[1201] | 1 | ;;; -*- Mode: Lisp -*-
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[98] | 2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 3 | ;;;
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| 4 | ;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
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| 5 | ;;;
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| 6 | ;;; This program is free software; you can redistribute it and/or modify
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| 7 | ;;; it under the terms of the GNU General Public License as published by
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| 8 | ;;; the Free Software Foundation; either version 2 of the License, or
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| 9 | ;;; (at your option) any later version.
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| 10 | ;;;
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| 11 | ;;; This program is distributed in the hope that it will be useful,
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| 12 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 14 | ;;; GNU General Public License for more details.
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| 15 | ;;;
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| 16 | ;;; You should have received a copy of the GNU General Public License
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| 17 | ;;; along with this program; if not, write to the Free Software
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| 18 | ;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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| 19 | ;;;
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| 20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 21 |
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[133] | 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 23 | ;;
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[268] | 24 | ;; Load this file into Maxima to bootstrap the Grobner package.
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[390] | 25 | ;; NOTE: This file does use symbols defined by Maxima, so it
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| 26 | ;; will not work when loaded in Common Lisp.
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[133] | 27 | ;;
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[268] | 28 | ;; DETAILS: This file implements an interface between the Grobner
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[374] | 29 | ;; basis package NGROBNER, which is a pure Common Lisp package, and
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| 30 | ;; Maxima. NGROBNER for efficiency uses its own representation of
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| 31 | ;; polynomials. Thus, it is necessary to convert Maxima representation
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| 32 | ;; to the internal representation and back. The facilities to do so
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| 33 | ;; are implemented in this file.
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[268] | 34 | ;;
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[270] | 35 | ;; Also, since the NGROBNER package consists of many Lisp files, it is
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[375] | 36 | ;; necessary to load the files. It is possible and preferrable to use
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| 37 | ;; ASDF for this purpose. The default is ASDF. It is also possible to
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| 38 | ;; simply used LOAD and COMPILE-FILE to accomplish this task.
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[270] | 39 | ;;
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[133] | 40 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 41 |
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[98] | 42 | (in-package :maxima)
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| 43 |
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[568] | 44 | (macsyma-module cgb-maxima)
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[98] | 45 |
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[568] | 46 |
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[98] | 47 | (eval-when
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| 48 | #+gcl (load eval)
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| 49 | #-gcl (:load-toplevel :execute)
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| 50 | (format t "~&Loading maxima-grobner ~a ~a~%"
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| 51 | "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
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| 52 |
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| 53 | ;;FUNCTS is loaded because it contains the definition of LCM
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[995] | 54 | ($load "functs")
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[568] | 55 | #+sbcl(progn (require 'asdf) (load "ngrobner.asd")(asdf:load-system :ngrobner))
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[152] | 56 |
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[571] | 57 | (use-package :ngrobner)
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[274] | 58 |
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[571] | 59 |
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[98] | 60 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 61 | ;;
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| 62 | ;; Maxima expression ring
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| 63 | ;;
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| 64 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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[521] | 65 | ;;
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| 66 | ;; This is how we perform operations on coefficients
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| 67 | ;; using Maxima functions.
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| 68 | ;;
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| 69 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 70 |
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[1669] | 71 | (defparameter +maxima-ring+
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[230] | 72 | (make-ring
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[98] | 73 | ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
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| 74 | :parse #'(lambda (expr)
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| 75 | (when modulus (setf expr ($rat expr)))
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| 76 | expr)
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| 77 | :unit #'(lambda () (if modulus ($rat 1) 1))
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| 78 | :zerop #'(lambda (expr)
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| 79 | ;;When is exactly a maxima expression equal to 0?
