| 1 | ;;; -*- Mode: Lisp -*-
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| 2 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 3 | ;;;
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| 4 | ;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
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| 5 | ;;;
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| 6 | ;;; This program is free software; you can redistribute it and/or modify
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| 7 | ;;; it under the terms of the GNU General Public License as published by
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| 8 | ;;; the Free Software Foundation; either version 2 of the License, or
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| 9 | ;;; (at your option) any later version.
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| 10 | ;;;
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| 11 | ;;; This program is distributed in the hope that it will be useful,
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| 12 | ;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
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| 13 | ;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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| 14 | ;;; GNU General Public License for more details.
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| 15 | ;;;
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| 16 | ;;; You should have received a copy of the GNU General Public License
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| 17 | ;;; along with this program; if not, write to the Free Software
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| 18 | ;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
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| 19 | ;;;
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| 20 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 21 |
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| 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 23 | ;;
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| 24 | ;; Run tests using 5am unit testing framework
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| 25 | ;;
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| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 27 |
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| 28 | ;; We assume that QuickLisp package manager is installed.
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| 29 | ;; See :
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| 30 | ;; https://www.quicklisp.org/beta/
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| 31 | ;;
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| 32 |
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| 33 | ;; The following is unnecessary after running:
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| 34 | ;; * (ql:add-to-init-file)
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| 35 | ;; at lisp prompt:
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| 36 | ;;(load "~/quicklisp/setup")
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| 37 |
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| 38 | (ql:quickload :fiveam)
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| 39 |
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| 40 | (defpackage #:5am-buchberger
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| 41 | (:use :cl :it.bese.fiveam :monom :polynomial :infix :symbolic-polynomial :division :priority-queue :buchberger :grobner-debug))
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| 42 |
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| 43 | (in-package :5am-buchberger)
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| 44 |
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| 45 | (def-suite buchberger-suite
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| 46 | :description "Buchberger algorithm suite")
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| 47 |
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| 48 | (in-suite buchberger-suite)
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| 49 |
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| 50 | (def-fixture buchberger-context ()
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| 51 | (let ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
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| 52 | (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y)))))
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| 53 | (&body)))
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| 54 |
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| 55 |
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| 56 | (test buchberger
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| 57 | "Buchberger algorithm"
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| 58 | (with-fixture buchberger-context ()
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| 59 | (is-true (grobner-test gb fl))
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| 60 | (is (every #'universal-equalp (buchberger fl) gb))
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| 61 | ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
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| 62 | )
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| 63 | )
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| 64 |
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| 65 | ;; poly_grobner([x-3*u-3*u*v^2+u^3,y-3*v-3*u^2*v+v^3,z-3*u^2+3*v^2],[u,v,x,y,z]);
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| 66 | (def-fixture buchberger-enneper-surface-context ()
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| 67 | (let ((fl (cdr (string->poly "[x-3*u-3*u*v^2+u^3,y-3*v-3*u^2*v+v^3,z-3*u^2+3*v^2]" '(u v x y z))))
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| 68 | (gb (cdr (string->poly "[x-3*u*v^2+u^3-3*u,y+v^3-3*u^2*v-3*v,z+3*v^2-3*u^2,
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| 69 | (-u*z)-3*x+6*u*v^2+9*u,(-v*z)+y-2*v^3-3*v,z^2+6*v^2*z-9*z-9*v*y+9*u*x,
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| 70 | 4*u*v*z-3*u*y+3*v*x,2*u*z^2+6*x*z-18*u*z-9*u*v*y+9*v^2*x,
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| 71 | (-8*u*z^3)-24*x*z^2+72*u*z^2-36*v^2*x*z+27*u*y^2-27*v*x*y,
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| 72 | z^3+18*v^2*z^2-18*z^2-54*v*y*z+54*v^2*z+81*z+27*y^2-27*x^2,
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| 73 | (-4*z^4)+48*z^3-108*v*y*z^2+108*z^2+135*y^2*z+324*v*y*z+108*x^2*z
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| 74 | -1296*v^2*z-1944*z-243*v^2*y^2-648*y^2+243*v^2*x^2+648*x^2,
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| 75 | 8*v*z^3-9*y*z^2+72*v*z^2+54*v^2*y*z-27*y*z-27*v*y^2+27*v*x^2,
