| 1 | ;;; -*- Mode: Lisp; Package: Maxima; Syntax: Common-Lisp; Base: 10 -*-
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| 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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| 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 23 | ;;
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| 24 | ;; Load this file into Maxima to bootstrap the Grobner package
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| 25 | ;;
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| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 27 |
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| 28 | (in-package :maxima)
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| 29 |
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| 30 | (macsyma-module cgb-maxima)
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| 31 |
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| 32 | (eval-when
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| 33 | #+gcl (load eval)
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| 34 | #-gcl (:load-toplevel :execute)
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| 35 | (format t "~&Loading maxima-grobner ~a ~a~%"
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| 36 | "$Revision: 2.0 $" "$Date: 2015/06/02 0:34:17 $"))
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| 37 |
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| 38 | ;;FUNCTS is loaded because it contains the definition of LCM
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| 39 | ($load "functs")
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| 40 |
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| 41 | ($load "ngrobner-package")
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| 42 | ($load "utils")
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| 43 | ($load "ngrobner")
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| 44 | ($load "monomial")
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| 45 | ($load "order")
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| 46 | ($load "order-mk")
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| 47 | ($load "term")
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| 48 | ($load "termlist")
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| 49 | ($load "polynomial")
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| 50 | ($load "priority-queue")
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| 51 | ($load "pair-queue")
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| 52 | ($load "division")
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| 53 | ($load "criterion")
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| 54 | ($load "buchberger")
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| 55 | ($load "gebauer-moeller")
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| 56 | ($load "gb-postprocessing")
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| 57 | ($load "ideal")
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| 58 |
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| 59 | (dolist (s '(buchberger buchberger-criterion coerce-coeff
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| 60 | coerce-to-maxima colon-ideal elimination-ideal grobner
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| 61 | grobner-equal grobner-member grobner-subsetp
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| 62 | ideal-intersection ideal-polysaturation
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| 63 | ideal-polysaturation-1 ideal-saturation
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| 64 | ideal-saturation-1 make-poly-from-termlist make-poly-zero
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| 65 | make-term make-variable minimization normal-form poly-add
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| 66 | poly-content poly-depends-p poly-exact-divide poly-expt
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| 67 | poly-lcm poly-lm poly-lt poly-mul poly-normalize
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| 68 | poly-normalize-list poly-primitive-part
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| 69 | poly-pseudo-divide poly-sub poly-uminus poly-zerop
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| 70 | polysaturation-extension reduced-grobner reduction
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| 71 | ring-unit saturation-extension spoly
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| 72 | with-parsed-polynomial make-ring))
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| 73 | (mtell "Importing ~M~%" s)
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| 74 | (shadowing-import s :ngrobner))
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| 75 |
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| 76 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 77 | ;;
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| 78 | ;; Maxima expression ring
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| 79 | ;;
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| 80 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 81 |
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| 82 | (defparameter *expression-ring*
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| 83 | (ngrobner:make-ring
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| 84 | ;;(defun coeff-zerop (expr) (meval1 `(($is) (($equal) ,expr 0))))
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| 85 | :parse #'(lambda (expr)
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| 86 | (when modulus (setf expr ($rat expr)))
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| 87 | expr)
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| 88 | :unit #'(lambda () (if modulus ($rat 1) 1))
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| 89 | :zerop #'(lambda (expr)
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| 90 | ;;When is exactly a maxima expression equal to 0?
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| 91 | (cond ((numberp expr)
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| 92 | (= expr 0))
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| 93 | ((atom expr) nil)
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| 94 | (t
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| 95 | (case (caar expr)
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| 96 | (mrat (eql ($ratdisrep expr) 0))
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| 97 | (otherwise (eql ($totaldisrep expr) 0))))))
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| 98 | :add #'(lambda (x y) (m+ x y))
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| 99 | :sub #'(lambda (x y) (m- x y))
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| 100 | :uminus #'(lambda (x) (m- x))
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| 101 | :mul #'(lambda (x y) (m* x y))
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| 102 | ;;(defun coeff-div (x y) (cadr ($divide x y)))
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| 103 | :div #'(lambda (x y) (m// x y))
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| 104 | :lcm #'(lambda (x y) (meval1 `((|$LCM|) ,x ,y)))
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| 105 | :ezgcd #'(lambda (x y) (apply #'values (cdr ($ezgcd ($totaldisrep x) ($totaldisrep y)))))
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| 106 | ;; :gcd #'(lambda (x y) (second ($ezgcd x y)))))
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| 107 | :gcd #'(lambda (x y) ($gcd x y))))
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| 108 |
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| 109 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 110 | ;;
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| 111 | ;; Maxima expression parsing
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| 112 | ;;
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| 113 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 114 |
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| 115 | (defun equal-test-p (expr1 expr2)
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| 116 | (alike1 expr1 expr2))
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| 117 |
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| 118 | (defun coerce-maxima-list (expr)
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| 119 | "convert a maxima list to lisp list."