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| 80 | (cond ((numberp expr)
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| 81 | (= expr 0))
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| 82 | ((atom expr) nil)
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| 83 | (t
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| 84 | (case (caar expr)
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| 85 | (mrat (eql ($ratdisrep expr) 0))
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| 86 | (otherwise (eql ($totaldisrep expr) 0))))))
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| 87 | :add #'(lambda (x y) (m+ x y))
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| 88 | :sub #'(lambda (x y) (m- x y))
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| 89 | :uminus #'(lambda (x) (m- x))
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| 90 | :mul #'(lambda (x y) (m* x y))
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| 91 | ;;(defun coeff-div (x y) (cadr ($divide x y)))
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| 92 | :div #'(lambda (x y) (m// x y))
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| 93 | :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
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| 94 | :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
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| 95 | ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
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| 96 | :gcd #'(lambda (x y) ($gcd x y))))
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| 97 |
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[619] | 98 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 99 | ;;
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| 100 | ;; Maxima expression parsing
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| 101 | ;;
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| 102 | ;;
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| 103 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 104 | ;;
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| 105 | ;; Functions and macros dealing with internal representation
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| 106 | ;; structure.
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| 107 | ;;
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| 108 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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[114] | 109 |
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[619] | 110 | (defun equal-test-p (expr1 expr2)
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| 111 | (alike1 expr1 expr2))
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| 112 |
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| 113 | (defun coerce-maxima-list (expr)
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| 114 | "Convert a Maxima list to Lisp list."
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| 115 | (cond
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| 116 | ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
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| 117 | (t expr)))
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| 118 |
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| 119 | (defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
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| 120 |
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[1642] | 121 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 122 | ;;
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| 123 | ;; Order utilities
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| 124 | ;;
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| 125 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 126 |
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[1674] | 127 | (defun find-ring-by-name (ring)
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[1644] | 128 | "This function returns the ring structure bases on input symbol."
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| 129 | (cond
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| 130 | ((null ring) nil)
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| 131 | ((symbolp ring)
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| 132 | (case ring
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[1650] | 133 | ((maxima-ring :maxima-ring #:maxima-ring $expression_ring #:expression_ring)
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[1669] | 134 | +maxima-ring+)
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| 135 | ((ring-of-integers :ring-of-integers #:ring-of-integers $ring_of_integers) +ring-of-integers+)
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[1644] | 136 | (otherwise
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| 137 | (mtell "~%Warning: Ring ~M not found. Using default.~%" ring))))
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| 138 | (t
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| 139 | (mtell "~%Ring specification ~M is not recognized. Using default.~%" ring)
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| 140 | nil)))
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| 141 |
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[1674] | 142 | (defun find-order-by-name (order)
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[1642] | 143 | "This function returns the order function bases on its name."
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| 144 | (cond
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| 145 | ((null order) nil)
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| 146 | ((symbolp order)
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| 147 | (case order
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[1650] | 148 | ((lex :lex $lex #:lex)
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[1649] | 149 | #'lex>)
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[1650] | 150 | ((grlex :grlex $grlex #:grlex)
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[1649] | 151 | #'grlex>)
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| 152 | ((grevlex :grevlex $grevlex #:grevlex)
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| 153 | #'grevlex>)
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[1650] | 154 | ((invlex :invlex $invlex #:invlex)
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[1649] | 155 | #'invlex>)
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[1642] | 156 | (otherwise
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| 157 | (mtell "~%Warning: Order ~M not found. Using default.~%" order))))
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| 158 | (t
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| 159 | (mtell "~%Order specification ~M is not recognized. Using default.~%" order)
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| 160 | nil)))
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| 161 |
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[1644] | 162 | (defun maxima->poly (expr vars
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| 163 | &optional
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[1674] | 164 | (ring (find-ring-by-name $poly_coefficient_ring))
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| 165 | (order (find-order-by-name $poly_monomial_order))
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[1678] | 166 | (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
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| 167 | (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order))
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[1644] | 168 | &aux
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| 169 | (vars (coerce-maxima-list vars))
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[1652] | 170 | (ring-and-order (make-ring-and-order
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[1674] | 171 | :ring ring
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| 172 | :order order
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[1675] | 173 | :primary-elimination-order primary-elimination-order
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| 174 | :secondary-elimination-order secondary-elimination-order))
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[1673] | 175 | (ring (ro-ring ring-and-order)))
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[1683] | 176 | "Convert a maxima polynomial expression EXPR in variables VARS to
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| 177 | internal form. This works by first converting the expression to Lisp,
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[1685] | 178 | and then evaluating the expression using polynomial arithmetic
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| 179 | implemented by the POLYNOMIAL package."
