplify (math-div num den)))))
 
 ;;; Returns expressions (num . denom).
 (defun math-to-ratpoly (expr)
   (let ((res (math-to-ratpoly-rec expr)))
-    (cons (math-simplify (car res)) (math-simplify (cdr res))))
-)
+    (cons (math-simplify (car res)) (math-simplify (cdr res)))))
 
 (defun math-to-ratpoly-rec (expr)
   (cond ((Math-primp expr)
@@ -933,8 +884,7 @@
        ((eq (car expr) 'neg)
         (let ((r1 (math-to-ratpoly-rec (nth 1 expr))))
           (cons (math-neg (car r1)) (cdr r1))))
-       (t (cons expr 1)))
-)
+       (t (cons expr 1))))
 
 
 (defun math-ratpoly-p (expr &optional var)
@@ -963,8 +913,7 @@
           (and p1 (* p1 (nth 2 expr)))))
        ((not var) 1)
        ((math-poly-depends expr var) nil)
-       (t 0))
-)
+       (t 0)))
 
 
 (defun calcFunc-apart (expr &optional var)
@@ -990,14 +939,12 @@
           (math-add q (or (and var
                                (math-expr-contains den var)
                                (math-partial-fractions r den var))
-                          (math-div r den))))))
-)
+                          (math-div r den)))))))
 
 
 (defun math-padded-polynomial (expr var deg)
   (let ((p (math-is-polynomial expr var deg)))
-    (append p (make-list (- deg (length p)) 0)))
-)
+    (append p (make-list (- deg (length p)) 0))))
 
 (defun math-partial-fractions (r den var)
   (let* ((fden (calcFunc-factors den var))
@@ -1063,8 +1010,7 @@
                              res (math-add res (math-div num (car dlist)))
                              num nil))
                    (setq dlist (cdr dlist)))
-                 (math-normalize res))))))
-)
+                 (math-normalize res)))))))
 
 
 
@@ -1096,12 +1042,10 @@
                            (list '^ (nth 1 expr) (1- (nth 2 expr)))))
                (if (< (nth 2 expr) 0)
                    (list '/ 1 (list '^ (nth 1 expr) (- (nth 2 expr))))))))
-       (t expr))
-)
+       (t expr)))
 
 (defun calcFunc-expand (expr &optional many)
-  (math-normalize (math-map-tree 'math-expand-term expr many))
-)
+  (math-normalize (math-map-tree 'math-expand-term expr many)))
 
 (defun math-expand-power (x n &optional var else-nil)
   (or (and (natnump n)
@@ -1184,12 +1128,9 @@
                         (setq p1 (cdr p1)))
                       accum))))))
       (and (not else-nil)
-          (list '^ x n)))
-)
+          (list '^ x n))))
 
 (defun calcFunc-expandpow (x n)
-  (math-normalize (math-expand-power x n))
-)
+  (math-normalize (math-expand-power x n)))
 
-
-
+;;; calc-poly.el ends here