-;; Calculator for GNU Emacs, part II [calc-poly.el]
-;; Copyright (C) 1990, 1991, 1992, 1993 Free Software Foundation, Inc.
-;; Written by Dave Gillespie, daveg@synaptics.com.
+;;; calc-poly.el --- polynomial functions for Calc
+
+;; Copyright (C) 1990, 1991, 1992, 1993, 2001, 2002, 2003, 2004,
+;; 2005, 2006, 2007 Free Software Foundation, Inc.
+
+;; Author: David Gillespie <daveg@synaptics.com>
+;; Maintainer: Jay Belanger <jay.p.belanger@gmail.com>
;; This file is part of GNU Emacs.
+;; GNU Emacs is free software; you can redistribute it and/or modify
+;; it under the terms of the GNU General Public License as published by
+;; the Free Software Foundation; either version 3, or (at your option)
+;; any later version.
+
;; 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.
+;; but WITHOUT ANY WARRANTY; without even the implied warranty of
+;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
+;; GNU General Public License for more 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.
+;; You should have received a copy of the GNU General Public License
+;; along with GNU Emacs; see the file COPYING. If not, write to the
+;; Free Software Foundation, Inc., 51 Franklin Street, Fifth Floor,
+;; Boston, MA 02110-1301, USA.
+;;; Commentary:
+;;; 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)
(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)
(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)
((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) '*)
(let ((p (math-is-polynomial expr var)))
(if (cdr p)
(nth (1- (length p)) p)
- 1))))
-)
+ 1)))))
;;; Originally by Ove Ewerlid (ewerlid@mizar.DoCS.UU.SE).
;;; Modifications and simplifications by daveg.
-(setq math-poly-modulus 1)
+(defvar math-poly-modulus 1)
;;; Return gcd of two polynomials
(defun calcFunc-pgcd (pn pd)
(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)
+
+;; calc-poly-div-remainder is a local variable for
+;; calc-poly-div (in calc-alg.el), but is used by
+;; calcFunc-pdiv, which is called by calc-poly-div.
+(defvar calc-poly-div-remainder)
+
(defun calcFunc-pdiv (pn pd &optional base)
(let* ((calc-prefer-frac t)
(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.
(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.
(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)
(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) '+)
((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).
+(defvar math-poly-div-base nil)
(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)))
-)
-(setq math-poly-div-base nil)
+ (math-do-poly-div (calcFunc-expand u) (calcFunc-expand v))))
(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)
(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)
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)
(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.
(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)
(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)
(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)
(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)))
(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.
(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.
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.
(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).
(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) ... ).
-;;; 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)))))
- nil
-)
-
-
-
-
-(defun calcFunc-factors (expr &optional var)
+ (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 (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))))))
-)
+ (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)
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)
-)
-
-(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) '(+ -))
+ x))
+
+(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)))))
+ (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))
- (throw 'factor res))))
-)
+ (throw 'factor res)))))
(defun math-accum-factors (fac pow facs)
(if math-to-list
(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)
+ (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-sort-terms
- (math-factor-expr (nth 1 p)))))))
+ (math-sort-terms
+ (math-add (math-factor-protect
+ (math-sort-terms
+ (math-factor-expr (car p))))
+ (math-mul math-fet-x (math-factor-protect
+ (math-sort-terms
+ (math-factor-expr (nth 1 p))))))))
;; If symbolic coefficients, use FactorRules.
((let ((pp 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.
(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)
(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)
(if (and (eq (car-safe x) '^)
(natnump (nth 2 x)))
(* (math-factor-contains (nth 1 x) a) (nth 2 x))
- 0)))
-)
+ 0))))
(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)
((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)
(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)
(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)
+ "Return a polynomial as list of coefficients.
+If EXPR is of the form \"a + bx + cx^2 + ...\" in the variable VAR, return
+the list (a b c ...) with at least DEG elements, else return NIL."
(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)
+ "Return R divided by DEN expressed in partial fractions of VAR.
+All whole factors of DEN have already been split off from R.
+If no partial fraction representation can be found, return nil."
(let* ((fden (calcFunc-factors den var))
(tdeg (math-polynomial-p den var))
(fp fden)
res (math-add res (math-div num (car dlist)))
num nil))
(setq dlist (cdr dlist)))
- (math-normalize res))))))
-)
+ (math-normalize res)))))))
((and (eq (car-safe expr) '^)
(memq (car-safe (nth 1 expr)) '(+ -))
(integerp (nth 2 expr))
- (if (> (nth 2 expr) 0)
- (or (and (or (> mmt-many 500000) (< mmt-many -500000))
- (math-expand-power (nth 1 expr) (nth 2 expr)
- nil t))
- (list '*
- (nth 1 expr)
- (list '^ (nth 1 expr) (1- (nth 2 expr)))))
- (if (< (nth 2 expr) 0)
- (list '/ 1 (list '^ (nth 1 expr) (- (nth 2 expr))))))))
- (t expr))
-)
+ (if (and
+ (or (math-known-matrixp (nth 1 (nth 1 expr)))
+ (math-known-matrixp (nth 2 (nth 1 expr)))
+ (and
+ calc-matrix-mode
+ (not (eq calc-matrix-mode 'scalar))
+ (not (and (math-known-scalarp (nth 1 (nth 1 expr)))
+ (math-known-scalarp (nth 2 (nth 1 expr)))))))
+ (> (nth 2 expr) 1))
+ (if (= (nth 2 expr) 2)
+ (math-add-or-sub (list '* (nth 1 (nth 1 expr)) (nth 1 expr))
+ (list '* (nth 2 (nth 1 expr)) (nth 1 expr))
+ nil (eq (car (nth 1 expr)) '-))
+ (math-add-or-sub (list '* (nth 1 (nth 1 expr))
+ (list '^ (nth 1 expr)
+ (1- (nth 2 expr))))
+ (list '* (nth 2 (nth 1 expr))
+ (list '^ (nth 1 expr)
+ (1- (nth 2 expr))))
+ nil (eq (car (nth 1 expr)) '-)))
+ (if (> (nth 2 expr) 0)
+ (or (and (or (> math-mt-many 500000) (< math-mt-many -500000))
+ (math-expand-power (nth 1 expr) (nth 2 expr)
+ nil t))
+ (list '*
+ (nth 1 expr)
+ (list '^ (nth 1 expr) (1- (nth 2 expr)))))
+ (if (< (nth 2 expr) 0)
+ (list '/ 1 (list '^ (nth 1 expr) (- (nth 2 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)
(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)))
+(provide 'calc-poly)
+;;; arch-tag: d2566c51-2ccc-45f1-8c50-f3462c2953ff
+;;; calc-poly.el ends here