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[1687] | 180 | (labels ((parse (arg) (maxima->poly arg vars
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| 181 | ring
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| 182 | order
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[1686] | 183 | primary-elimination-order
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| 184 | secondary-elimination-order))
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[619] | 185 | (parse-list (args) (mapcar #'parse args)))
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| 186 | (cond
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| 187 | ((eql expr 0) (make-poly-zero))
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| 188 | ((member expr vars :test #'equal-test-p)
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| 189 | (let ((pos (position expr vars :test #'equal-test-p)))
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[1672] | 190 | (make-poly-variable (ro-ring ring-and-order) (length vars) pos)))
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[619] | 191 | ((free-of-vars expr vars)
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| 192 | ;;This means that variable-free CRE and Poisson forms will be converted
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| 193 | ;;to coefficients intact
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[1672] | 194 | (coerce-coeff (ro-ring ring-and-order) expr vars))
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[619] | 195 | (t
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| 196 | (case (caar expr)
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[1654] | 197 | (mplus (reduce #'(lambda (x y) (poly-add ring-and-order x y)) (parse-list (cdr expr))))
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[1672] | 198 | (mminus (poly-uminus (ro-ring ring-and-order) (parse (cadr expr))))
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[619] | 199 | (mtimes
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| 200 | (if (endp (cddr expr)) ;unary
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| 201 | (parse (cdr expr))
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[1655] | 202 | (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (parse-list (cdr expr)))))
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[619] | 203 | (mexpt
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| 204 | (cond
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| 205 | ((member (cadr expr) vars :test #'equal-test-p)
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| 206 | ;;Special handling of (expt var pow)
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| 207 | (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
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[1672] | 208 | (make-poly-variable (ro-ring ring-and-order) (length vars) pos (caddr expr))))
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[619] | 209 | ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
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| 210 | ;; Negative power means division in coefficient ring
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| 211 | ;; Non-integer power means non-polynomial coefficient
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| 212 | (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
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| 213 | expr)
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[1672] | 214 | (coerce-coeff (ro-ring ring-and-order) expr vars))
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| 215 | (t (poly-expt (ro-ring ring-and-order) (parse (cadr expr)) (caddr expr)))))
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[619] | 216 | (mrat (parse ($ratdisrep expr)))
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| 217 | (mpois (parse ($outofpois expr)))
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| 218 | (otherwise
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[1673] | 219 | (coerce-coeff (ro-ring ring-and-order) expr vars)))))))
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[619] | 220 |
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[1688] | 221 | (defun parse-poly-list (expr vars
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| 222 | &optional
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| 223 | (ring (find-ring-by-name $poly_coefficient_ring))
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| 224 | (order (find-order-by-name $poly_monomial_order))
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| 225 | (primary-elimination-order (find-order-by-name $poly_primary_elimination_order))
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| 226 | (secondary-elimination-order (find-order-by-name $poly_secondary_elimination_order)))
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[619] | 227 | "Parse a Maxima representation of a list of polynomials."
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| 228 | (case (caar expr)
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[1688] | 229 | (mlist (mapcar #'(lambda (p)
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| 230 | (parse-poly p vars ring order primary-elimination-order secondary-elimination-order))
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| 231 | (cdr expr)))
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[619] | 232 | (t (merror "Expression ~M is not a list of polynomials in variables ~M."
