[1201] | 1 | ;;; -*- Mode: Lisp -*-
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[77] | 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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[431] | 22 | (defpackage "POLYNOMIAL"
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[2462] | 23 | (:use :cl :ring :monom :order :term #| :infix |# )
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[2596] | 24 | (:export "POLY"
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| 25 | "POLY-TERMLIST"
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| 26 | "POLY-TERM-ORDER")
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[2522] | 27 | (:documentation "Implements polynomials"))
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[143] | 28 |
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[431] | 29 | (in-package :polynomial)
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| 30 |
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[1927] | 31 | (proclaim '(optimize (speed 3) (space 0) (safety 0) (debug 0)))
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[52] | 32 |
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[2442] | 33 | (defclass poly ()
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[2697] | 34 | ((termlist :initarg :termlist :accessor poly-termlist
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| 35 | :documentation "List of terms.")
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| 36 | (order :initarg :order :accessor poly-term-order
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| 37 | :documentation "Monomial/term order."))
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[2695] | 38 | (:default-initargs :termlist nil :order #'lex>)
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| 39 | (:documentation "A polynomial with a list of terms TERMLIST, ordered
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[2696] | 40 | according to term order ORDER, which defaults to LEX>."))
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[2442] | 41 |
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[2471] | 42 | (defmethod print-object ((self poly) stream)
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[2600] | 43 | (format stream "#<POLY TERMLIST=~A ORDER=~A>"
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[2595] | 44 | (poly-termlist self)
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| 45 | (poly-term-order self)))
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[2469] | 46 |
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[2650] | 47 | (defmethod r-equalp ((self poly) (other poly))
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[2680] | 48 | "POLY instances are R-EQUALP if they have the same
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| 49 | order and if all terms are R-EQUALP."
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[2651] | 50 | (and (every #'r-equalp (poly-termlist self) (poly-termlist other))
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| 51 | (eq (poly-term-order self) (poly-term-order other))))
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[2650] | 52 |
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[2513] | 53 | (defmethod insert-item ((self poly) (item term))
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| 54 | (push item (poly-termlist self))
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[2514] | 55 | self)
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[2464] | 56 |
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[2513] | 57 | (defmethod append-item ((self poly) (item term))
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| 58 | (setf (cdr (last (poly-termlist self))) (list item))
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| 59 | self)
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[2466] | 60 |
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[52] | 61 | ;; Leading term
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[2442] | 62 | (defgeneric leading-term (object)
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| 63 | (:method ((self poly))
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[2525] | 64 | (car (poly-termlist self)))
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| 65 | (:documentation "The leading term of a polynomial, or NIL for zero polynomial."))
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[52] | 66 |
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| 67 | ;; Second term
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[2442] | 68 | (defgeneric second-leading-term (object)
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| 69 | (:method ((self poly))
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[2525] | 70 | (cadar (poly-termlist self)))
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| 71 | (:documentation "The second leading term of a polynomial, or NIL for a polynomial with at most one term."))
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[52] | 72 |
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| 73 | ;; Leading coefficient
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[2442] | 74 | (defgeneric leading-coefficient (object)
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| 75 | (:method ((self poly))
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[2526] | 76 | (r-coeff (leading-term self)))
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[2545] | 77 | (:documentation "The leading coefficient of a polynomial. It signals error for a zero polynomial."))
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[52] | 78 |
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| 79 | ;; Second coefficient
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[2442] | 80 | (defgeneric second-leading-coefficient (object)
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| 81 | (:method ((self poly))
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[2526] | 82 | (r-coeff (second-leading-term self)))
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[2906] | 83 | (:documentation "The second leading coefficient of a polynomial. It
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| 84 | signals error for a polynomial with at most one term."))
