| 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) 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 | (in-package :maxima)
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| 23 |
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| 24 | (macsyma-module f4-maxima)
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| 25 |
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| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 27 | ;;
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| 28 | ;; An implementation of the normal form
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| 29 | ;;
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| 30 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 31 |
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| 32 | (defun normal-form-step (ring fl p r c division-count
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| 33 | &aux (g (find (poly-lm p) fl
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| 34 | :test #'monom-divisible-by-p
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| 35 | :key #'poly-lm)))
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| 36 | (cond
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| 37 | (g ;division possible
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| 38 | (incf division-count)
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| 39 | (multiple-value-bind (gcd cg cp)
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| 40 | (funcall (ring-ezgcd ring) (poly-lc g) (poly-lc p))
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| 41 | (declare (ignore gcd))
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| 42 | (let ((m (monom-div (poly-lm p) (poly-lm g))))
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| 43 | ;; Multiply the equation c*f=sum ai*fi+r+p by cg.
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| 44 | (setf r (scalar-times-poly ring cg r)
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| 45 | c (funcall (ring-mul ring) c cg)
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| 46 | ;; p := cg*p-cp*m*g
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| 47 | p (grobner-op ring cp cg m p g))))
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| 48 | (debug-cgb "/"))
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| 49 | (t ;no division possible
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| 50 | (push (poly-lt p) (poly-termlist r)) ;move lt(p) to remainder
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| 51 | (setf (poly-sugar r) (max (poly-sugar r) (term-sugar (poly-lt p))))
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| 52 | (pop (poly-termlist p)) ;remove lt(p) from p
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| 53 | (debug-cgb "+")))
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| 54 | (values p r c division-count))
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| 55 |
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| 56 | ;; Merge it sometime with poly-pseudo-divide
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| 57 | (defun normal-form (ring f fl &optional (top-reduction-only $poly_top_reduction_only))
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| 58 | ;; Loop invariant: c*f0=sum ai*fi+r+f, where f0 is the initial value of f
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| 59 | #+grobner-check(when (null fl) (warn "normal-form: empty divisor list."))
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| 60 | (do ((r (make-poly-zero))
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| 61 | (c (funcall (ring-unit ring)))
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| 62 | (division-count 0))
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| 63 | ((or (poly-zerop f)
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| 64 | ;;(endp fl)
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| 65 | (and top-reduction-only (not (poly-zerop r))))
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| 66 | (progn
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| 67 | (debug-cgb "~&~3T~d reduction~:p" division-count)
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| 68 | (when (poly-zerop r)
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| 69 | (debug-cgb " ---> 0")))
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| 70 | (setf (poly-termlist f) (nreconc (poly-termlist r) (poly-termlist f)))
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| 71 | (values f c division-count))
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| 72 | (declare (fixnum division-count)
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| 73 | (type poly r))
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| 74 | (multiple-value-setq (f r c division-count)
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| 75 | (normal-form-step ring fl f r c division-count))))
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