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| 233 | expr vars))))
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| 234 |
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[1688] | 235 | #|
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| 236 |
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[619] | 237 | (defun parse-poly-list-list (poly-list-list vars)
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| 238 | "Parse a Maxima representation of a list of lists of polynomials."
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| 239 | (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
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| 240 |
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| 241 |
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[1688] | 242 |
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| 243 |
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[111] | 244 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 245 | ;;
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[241] | 246 | ;; Conversion from internal form to Maxima general form
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| 247 | ;;
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| 248 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 249 |
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| 250 | (defun maxima-head ()
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| 251 | (if $poly_return_term_list
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| 252 | '(mlist)
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| 253 | '(mplus)))
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| 254 |
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| 255 | (defun coerce-to-maxima (poly-type object vars)
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| 256 | (case poly-type
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| 257 | (:polynomial
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| 258 | `(,(maxima-head) ,@(mapcar #'(lambda (term) (coerce-to-maxima :term term vars)) (poly-termlist object))))
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| 259 | (:poly-list
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| 260 | `((mlist) ,@(mapcar #'(lambda (p) (funcall *ratdisrep-fun* (coerce-to-maxima :polynomial p vars))) object)))
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| 261 | (:term
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| 262 | `((mtimes) ,(funcall *ratdisrep-fun* (term-coeff object))
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| 263 | ,@(mapcar #'(lambda (var power) `((mexpt) ,var ,power))
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[882] | 264 | vars (coerce (term-monom object) 'list))))
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[241] | 265 | ;; Assumes that Lisp and Maxima logicals coincide
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| 266 | (:logical object)
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| 267 | (otherwise
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| 268 | object)))
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| 269 |
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| 270 |
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| 271 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 272 | ;;
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[111] | 273 | ;; Unary and binary operation definition facility
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| 274 | ;;
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| 275 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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[98] | 276 |
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[111] | 277 | (defmacro define-unop (maxima-name fun-name
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| 278 | &optional (documentation nil documentation-supplied-p))
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| 279 | "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
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| 280 | `(defun ,maxima-name (p vars
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| 281 | &aux
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| 282 | (vars (coerce-maxima-list vars))
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| 283 | (p (parse-poly p vars)))
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| 284 | ,@(when documentation-supplied-p (list documentation))
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[1669] | 285 | (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p) vars)))
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[111] | 286 |
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| 287 | (defmacro define-binop (maxima-name fun-name
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| 288 | &optional (documentation nil documentation-supplied-p))
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| 289 | "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
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| 290 | `(defmfun ,maxima-name (p q vars
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| 291 | &aux
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| 292 | (vars (coerce-maxima-list vars))
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| 293 | (p (parse-poly p vars))
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| 294 | (q (parse-poly q vars)))
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| 295 | ,@(when documentation-supplied-p (list documentation))
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[1669] | 296 | (coerce-to-maxima :polynomial (,fun-name +maxima-ring+ p q) vars)))
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[111] | 297 |
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| 298 |
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[219] | 299 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 300 | ;;
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| 301 | ;; Facilities for evaluating Grobner package expressions
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| 302 | ;; within a prepared environment
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| 303 | ;;
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| 304 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 305 |
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| 306 | (defmacro with-monomial-order ((order) &body body)
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| 307 | "Evaluate BODY with monomial order set to ORDER."
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| 308 | `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
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| 309 | . ,body))
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| 310 |
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| 311 | (defmacro with-coefficient-ring ((ring) &body body)
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| 312 | "Evaluate BODY with coefficient ring set to RING."
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[1669] | 313 | `(let ((+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
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[219] | 314 | . ,body))
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| 315 |
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[863] | 316 | (defmacro with-ring-and-order ((ring order) &body body)
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[830] | 317 | "Evaluate BODY with monomial order set to ORDER and coefficient ring set to RING."