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[52] | 85 |
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| 86 | ;; Testing for a zero polynomial
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[2445] | 87 | (defmethod r-zerop ((self poly))
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| 88 | (null (poly-termlist self)))
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[52] | 89 |
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| 90 | ;; The number of terms
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[2445] | 91 | (defmethod r-length ((self poly))
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| 92 | (length (poly-termlist self)))
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[52] | 93 |
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[2483] | 94 | (defmethod multiply-by ((self poly) (other monom))
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[2501] | 95 | (mapc #'(lambda (term) (multiply-by term other))
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| 96 | (poly-termlist self))
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[2483] | 97 | self)
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[2469] | 98 |
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[2501] | 99 | (defmethod multiply-by ((self poly) (other scalar))
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[2502] | 100 | (mapc #'(lambda (term) (multiply-by term other))
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[2501] | 101 | (poly-termlist self))
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[2487] | 102 | self)
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| 103 |
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[2607] | 104 |
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[2761] | 105 | (defmacro fast-add/subtract (p q order-fn add/subtract-fn uminus-fn)
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[2755] | 106 | "Return an expression which will efficiently adds/subtracts two
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| 107 | polynomials, P and Q. The addition/subtraction of coefficients is
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| 108 | performed by calling ADD/SUBTRACT-METHOD-NAME. If UMINUS-METHOD-NAME
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| 109 | is supplied, it is used to negate the coefficients of Q which do not
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[2756] | 110 | have a corresponding coefficient in P. The code implements an
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| 111 | efficient algorithm to add two polynomials represented as sorted lists
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| 112 | of terms. The code destroys both arguments, reusing the terms to build
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| 113 | the result."
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[2742] | 114 | `(macrolet ((lc (x) `(r-coeff (car ,x))))
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| 115 | (do ((p ,p)
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| 116 | (q ,q)
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| 117 | r)
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| 118 | ((or (endp p) (endp q))
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| 119 | ;; NOTE: R contains the result in reverse order. Can it
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| 120 | ;; be more efficient to produce the terms in correct order?
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[2774] | 121 | (unless (endp q)
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[2776] | 122 | ;; Upon subtraction, we must change the sign of
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| 123 | ;; all coefficients in q
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[2774] | 124 | ,@(when uminus-fn
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[2775] | 125 | `((mapc #'(lambda (x) (setf x (funcall ,uminus-fn x))) q)))
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[2774] | 126 | (setf r (nreconc r q)))
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[2742] | 127 | r)
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| 128 | (multiple-value-bind
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| 129 | (greater-p equal-p)
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[2766] | 130 | (funcall ,order-fn (car p) (car q))
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[2742] | 131 | (cond
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| 132 | (greater-p
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| 133 | (rotatef (cdr p) r p)
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| 134 | )
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| 135 | (equal-p
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[2766] | 136 | (let ((s (funcall ,add/subtract-fn (lc p) (lc q))))
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[2742] | 137 | (cond
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| 138 | ((r-zerop s)
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| 139 | (setf p (cdr p))
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| 140 | )
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| 141 | (t
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| 142 | (setf (lc p) s)
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| 143 | (rotatef (cdr p) r p))))
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| 144 | (setf q (cdr q))
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| 145 | )
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| 146 | (t
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[2743] | 147 | ;;Negate the term of Q if UMINUS provided, signallig
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| 148 | ;;that we are doing subtraction
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[2908] | 149 | ,(when uminus-fn
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| 150 | `(setf (lc q) (funcall ,uminus-fn (lc q))))
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[2743] | 151 | (rotatef (cdr q) r q)))))))
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[2585] | 152 |
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[2655] | 153 |
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[2763] | 154 | (defmacro def-add/subtract-method (add/subtract-method-name
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[2752] | 155 | uminus-method-name
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| 156 | &optional
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| 157 | (doc-string nil doc-string-supplied-p))
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[2615] | 158 | "This macro avoids code duplication for two similar operations: ADD-TO and SUBTRACT-FROM."
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[2749] | 159 | `(defmethod ,add/subtract-method-name ((self poly) (other poly))
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[2615] | 160 | ,@(when doc-string-supplied-p `(,doc-string))
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[2769] | 161 | ;; Ensure orders are compatible
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[2773] | 162 | (unless (eq (poly-term-order self) (poly-term-order other))
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[2769] | 163 | (setf (poly-termlist other) (sort (poly-termlist other) (poly-term-order self))
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[2770] | 164 | (poly-term-order other) (poly-term-order self)))
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[2772] | 165 | (setf (poly-termlist self) (fast-add/subtract
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| 166 | (poly-termlist self) (poly-termlist other)
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| 167 | (poly-term-order self)
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| 168 | #',add/subtract-method-name
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| 169 | ,(when uminus-method-name `(function ,uminus-method-name))))
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[2609] | 170 | self))
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[2487] | 171 |
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[2777] | 172 | (eval-when (:compile-toplevel :load-toplevel :execute)
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| 173 |
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| 174 | (def-add/subtract-method add-to nil
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| 175 | "Adds to polynomial SELF another polynomial OTHER.