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| 120 | (cond
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| 121 | ((and (consp (car expr)) (eql (caar expr) 'mlist)) (cdr expr))
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| 122 | (t expr)))
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| 123 |
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| 124 | (defun free-of-vars (expr vars) (apply #'$freeof `(,@vars ,expr)))
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| 125 |
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| 126 | (defun parse-poly (expr vars &aux (vars (coerce-maxima-list vars)))
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| 127 | "Convert a maxima polynomial expression EXPR in variables VARS to internal form."
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| 128 | (labels ((parse (arg) (parse-poly arg vars))
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| 129 | (parse-list (args) (mapcar #'parse args)))
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| 130 | (cond
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| 131 | ((eql expr 0) (make-poly-zero))
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| 132 | ((member expr vars :test #'equal-test-p)
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| 133 | (let ((pos (position expr vars :test #'equal-test-p)))
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| 134 | (make-variable *maxima-ring* (length vars) pos)))
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| 135 | ((free-of-vars expr vars)
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| 136 | ;;This means that variable-free CRE and Poisson forms will be converted
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| 137 | ;;to coefficients intact
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| 138 | (coerce-coeff *maxima-ring* expr vars))
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| 139 | (t
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| 140 | (case (caar expr)
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| 141 | (mplus (reduce #'(lambda (x y) (poly-add *maxima-ring* x y)) (parse-list (cdr expr))))
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| 142 | (mminus (poly-uminus *maxima-ring* (parse (cadr expr))))
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| 143 | (mtimes
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| 144 | (if (endp (cddr expr)) ;unary
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| 145 | (parse (cdr expr))
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| 146 | (reduce #'(lambda (p q) (poly-mul *maxima-ring* p q)) (parse-list (cdr expr)))))
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| 147 | (mexpt
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| 148 | (cond
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| 149 | ((member (cadr expr) vars :test #'equal-test-p)
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| 150 | ;;Special handling of (expt var pow)
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| 151 | (let ((pos (position (cadr expr) vars :test #'equal-test-p)))
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| 152 | (make-variable *maxima-ring* (length vars) pos (caddr expr))))
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| 153 | ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
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| 154 | ;; Negative power means division in coefficient ring
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| 155 | ;; Non-integer power means non-polynomial coefficient
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| 156 | (mtell "~%Warning: Expression ~%~M~%contains power which is not a positive integer. Parsing as coefficient.~%"
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| 157 | expr)
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| 158 | (coerce-coeff *maxima-ring* expr vars))
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| 159 | (t (poly-expt *maxima-ring* (parse (cadr expr)) (caddr expr)))))
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| 160 | (mrat (parse ($ratdisrep expr)))
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| 161 | (mpois (parse ($outofpois expr)))
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| 162 | (otherwise
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| 163 | (coerce-coeff *maxima-ring* expr vars)))))))
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| 164 |
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| 165 | (defun parse-poly-list (expr vars)
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| 166 | (case (caar expr)
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| 167 | (mlist (mapcar #'(lambda (p) (parse-poly p vars)) (cdr expr)))
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| 168 | (t (merror "Expression ~M is not a list of polynomials in variables ~M."
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| 169 | expr vars))))
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| 170 | (defun parse-poly-list-list (poly-list-list vars)
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| 171 | (mapcar #'(lambda (g) (parse-poly-list g vars)) (coerce-maxima-list poly-list-list)))
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| 172 |
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| 173 |
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| 174 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 175 | ;;
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| 176 | ;; Unary and binary operation definition facility
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| 177 | ;;
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| 178 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 179 |
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| 180 | (defmacro define-unop (maxima-name fun-name
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| 181 | &optional (documentation nil documentation-supplied-p))
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| 182 | "Define a MAXIMA-level unary operator MAXIMA-NAME corresponding to unary function FUN-NAME."
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| 183 | `(defun ,maxima-name (p vars
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| 184 | &aux
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| 185 | (vars (coerce-maxima-list vars))
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| 186 | (p (parse-poly p vars)))
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| 187 | ,@(when documentation-supplied-p (list documentation))
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| 188 | (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p) vars)))
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| 189 |
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| 190 | (defmacro define-binop (maxima-name fun-name
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| 191 | &optional (documentation nil documentation-supplied-p))
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| 192 | "Define a MAXIMA-level binary operator MAXIMA-NAME corresponding to binary function FUN-NAME."
