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