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[2610] | 176 | This operation destructively modifies both polynomials.
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| 177 | The result is stored in SELF. This implementation does
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[2752] | 178 | no consing, entirely reusing the sells of SELF and OTHER.")
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[2609] | 179 |
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[2777] | 180 | (def-add/subtract-method subtract-from unary-minus
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[2753] | 181 | "Subtracts from polynomial SELF another polynomial OTHER.
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[2610] | 182 | This operation destructively modifies both polynomials.
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| 183 | The result is stored in SELF. This implementation does
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[2752] | 184 | no consing, entirely reusing the sells of SELF and OTHER.")
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[2610] | 185 |
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[2777] | 186 | )
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| 187 |
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[2910] | 188 |
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[2691] | 189 | (defmethod unary-minus ((self poly))
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[2694] | 190 | "Destructively modifies the coefficients of the polynomial SELF,
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| 191 | by changing their sign."
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[2692] | 192 | (mapc #'unary-minus (poly-termlist self))
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[2683] | 193 | self)
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[52] | 194 |
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[2727] | 195 |
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[2795] | 196 | (defun add-termlists (p q order-fn)
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[2794] | 197 | "Destructively adds two termlists P and Q ordered according to ORDER-FN."
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| 198 | (fast-add/subtract p q order-fn add-to nil))
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| 199 |
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[2800] | 200 | (defmacro multiply-term-by-termlist-dropping-zeros (term termlist
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| 201 | &optional (reverse-order nil))
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[2799] | 202 | "Multiplies term TERM by a list of term, TERMLIST.
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[2792] | 203 | Takes into accound divisors of zero in the ring, by
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| 204 | deleting zero terms."
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[2800] | 205 | `(mapcan #'(lambda (other-term)
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[2907] | 206 | (let ((prod (r*
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[2804] | 207 | ,(cond
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[2801] | 208 | (reverse-order
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| 209 | `(other-term ,term)
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| 210 | `(,term other-term))))))
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[2800] | 211 | (cond
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| 212 | ((r-zerop prod) nil)
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| 213 | (t (list prod)))))
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| 214 | ,termlist))
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[2790] | 215 |
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[2796] | 216 | (defun multiply-termlists (p q order-fn)
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[2787] | 217 | (cond
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| 218 | ((or (endp p) (endp q)) nil) ;p or q is 0 (represented by NIL)
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[2789] | 219 | ;; If p= p0+p1 and q=q0+q1 then p*q=p0*q0+p0*q1+p1*q
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[2787] | 220 | ((endp (cdr p))
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[2802] | 221 | (multiply-term-by-termlist-dropping-zeros (car p) q)
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[2787] | 222 | ((endp (cdr q))
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[2802] | 223 | (multiply-term-by-termlist-dropping-zeros (car q) p t)
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| 224 | (t
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| 225 | (nconc (multiply-terms (car p) (car q))
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| 226 | (tail (add-termlists
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| 227 | (multiply-term-by-termlist-dropping-zeros (car p) (cdr q))
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| 228 | (multiply-termlists (cdr p) q)
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| 229 | order-fn))))))))
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[2793] | 230 |
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[2802] | 231 |
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[2803] | 232 | (defmethod multiply-by ((self poly) (other poly))
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| 233 | (setf (poly-termlist self) (multiply-termlists (poly-termlist self)
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| 234 | (poly-termlist other)
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| 235 | (poly-term-order self)))
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| 236 | self)
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| 237 |
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[2785] | 238 | #|
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| 239 |
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[52] | 240 | (defun poly-standard-extension (plist &aux (k (length plist)))
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[2716] | 241 | "Calculate [U1*P1,U2*P2,...,UK*PK], where PLIST=[P1,P2,...,PK]
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| 242 | is a list of polynomials."