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| 318 | `(let ((*monomial-order* (or (find-order ,order) *monomial-order*))
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[1669] | 319 | (+maxima-ring+ (or (find-ring ,ring) +maxima-ring+)))
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[830] | 320 | . ,body))
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| 321 |
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[219] | 322 | (defmacro with-elimination-orders ((primary secondary elimination-order)
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| 323 | &body body)
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| 324 | "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
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| 325 | `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
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| 326 | (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
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| 327 | (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
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| 328 | . ,body))
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| 329 |
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| 330 |
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[98] | 331 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 332 | ;;
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| 333 | ;; Maxima-level interface functions
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| 334 | ;;
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| 335 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 336 |
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| 337 | ;; Auxillary function for removing zero polynomial
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| 338 | (defun remzero (plist) (remove #'poly-zerop plist))
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| 339 |
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| 340 | ;;Simple operators
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| 341 |
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| 342 | (define-binop $poly_add poly-add
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| 343 | "Adds two polynomials P and Q")
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| 344 |
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| 345 | (define-binop $poly_subtract poly-sub
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| 346 | "Subtracts a polynomial Q from P.")
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| 347 |
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| 348 | (define-binop $poly_multiply poly-mul
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| 349 | "Returns the product of polynomials P and Q.")
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| 350 |
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| 351 | (define-binop $poly_s_polynomial spoly
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| 352 | "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
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| 353 |
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| 354 | (define-unop $poly_primitive_part poly-primitive-part
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| 355 | "Returns the polynomial P divided by GCD of its coefficients.")
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| 356 |
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| 357 | (define-unop $poly_normalize poly-normalize
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| 358 | "Returns the polynomial P divided by the leading coefficient.")
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| 359 |
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[222] | 360 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 361 | ;;
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| 362 | ;; Macro facility for writing Maxima-level wrappers for
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| 363 | ;; functions operating on internal representation
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| 364 | ;;
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| 365 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 366 |
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| 367 | (defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
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| 368 | &key (polynomials nil)
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[1288] | 369 | (poly-lists nil)
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| 370 | (poly-list-lists nil)
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| 371 | (value-type nil))
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[222] | 372 | &body body
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| 373 | &aux (vars (gensym))
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[1288] | 374 | (new-vars (gensym)))
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[222] | 375 | `(let ((,vars (coerce-maxima-list ,maxima-vars))
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| 376 | ,@(when new-vars-supplied-p
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[1288] | 377 | (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
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[222] | 378 | (coerce-to-maxima
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| 379 | ,value-type
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| 380 | (with-coefficient-ring ($poly_coefficient_ring)
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| 381 | (with-monomial-order ($poly_monomial_order)
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| 382 | (with-elimination-orders ($poly_primary_elimination_order
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| 383 | $poly_secondary_elimination_order
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| 384 | $poly_elimination_order)
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| 385 | (let ,(let ((args nil))
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[1288] | 386 | (dolist (p polynomials args)
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| 387 | (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
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| 388 | (dolist (p poly-lists args)
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| 389 | (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
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| 390 | (dolist (p poly-list-lists args)
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| 391 | (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
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[222] | 392 | . ,body))))
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| 393 | ,(if new-vars-supplied-p
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| 394 | `(append ,vars ,new-vars)
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[1288] | 395 | vars))))
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[222] | 396 |
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| 397 |
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[98] | 398 | ;;Functions
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| 399 |
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| 400 | (defmfun $poly_expand (p vars)
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| 401 | "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
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| 402 | If the representation is not compatible with a polynomial in variables VARS,
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| 403 | the result is an error."