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| 193 | `(defmfun ,maxima-name (p q vars
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| 194 | &aux
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| 195 | (vars (coerce-maxima-list vars))
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| 196 | (p (parse-poly p vars))
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| 197 | (q (parse-poly q vars)))
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| 198 | ,@(when documentation-supplied-p (list documentation))
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| 199 | (coerce-to-maxima :polynomial (,fun-name *maxima-ring* p q) vars)))
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| 200 |
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| 201 |
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| 202 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 203 | ;;
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| 204 | ;; Facilities for evaluating Grobner package expressions
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| 205 | ;; within a prepared environment
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| 206 | ;;
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| 207 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 208 |
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| 209 | (defmacro with-monomial-order ((order) &body body)
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| 210 | "Evaluate BODY with monomial order set to ORDER."
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| 211 | `(let ((*monomial-order* (or (find-order ,order) *monomial-order*)))
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| 212 | . ,body))
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| 213 |
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| 214 | (defmacro with-coefficient-ring ((ring) &body body)
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| 215 | "Evaluate BODY with coefficient ring set to RING."
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| 216 | `(let ((*coefficient-ring* (or (find-ring ,ring) *coefficient-ring*)))
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| 217 | . ,body))
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| 218 |
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| 219 | (defmacro with-elimination-orders ((primary secondary elimination-order)
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| 220 | &body body)
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| 221 | "Evaluate BODY with primary and secondary elimination orders set to PRIMARY and SECONDARY."
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| 222 | `(let ((*primary-elimination-order* (or (find-order ,primary) *primary-elimination-order*))
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| 223 | (*secondary-elimination-order* (or (find-order ,secondary) *secondary-elimination-order*))
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| 224 | (*elimination-order* (or (find-order ,elimination-order) *elimination-order*)))
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| 225 | . ,body))
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| 226 |
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| 227 |
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| 228 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 229 | ;;
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| 230 | ;; Maxima-level interface functions
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| 231 | ;;
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| 232 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 233 |
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| 234 | ;; Auxillary function for removing zero polynomial
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| 235 | (defun remzero (plist) (remove #'poly-zerop plist))
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| 236 |
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| 237 | ;;Simple operators
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| 238 |
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| 239 | (define-binop $poly_add poly-add
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| 240 | "Adds two polynomials P and Q")
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| 241 |
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| 242 | (define-binop $poly_subtract poly-sub
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| 243 | "Subtracts a polynomial Q from P.")
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| 244 |
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| 245 | (define-binop $poly_multiply poly-mul
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| 246 | "Returns the product of polynomials P and Q.")
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| 247 |
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| 248 | (define-binop $poly_s_polynomial spoly
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| 249 | "Returns the syzygy polynomial (S-polynomial) of two polynomials P and Q.")
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| 250 |
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| 251 | (define-unop $poly_primitive_part poly-primitive-part
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| 252 | "Returns the polynomial P divided by GCD of its coefficients.")
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| 253 |
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| 254 | (define-unop $poly_normalize poly-normalize
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| 255 | "Returns the polynomial P divided by the leading coefficient.")
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| 256 |
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| 257 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 258 | ;;
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| 259 | ;; Macro facility for writing Maxima-level wrappers for
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| 260 | ;; functions operating on internal representation
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| 261 | ;;
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| 262 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 263 |
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| 264 | (defmacro with-parsed-polynomials (((maxima-vars &optional (maxima-new-vars nil new-vars-supplied-p))
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| 265 | &key (polynomials nil)
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| 266 | (poly-lists nil)
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| 267 | (poly-list-lists nil)
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| 268 | (value-type nil))
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| 269 | &body body
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| 270 | &aux (vars (gensym))
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| 271 | (new-vars (gensym)))
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| 272 | `(let ((,vars (coerce-maxima-list ,maxima-vars))
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| 273 | ,@(when new-vars-supplied-p
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| 274 | (list `(,new-vars (coerce-maxima-list ,maxima-new-vars)))))
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| 275 | (coerce-to-maxima
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| 276 | ,value-type
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| 277 | (with-coefficient-ring ($poly_coefficient_ring)
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| 278 | (with-monomial-order ($poly_monomial_order)
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| 279 | (with-elimination-orders ($poly_primary_elimination_order
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| 280 | $poly_secondary_elimination_order
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| 281 | $poly_elimination_order)
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| 282 | (let ,(let ((args nil))
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| 283 | (dolist (p polynomials args)
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| 284 | (setf args (cons `(,p (parse-poly ,p ,vars)) args)))
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| 285 | (dolist (p poly-lists args)
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| 286 | (setf args (cons `(,p (parse-poly-list ,p ,vars)) args)))
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| 287 | (dolist (p poly-list-lists args)
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| 288 | (setf args (cons `(,p (parse-poly-list-list ,p ,vars)) args))))
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| 289 | . ,body))))
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| 290 | ,(if new-vars-supplied-p
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| 291 | `(append ,vars ,new-vars)
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| 292 | vars))))
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| 293 |
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| 294 |
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| 295 | ;;Functions
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| 296 |
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| 297 | (defmfun $poly_expand (p vars)
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| 298 | "This function is equivalent to EXPAND(P) if P parses correctly to a polynomial.