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[52] | 243 | (declare (list plist) (fixnum k))
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| 244 | (labels ((incf-power (g i)
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| 245 | (dolist (x (poly-termlist g))
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| 246 | (incf (monom-elt (term-monom x) i)))
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| 247 | (incf (poly-sugar g))))
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| 248 | (setf plist (poly-list-add-variables plist k))
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| 249 | (dotimes (i k plist)
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| 250 | (incf-power (nth i plist) i))))
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| 251 |
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[2716] | 252 |
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[2785] | 253 |
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[1473] | 254 | (defun saturation-extension (ring f plist
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| 255 | &aux
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| 256 | (k (length plist))
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[1474] | 257 | (d (monom-dimension (poly-lm (car plist))))
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| 258 | f-x plist-x)
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[52] | 259 | "Calculate [F, U1*P1-1,U2*P2-1,...,UK*PK-1], where PLIST=[P1,P2,...,PK]."
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[1907] | 260 | (declare (type ring ring))
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[1474] | 261 | (setf f-x (poly-list-add-variables f k)
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| 262 | plist-x (mapcar #'(lambda (x)
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[1843] | 263 | (setf (poly-termlist x)
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| 264 | (nconc (poly-termlist x)
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| 265 | (list (make-term :monom (make-monom :dimension d)
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[1844] | 266 | :coeff (funcall (ring-uminus ring)
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| 267 | (funcall (ring-unit ring)))))))
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[1474] | 268 | x)
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| 269 | (poly-standard-extension plist)))
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| 270 | (append f-x plist-x))
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[52] | 271 |
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| 272 |
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[1475] | 273 | (defun polysaturation-extension (ring f plist
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| 274 | &aux
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| 275 | (k (length plist))
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[1476] | 276 | (d (+ k (monom-dimension (poly-lm (car plist)))))
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[1494] | 277 | ;; Add k variables to f
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[1493] | 278 | (f (poly-list-add-variables f k))
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[1495] | 279 | ;; Set PLIST to [U1*P1,U2*P2,...,UK*PK]
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[1493] | 280 | (plist (apply #'poly-append (poly-standard-extension plist))))
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[1497] | 281 | "Calculate [F, U1*P1+U2*P2+...+UK*PK-1], where PLIST=[P1,P2,...,PK]. It destructively modifies F."
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[1493] | 282 | ;; Add -1 as the last term
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[1908] | 283 | (declare (type ring ring))
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[1493] | 284 | (setf (cdr (last (poly-termlist plist)))
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[1845] | 285 | (list (make-term :monom (make-monom :dimension d)
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| 286 | :coeff (funcall (ring-uminus ring) (funcall (ring-unit ring))))))
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[1493] | 287 | (append f (list plist)))
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[52] | 288 |
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[1477] | 289 | (defun saturation-extension-1 (ring f p)
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[1497] | 290 | "Calculate [F, U*P-1]. It destructively modifies F."
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[1908] | 291 | (declare (type ring ring))
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[1477] | 292 | (polysaturation-extension ring f (list p)))
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[53] | 293 |
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| 294 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 295 | ;;
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| 296 | ;; Evaluation of polynomial (prefix) expressions
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| 297 | ;;
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| 298 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 299 |
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| 300 | (defun coerce-coeff (ring expr vars)
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| 301 | "Coerce an element of the coefficient ring to a constant polynomial."
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| 302 | ;; Modular arithmetic handler by rat
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[1908] | 303 | (declare (type ring ring))
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[1846] | 304 | (make-poly-from-termlist (list (make-term :monom (make-monom :dimension (length vars))
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| 305 | :coeff (funcall (ring-parse ring) expr)))
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[53] | 306 | 0))
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| 307 |
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[1046] | 308 | (defun poly-eval (expr vars
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| 309 | &optional
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[1668] | 310 | (ring +ring-of-integers+)
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[1048] | 311 | (order #'lex>)
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[1170] | 312 | (list-marker :[)
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[1047] | 313 | &aux
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| 314 | (ring-and-order (make-ring-and-order :ring ring :order order)))
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[1168] | 315 | "Evaluate Lisp form EXPR to a polynomial or a list of polynomials in
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[1208] | 316 | variables VARS. Return the resulting polynomial or list of
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| 317 | polynomials. Standard arithmetical operators in form EXPR are
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| 318 | replaced with their analogues in the ring of polynomials, and the
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| 319 | resulting expression is evaluated, resulting in a polynomial or a list
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[1209] | 320 | of polynomials in internal form. A similar operation in another computer
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| 321 | algebra system could be called 'expand' or so."