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| 404 | (with-parsed-polynomials ((vars) :polynomials (p)
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| 405 | :value-type :polynomial)
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| 406 | p))
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| 407 |
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| 408 | (defmfun $poly_expt (p n vars)
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| 409 | (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
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[1669] | 410 | (poly-expt +maxima-ring+ p n)))
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[98] | 411 |
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| 412 | (defmfun $poly_content (p vars)
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| 413 | (with-parsed-polynomials ((vars) :polynomials (p))
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[1669] | 414 | (poly-content +maxima-ring+ p)))
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[98] | 415 |
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| 416 | (defmfun $poly_pseudo_divide (f fl vars
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| 417 | &aux (vars (coerce-maxima-list vars))
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| 418 | (f (parse-poly f vars))
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| 419 | (fl (parse-poly-list fl vars)))
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| 420 | (multiple-value-bind (quot rem c division-count)
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[1669] | 421 | (poly-pseudo-divide +maxima-ring+ f fl)
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[98] | 422 | `((mlist)
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| 423 | ,(coerce-to-maxima :poly-list quot vars)
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| 424 | ,(coerce-to-maxima :polynomial rem vars)
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| 425 | ,c
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| 426 | ,division-count)))
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| 427 |
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| 428 | (defmfun $poly_exact_divide (f g vars)
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| 429 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
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[1669] | 430 | (poly-exact-divide +maxima-ring+ f g)))
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[98] | 431 |
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| 432 | (defmfun $poly_normal_form (f fl vars)
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| 433 | (with-parsed-polynomials ((vars) :polynomials (f)
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| 434 | :poly-lists (fl)
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| 435 | :value-type :polynomial)
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[1669] | 436 | (normal-form +maxima-ring+ f (remzero fl) nil)))
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[98] | 437 |
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| 438 | (defmfun $poly_buchberger_criterion (g vars)
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| 439 | (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
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[1669] | 440 | (buchberger-criterion +maxima-ring+ g)))
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[98] | 441 |
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| 442 | (defmfun $poly_buchberger (fl vars)
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| 443 | (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
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[1669] | 444 | (buchberger +maxima-ring+ (remzero fl) 0 nil)))
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[98] | 445 |
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| 446 | (defmfun $poly_reduction (plist vars)
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| 447 | (with-parsed-polynomials ((vars) :poly-lists (plist)
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| 448 | :value-type :poly-list)
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[1669] | 449 | (reduction +maxima-ring+ plist)))
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[98] | 450 |
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| 451 | (defmfun $poly_minimization (plist vars)
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| 452 | (with-parsed-polynomials ((vars) :poly-lists (plist)
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| 453 | :value-type :poly-list)
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| 454 | (minimization plist)))
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| 455 |
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| 456 | (defmfun $poly_normalize_list (plist vars)
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| 457 | (with-parsed-polynomials ((vars) :poly-lists (plist)
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| 458 | :value-type :poly-list)
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[1669] | 459 | (poly-normalize-list +maxima-ring+ plist)))
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[98] | 460 |
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| 461 | (defmfun $poly_grobner (f vars)
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| 462 | (with-parsed-polynomials ((vars) :poly-lists (f)
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| 463 | :value-type :poly-list)
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[1669] | 464 | (grobner +maxima-ring+ (remzero f))))
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[98] | 465 |
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| 466 | (defmfun $poly_reduced_grobner (f vars)
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| 467 | (with-parsed-polynomials ((vars) :poly-lists (f)
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| 468 | :value-type :poly-list)
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[1669] | 469 | (reduced-grobner +maxima-ring+ (remzero f))))
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[98] | 470 |
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| 471 | (defmfun $poly_depends_p (p var mvars
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| 472 | &aux (vars (coerce-maxima-list mvars))
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| 473 | (pos (position var vars)))
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| 474 | (if (null pos)
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| 475 | (merror "~%Variable ~M not in the list of variables ~M." var mvars)
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| 476 | (poly-depends-p (parse-poly p vars) pos)))
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| 477 |
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| 478 | (defmfun $poly_elimination_ideal (flist k vars)