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| 299 | If the representation is not compatible with a polynomial in variables VARS,
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| 300 | the result is an error."
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| 301 | (with-parsed-polynomials ((vars) :polynomials (p)
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| 302 | :value-type :polynomial)
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| 303 | p))
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| 304 |
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| 305 | (defmfun $poly_expt (p n vars)
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| 306 | (with-parsed-polynomials ((vars) :polynomials (p) :value-type :polynomial)
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| 307 | (poly-expt *maxima-ring* p n)))
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| 308 |
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| 309 | (defmfun $poly_content (p vars)
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| 310 | (with-parsed-polynomials ((vars) :polynomials (p))
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| 311 | (poly-content *maxima-ring* p)))
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| 312 |
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| 313 | (defmfun $poly_pseudo_divide (f fl vars
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| 314 | &aux (vars (coerce-maxima-list vars))
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| 315 | (f (parse-poly f vars))
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| 316 | (fl (parse-poly-list fl vars)))
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| 317 | (multiple-value-bind (quot rem c division-count)
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| 318 | (poly-pseudo-divide *maxima-ring* f fl)
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| 319 | `((mlist)
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| 320 | ,(coerce-to-maxima :poly-list quot vars)
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| 321 | ,(coerce-to-maxima :polynomial rem vars)
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| 322 | ,c
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| 323 | ,division-count)))
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| 324 |
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| 325 | (defmfun $poly_exact_divide (f g vars)
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| 326 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
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| 327 | (poly-exact-divide *maxima-ring* f g)))
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| 328 |
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| 329 | (defmfun $poly_normal_form (f fl vars)
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| 330 | (with-parsed-polynomials ((vars) :polynomials (f)
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| 331 | :poly-lists (fl)
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| 332 | :value-type :polynomial)
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| 333 | (normal-form *maxima-ring* f (remzero fl) nil)))
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| 334 |
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| 335 | (defmfun $poly_buchberger_criterion (g vars)
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| 336 | (with-parsed-polynomials ((vars) :poly-lists (g) :value-type :logical)
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| 337 | (buchberger-criterion *maxima-ring* g)))
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| 338 |
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| 339 | (defmfun $poly_buchberger (fl vars)
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| 340 | (with-parsed-polynomials ((vars) :poly-lists (fl) :value-type :poly-list)
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| 341 | (buchberger *maxima-ring* (remzero fl) 0 nil)))
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| 342 |
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| 343 | (defmfun $poly_reduction (plist vars)
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| 344 | (with-parsed-polynomials ((vars) :poly-lists (plist)
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| 345 | :value-type :poly-list)
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| 346 | (reduction *maxima-ring* plist)))
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| 347 |
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| 348 | (defmfun $poly_minimization (plist vars)
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| 349 | (with-parsed-polynomials ((vars) :poly-lists (plist)
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| 350 | :value-type :poly-list)
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| 351 | (minimization plist)))
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| 352 |
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| 353 | (defmfun $poly_normalize_list (plist vars)
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| 354 | (with-parsed-polynomials ((vars) :poly-lists (plist)
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| 355 | :value-type :poly-list)
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| 356 | (poly-normalize-list *maxima-ring* plist)))
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| 357 |
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| 358 | (defmfun $poly_grobner (f vars)
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| 359 | (with-parsed-polynomials ((vars) :poly-lists (f)
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| 360 | :value-type :poly-list)
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| 361 | (grobner *maxima-ring* (remzero f))))
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| 362 |
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| 363 | (defmfun $poly_reduced_grobner (f vars)
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| 364 | (with-parsed-polynomials ((vars) :poly-lists (f)
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| 365 | :value-type :poly-list)
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| 366 | (reduced-grobner *maxima-ring* (remzero f))))
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| 367 |
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| 368 | (defmfun $poly_depends_p (p var mvars
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| 369 | &aux (vars (coerce-maxima-list mvars))
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| 370 | (pos (position var vars)))
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| 371 | (if (null pos)
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| 372 | (merror "~%Variable ~M not in the list of variables ~M." var mvars)
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| 373 | (poly-depends-p (parse-poly p vars) pos)))
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| 374 |