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[1909] | 322 | (declare (type ring ring))
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[1050] | 323 | (labels ((p-eval (arg) (poly-eval arg vars ring order))
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[1140] | 324 | (p-eval-scalar (arg) (poly-eval-scalar arg))
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[53] | 325 | (p-eval-list (args) (mapcar #'p-eval args))
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[989] | 326 | (p-add (x y) (poly-add ring-and-order x y)))
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[53] | 327 | (cond
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[1128] | 328 | ((null expr) (error "Empty expression"))
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[53] | 329 | ((eql expr 0) (make-poly-zero))
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| 330 | ((member expr vars :test #'equalp)
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| 331 | (let ((pos (position expr vars :test #'equalp)))
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[1657] | 332 | (make-poly-variable ring (length vars) pos)))
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[53] | 333 | ((atom expr)
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| 334 | (coerce-coeff ring expr vars))
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| 335 | ((eq (car expr) list-marker)
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| 336 | (cons list-marker (p-eval-list (cdr expr))))
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| 337 | (t
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| 338 | (case (car expr)
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| 339 | (+ (reduce #'p-add (p-eval-list (cdr expr))))
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| 340 | (- (case (length expr)
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| 341 | (1 (make-poly-zero))
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| 342 | (2 (poly-uminus ring (p-eval (cadr expr))))
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[989] | 343 | (3 (poly-sub ring-and-order (p-eval (cadr expr)) (p-eval (caddr expr))))
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| 344 | (otherwise (poly-sub ring-and-order (p-eval (cadr expr))
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[53] | 345 | (reduce #'p-add (p-eval-list (cddr expr)))))))
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| 346 | (*
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| 347 | (if (endp (cddr expr)) ;unary
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| 348 | (p-eval (cdr expr))
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[989] | 349 | (reduce #'(lambda (p q) (poly-mul ring-and-order p q)) (p-eval-list (cdr expr)))))
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[1106] | 350 | (/
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| 351 | ;; A polynomial can be divided by a scalar
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[1115] | 352 | (cond
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| 353 | ((endp (cddr expr))
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[1117] | 354 | ;; A special case (/ ?), the inverse
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[1119] | 355 | (coerce-coeff ring (apply (ring-div ring) (cdr expr)) vars))
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[1128] | 356 | (t
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[1115] | 357 | (let ((num (p-eval (cadr expr)))
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[1142] | 358 | (denom-inverse (apply (ring-div ring)
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| 359 | (cons (funcall (ring-unit ring))
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| 360 | (mapcar #'p-eval-scalar (cddr expr))))))
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[1118] | 361 | (scalar-times-poly ring denom-inverse num)))))
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[53] | 362 | (expt
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| 363 | (cond
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| 364 | ((member (cadr expr) vars :test #'equalp)
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| 365 | ;;Special handling of (expt var pow)
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| 366 | (let ((pos (position (cadr expr) vars :test #'equalp)))
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[1657] | 367 | (make-poly-variable ring (length vars) pos (caddr expr))))
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[53] | 368 | ((not (and (integerp (caddr expr)) (plusp (caddr expr))))
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| 369 | ;; Negative power means division in coefficient ring
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| 370 | ;; Non-integer power means non-polynomial coefficient
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| 371 | (coerce-coeff ring expr vars))
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[989] | 372 | (t (poly-expt ring-and-order (p-eval (cadr expr)) (caddr expr)))))
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[53] | 373 | (otherwise
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| 374 | (coerce-coeff ring expr vars)))))))
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| 375 |
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[1133] | 376 | (defun poly-eval-scalar (expr
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| 377 | &optional
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[1668] | 378 | (ring +ring-of-integers+)
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[1133] | 379 | &aux
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| 380 | (order #'lex>))
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| 381 | "Evaluate a scalar expression EXPR in ring RING."