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| 479 | (with-parsed-polynomials ((vars) :poly-lists (flist)
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| 480 | :value-type :poly-list)
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[1669] | 481 | (elimination-ideal +maxima-ring+ flist k nil 0)))
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[98] | 482 |
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| 483 | (defmfun $poly_colon_ideal (f g vars)
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| 484 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
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[1669] | 485 | (colon-ideal +maxima-ring+ f g nil)))
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[98] | 486 |
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| 487 | (defmfun $poly_ideal_intersection (f g vars)
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| 488 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
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[1669] | 489 | (ideal-intersection +maxima-ring+ f g nil)))
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[98] | 490 |
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| 491 | (defmfun $poly_lcm (f g vars)
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| 492 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
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[1669] | 493 | (poly-lcm +maxima-ring+ f g)))
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[98] | 494 |
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| 495 | (defmfun $poly_gcd (f g vars)
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| 496 | ($first ($divide (m* f g) ($poly_lcm f g vars))))
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| 497 |
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| 498 | (defmfun $poly_grobner_equal (g1 g2 vars)
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| 499 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
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[1669] | 500 | (grobner-equal +maxima-ring+ g1 g2)))
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[98] | 501 |
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| 502 | (defmfun $poly_grobner_subsetp (g1 g2 vars)
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| 503 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
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[1669] | 504 | (grobner-subsetp +maxima-ring+ g1 g2)))
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[98] | 505 |
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| 506 | (defmfun $poly_grobner_member (p g vars)
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| 507 | (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
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[1669] | 508 | (grobner-member +maxima-ring+ p g)))
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[98] | 509 |
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| 510 | (defmfun $poly_ideal_saturation1 (f p vars)
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| 511 | (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
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| 512 | :value-type :poly-list)
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[1669] | 513 | (ideal-saturation-1 +maxima-ring+ f p 0)))
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[98] | 514 |
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| 515 | (defmfun $poly_saturation_extension (f plist vars new-vars)
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| 516 | (with-parsed-polynomials ((vars new-vars)
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| 517 | :poly-lists (f plist)
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| 518 | :value-type :poly-list)
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[1669] | 519 | (saturation-extension +maxima-ring+ f plist)))
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[98] | 520 |
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| 521 | (defmfun $poly_polysaturation_extension (f plist vars new-vars)
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| 522 | (with-parsed-polynomials ((vars new-vars)
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| 523 | :poly-lists (f plist)
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| 524 | :value-type :poly-list)
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[1669] | 525 | (polysaturation-extension +maxima-ring+ f plist)))
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[98] | 526 |
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| 527 | (defmfun $poly_ideal_polysaturation1 (f plist vars)
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| 528 | (with-parsed-polynomials ((vars) :poly-lists (f plist)
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| 529 | :value-type :poly-list)
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[1669] | 530 | (ideal-polysaturation-1 +maxima-ring+ f plist 0 nil)))
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[98] | 531 |
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| 532 | (defmfun $poly_ideal_saturation (f g vars)
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| 533 | (with-parsed-polynomials ((vars) :poly-lists (f g)
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| 534 | :value-type :poly-list)
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[1669] | 535 | (ideal-saturation +maxima-ring+ f g 0 nil)))
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[98] | 536 |
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| 537 | (defmfun $poly_ideal_polysaturation (f ideal-list vars)
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| 538 | (with-parsed-polynomials ((vars) :poly-lists (f)
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| 539 | :poly-list-lists (ideal-list)
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| 540 | :value-type :poly-list)
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[1669] | 541 | (ideal-polysaturation +maxima-ring+ f ideal-list 0 nil)))
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[98] | 542 |
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| 543 | (defmfun $poly_lt (f vars)
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| 544 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
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| 545 | (make-poly-from-termlist (list (poly-lt f)))))
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| 546 |
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| 547 | (defmfun $poly_lm (f vars)
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| 548 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
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[1669] | 549 | (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit +maxima-ring+)))))))
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[98] | 550 |
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[1640] | 551 | |#
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