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| 375 | (defmfun $poly_elimination_ideal (flist k vars)
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| 376 | (with-parsed-polynomials ((vars) :poly-lists (flist)
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| 377 | :value-type :poly-list)
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| 378 | (elimination-ideal *maxima-ring* flist k nil 0)))
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| 379 |
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| 380 | (defmfun $poly_colon_ideal (f g vars)
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| 381 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
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| 382 | (colon-ideal *maxima-ring* f g nil)))
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| 383 |
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| 384 | (defmfun $poly_ideal_intersection (f g vars)
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| 385 | (with-parsed-polynomials ((vars) :poly-lists (f g) :value-type :poly-list)
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| 386 | (ideal-intersection *maxima-ring* f g nil)))
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| 387 |
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| 388 | (defmfun $poly_lcm (f g vars)
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| 389 | (with-parsed-polynomials ((vars) :polynomials (f g) :value-type :polynomial)
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| 390 | (poly-lcm *maxima-ring* f g)))
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| 391 |
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| 392 | (defmfun $poly_gcd (f g vars)
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| 393 | ($first ($divide (m* f g) ($poly_lcm f g vars))))
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| 394 |
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| 395 | (defmfun $poly_grobner_equal (g1 g2 vars)
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| 396 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
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| 397 | (grobner-equal *maxima-ring* g1 g2)))
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| 398 |
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| 399 | (defmfun $poly_grobner_subsetp (g1 g2 vars)
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| 400 | (with-parsed-polynomials ((vars) :poly-lists (g1 g2))
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| 401 | (grobner-subsetp *maxima-ring* g1 g2)))
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| 402 |
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| 403 | (defmfun $poly_grobner_member (p g vars)
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| 404 | (with-parsed-polynomials ((vars) :polynomials (p) :poly-lists (g))
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| 405 | (grobner-member *maxima-ring* p g)))
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| 406 |
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| 407 | (defmfun $poly_ideal_saturation1 (f p vars)
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| 408 | (with-parsed-polynomials ((vars) :poly-lists (f) :polynomials (p)
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| 409 | :value-type :poly-list)
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| 410 | (ideal-saturation-1 *maxima-ring* f p 0)))
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| 411 |
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| 412 | (defmfun $poly_saturation_extension (f plist vars new-vars)
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| 413 | (with-parsed-polynomials ((vars new-vars)
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| 414 | :poly-lists (f plist)
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| 415 | :value-type :poly-list)
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| 416 | (saturation-extension *maxima-ring* f plist)))
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| 417 |
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| 418 | (defmfun $poly_polysaturation_extension (f plist vars new-vars)
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| 419 | (with-parsed-polynomials ((vars new-vars)
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| 420 | :poly-lists (f plist)
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| 421 | :value-type :poly-list)
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| 422 | (polysaturation-extension *maxima-ring* f plist)))
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| 423 |
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| 424 | (defmfun $poly_ideal_polysaturation1 (f plist vars)
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| 425 | (with-parsed-polynomials ((vars) :poly-lists (f plist)
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| 426 | :value-type :poly-list)
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| 427 | (ideal-polysaturation-1 *maxima-ring* f plist 0 nil)))
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| 428 |
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| 429 | (defmfun $poly_ideal_saturation (f g vars)
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| 430 | (with-parsed-polynomials ((vars) :poly-lists (f g)
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| 431 | :value-type :poly-list)
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| 432 | (ideal-saturation *maxima-ring* f g 0 nil)))
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| 433 |
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| 434 | (defmfun $poly_ideal_polysaturation (f ideal-list vars)
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| 435 | (with-parsed-polynomials ((vars) :poly-lists (f)
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| 436 | :poly-list-lists (ideal-list)
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| 437 | :value-type :poly-list)
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| 438 | (ideal-polysaturation *maxima-ring* f ideal-list 0 nil)))
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| 439 |
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| 440 | (defmfun $poly_lt (f vars)
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| 441 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
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| 442 | (make-poly-from-termlist (list (poly-lt f)))))
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| 443 |
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| 444 | (defmfun $poly_lm (f vars)
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| 445 | (with-parsed-polynomials ((vars) :polynomials (f) :value-type :polynomial)
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| 446 | (make-poly-from-termlist (list (make-term (poly-lm f) (funcall (ring-unit *maxima-ring*)))))))
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| 447 |
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