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[1910] | 382 | (declare (type ring ring))
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[1133] | 383 | (poly-lc (poly-eval expr nil ring order)))
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| 384 |
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[1189] | 385 | (defun spoly (ring-and-order f g
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| 386 | &aux
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| 387 | (ring (ro-ring ring-and-order)))
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[55] | 388 | "It yields the S-polynomial of polynomials F and G."
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[1911] | 389 | (declare (type ring-and-order ring-and-order) (type poly f g))
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[55] | 390 | (let* ((lcm (monom-lcm (poly-lm f) (poly-lm g)))
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| 391 | (mf (monom-div lcm (poly-lm f)))
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| 392 | (mg (monom-div lcm (poly-lm g))))
|
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| 393 | (declare (type monom mf mg))
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| 394 | (multiple-value-bind (c cf cg)
|
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| 395 | (funcall (ring-ezgcd ring) (poly-lc f) (poly-lc g))
|
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| 396 | (declare (ignore c))
|
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| 397 | (poly-sub
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[1189] | 398 | ring-and-order
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[55] | 399 | (scalar-times-poly ring cg (monom-times-poly mf f))
|
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| 400 | (scalar-times-poly ring cf (monom-times-poly mg g))))))
|
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[53] | 401 |
|
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| 402 |
|
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[55] | 403 | (defun poly-primitive-part (ring p)
|
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| 404 | "Divide polynomial P with integer coefficients by gcd of its
|
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| 405 | coefficients and return the result."
|
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[1912] | 406 | (declare (type ring ring) (type poly p))
|
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[55] | 407 | (if (poly-zerop p)
|
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| 408 | (values p 1)
|
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| 409 | (let ((c (poly-content ring p)))
|
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[1203] | 410 | (values (make-poly-from-termlist
|
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| 411 | (mapcar
|
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| 412 | #'(lambda (x)
|
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[1847] | 413 | (make-term :monom (term-monom x)
|
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| 414 | :coeff (funcall (ring-div ring) (term-coeff x) c)))
|
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[1203] | 415 | (poly-termlist p))
|
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| 416 | (poly-sugar p))
|
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| 417 | c))))
|
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[55] | 418 |
|
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| 419 | (defun poly-content (ring p)
|
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| 420 | "Greatest common divisor of the coefficients of the polynomial P. Use the RING structure
|
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| 421 | to compute the greatest common divisor."
|
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[1913] | 422 | (declare (type ring ring) (type poly p))
|
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[55] | 423 | (reduce (ring-gcd ring) (mapcar #'term-coeff (rest (poly-termlist p))) :initial-value (poly-lc p)))
|
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[1066] | 424 |
|
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[1091] | 425 | (defun read-infix-form (&key (stream t))
|
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[1066] | 426 | "Parser of infix expressions with integer/rational coefficients
|
---|
| 427 | The parser will recognize two kinds of polynomial expressions:
|
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| 428 |
|
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| 429 | - polynomials in fully expanded forms with coefficients
|
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| 430 | written in front of symbolic expressions; constants can be optionally
|
---|
| 431 | enclosed in (); for example, the infix form
|
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| 432 | X^2-Y^2+(-4/3)*U^2*W^3-5
|
---|
| 433 | parses to
|
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| 434 | (+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))
|
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| 435 |
|
---|
| 436 | - lists of polynomials; for example
|
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| 437 | [X-Y, X^2+3*Z]
|
---|
| 438 | parses to
|
---|
| 439 | (:[ (- X Y) (+ (EXPT X 2) (* 3 Z)))
|
---|
| 440 | where the first symbol [ marks a list of polynomials.
|
---|
| 441 |
|
---|
| 442 | -other infix expressions, for example
|
---|
| 443 | [(X-Y)*(X+Y)/Z,(X+1)^2]
|
---|
| 444 | parses to:
|
---|
| 445 | (:[ (/ (* (- X Y) (+ X Y)) Z) (EXPT (+ X 1) 2))
|
---|
| 446 | Currently this function is implemented using M. Kantrowitz's INFIX package."
|
---|
| 447 | (read-from-string
|
---|
| 448 | (concatenate 'string
|
---|
| 449 | "#I("
|
---|
| 450 | (with-output-to-string (s)
|
---|
| 451 | (loop
|
---|
| 452 | (multiple-value-bind (line eof)
|
---|
| 453 | (read-line stream t)
|
---|
| 454 | (format s "~A" line)
|
---|
| 455 | (when eof (return)))))
|
---|
| 456 | ")")))
|
---|
| 457 |
|
---|
[1145] | 458 | (defun read-poly (vars &key
|
---|
| 459 | (stream t)
|
---|
[1668] | 460 | (ring +ring-of-integers+)
|
---|
[1145] | 461 | (order #'lex>))
|
---|
[1067] | 462 | "Reads an expression in prefix form from a stream STREAM.
|
---|
[1144] | 463 | The expression read from the strem should represent a polynomial or a
|
---|
| 464 | list of polynomials in variables VARS, over the ring RING. The
|
---|
| 465 | polynomial or list of polynomials is returned, with terms in each
|
---|
| 466 | polynomial ordered according to monomial order ORDER."
|
---|
[1146] | 467 | (poly-eval (read-infix-form :stream stream) vars ring order))
|
---|
[1092] | 468 |
|
---|
[1146] | 469 | (defun string->poly (str vars
|
---|
[1164] | 470 | &optional
|
---|
[1668] | 471 | (ring +ring-of-integers+)
|
---|
[1146] | 472 | (order #'lex>))
|
---|
| 473 | "Converts a string STR to a polynomial in variables VARS."
|
---|
[1097] | 474 | (with-input-from-string (s str)
|
---|
[1165] | 475 | (read-poly vars :stream s :ring ring :order order)))
|
---|
[1095] | 476 |
|
---|
[1143] | 477 | (defun poly->alist (p)
|
---|
| 478 | "Convert a polynomial P to an association list. Thus, the format of the
|
---|
| 479 | returned value is ((MONOM[0] . COEFF[0]) (MONOM[1] . COEFF[1]) ...), where
|
---|
| 480 | MONOM[I] is a list of exponents in the monomial and COEFF[I] is the
|
---|
| 481 | corresponding coefficient in the ring."
|
---|
[1171] | 482 | (cond
|
---|
| 483 | ((poly-p p)
|
---|
| 484 | (mapcar #'term->cons (poly-termlist p)))
|
---|
| 485 | ((and (consp p) (eq (car p) :[))
|
---|
[1172] | 486 | (cons :[ (mapcar #'poly->alist (cdr p))))))
|
---|
[1143] | 487 |
|
---|
[1164] | 488 | (defun string->alist (str vars
|
---|
| 489 | &optional
|
---|
[1668] | 490 | (ring +ring-of-integers+)
|
---|
[1164] | 491 | (order #'lex>))
|
---|
[1143] | 492 | "Convert a string STR representing a polynomial or polynomial list to
|
---|
[1158] | 493 | an association list (... (MONOM . COEFF) ...)."
|
---|
[1166] | 494 | (poly->alist (string->poly str vars ring order)))
|
---|
[1440] | 495 |
|
---|
| 496 | (defun poly-equal-no-sugar-p (p q)
|
---|
| 497 | "Compare polynomials for equality, ignoring sugar."
|
---|
[1914] | 498 | (declare (type poly p q))
|
---|
[1440] | 499 | (equalp (poly-termlist p) (poly-termlist q)))
|
---|
[1559] | 500 |
|
---|
| 501 | (defun poly-set-equal-no-sugar-p (p q)
|
---|
| 502 | "Compare polynomial sets P and Q for equality, ignoring sugar."
|
---|
| 503 | (null (set-exclusive-or p q :test #'poly-equal-no-sugar-p )))
|
---|
[1560] | 504 |
|
---|
| 505 | (defun poly-list-equal-no-sugar-p (p q)
|
---|
| 506 | "Compare polynomial lists P and Q for equality, ignoring sugar."
|
---|
| 507 | (every #'poly-equal-no-sugar-p p q))
|
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[2456] | 508 | |#
|
---|