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| 76 | (-8*v*z^4)+12*y*z^3-96*v*z^3-216*v*z^2-135*v*y^2*z+324*y*z-27*v*x^2*z
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| 77 | +81*y^3+81*v*y^2-81*x^2*y-81*v*x^2,
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| 78 | (-64*v*z^6)+120*y*z^5-1152*v*z^5+288*y*z^4-5184*v*z^4-648*v*y^2*z^3
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| 79 | -216*y*z^3+6912*v*z^3+81*y^3*z^2-9720*v*y^2*z^2
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| 80 | -1539*x^2*y*z^2+31104*y*z^2+62208*v*z^2+8505*y^3*z
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| 81 | +46656*v*y^2*z-8505*x^2*y*z-93312*y*z+729*v*y^4-23328*y^3
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| 82 | -1458*v*x^2*y^2-23328*v*y^2+23328*x^2*y+729*v*x^4
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| 83 | +23328*v*x^2,
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| 84 | 8*z^6-72*z^5+648*v*y*z^4-648*z^4-945*y^2*z^3+5184*v*y*z^3-189*x^2*z^3
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| 85 | +5832*z^3+972*y^2*z^2+17496*v*y*z^2-2430*x^2*z^2+8748*v*y^3*z
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| 86 | -19683*y^2*z+2187*x^2*z-5103*y^4-4374*v*y^3+5832*x^2*y^2
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| 87 | +4374*v*x^2*y-729*x^4,
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| 88 | 8*z^7-48*z^6+648*v*y*z^5-864*z^5-945*y^2*z^4+5832*v*y*z^4-189*x^2*z^4
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| 89 | +3888*z^4+81*y^2*z^3+17496*v*y*z^3-2997*x^2*z^3+17496*z^3
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| 90 | +8748*v*y^3*z^2-16767*y^2*z^2+17496*v*y*z^2-5103*x^2*z^2
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| 91 | -5103*y^4*z+5832*x^2*y^2*z-6561*y^2*z-729*x^4*z+6561*x^2*z
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| 92 | -2187*y^4+4374*x^2*y^2-2187*x^4,
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| 93 | 64*z^9-10368*z^7+1296*y^2*z^6-1296*x^2*z^6-34992*y^2*z^5-34992*x^2*z^5
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| 94 | +419904*z^5+174960*y^2*z^4-174960*x^2*z^4-10935*y^4*z^3
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| 95 | -56862*x^2*y^2*z^3+314928*y^2*z^3-10935*x^4*z^3+314928*x^2*z^3
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| 96 | +118098*y^4*z^2-118098*x^4*z^2+59049*y^4*z-118098*x^2*y^2*z
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| 97 | +59049*x^4*z+19683*y^6-59049*x^2*y^4+59049*x^4*y^2-19683*x^6]" '(u v x y z)))))
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| 98 | (&body)))
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| 99 |
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| 100 |
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| 101 | (test buchberger-enneper-surface
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| 102 | "Buchberger algorithm - Enneper surface"
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| 103 | (with-fixture buchberger-enneper-surface-context ()
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| 104 | (is-true (grobner-test gb fl))
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| 105 | ;; NOTE: Cannot compare using SET-EXCLUSIVE-OR, as the Grobner basis
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| 106 | ;; FL was computed using "sugar" strategy and is different from
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| 107 | ;; the one obtained with BUCHBERGER, which uses the "normal" strategy.
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| 108 | (is (grobner-equal (buchberger fl) gb))
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| 109 | ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
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| 110 | )
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| 111 | )
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| 112 |
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| 113 | ;; Cyclic roots of degree 5
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| 114 | ;; poly_reduced_grobner([x+y+z+u+v,x*y+y*z+z*u+u*v+v*x,x*y*z+y*z*u+z*u*v+u*v*x+v*x*y,x*y*z*u+y*z*u*v+z*u*v*x+u*v*x*y+v*x*y*z,x*y*z*u*v-1],[u,v,x,y,z]);
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| 115 | (def-fixture buchberger-cyclic-5-context ()
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| 116 | (let ((fl
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| 117 | (cdr (string->poly
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| 118 | "[x+y+z+u+v,x*y+y*z+z*u+u*v+v*x,x*y*z+y*z*u+z*u*v+u*v*x+v*x*y,x*y*z*u+y*z*u*v+z*u*v*x+u*v*x*y+v*x*y*z,x*y*z*u*v-1]"
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| 119 | '(u v x y z))))
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| 120 | (gb (cdr (string->poly "[z+y+x+v+u,
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| 121 | 8*z^12+2*y*z^11+979*z^7+231*y*z^6-55*y^2*z^5-987*z^2-233*y*z+55*y^2,
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| 122 | z^15+122*z^10-122*z^5-1,
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| 123 | 1467*z^12+566*y*z^11+178981*z^7+69003*y*z^6+550*y^3*z^4-275*y^4*z^3
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| 124 | -1650*y^5*z^2-179073*z^2-550*y^6*z-69019*y*z-825*v*z-275*y^2
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| 125 | -275*v^2,(-z^11)-143*z^6-55*v*z^5+144*z+55*v,
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| 126 | (-346*z^12)-124*y*z^11-42218*z^7-15092*y*z^6-275*y^3*z^4+275*y^4*z^3
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| 127 | +440*y^5*z^2+42124*z^2+110*y^6*z+15106*y*z+275*v*z-275*v*y,
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| 128 | 867*z^12+334*y*z^11+105776*z^7+40722*y*z^6+275*y^3*z^4-275*y^4*z^3
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| 129 | -1045*y^5*z^2-105873*z^2-330*y^6*z-40726*y*z+550*x*z-275*v*z
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| 130 | -550*y^2+275*x^2+275*v*x,
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| 131 | (-568*z^13)-232*y*z^12-69289*z^8-28336*y*z^7-550*y^4*z^4+550*y^5*z^3
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| 132 | +69307*z^3+275*y^6*z^2+28018*y*z^2-550*x*z^2+550*y^2*z
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| 133 | +550*x^2*z+275*x^3,(-z^11)-143*z^6-55*x*z^5+144*z+55*x,
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| 134 | 1121*z^12+442*y*z^11+136763*z^7+53911*y*z^6+275*y^3*z^4-1210*y^5*z^2
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| 135 | -136674*z^2-440*y^6*z-53913*y*z+275*x*z-275*y^2-275*x*y,
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| 136 | 1042*z^12+398*y*z^11+127116*z^7+48554*y*z^6-55*y^5*z^2-128103*z^2
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| 137 | -165*y^6*z-48787*y*z-55*y^7+55*y^2]" '(u v x y z)))))
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| 138 | (&body)))
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| 139 |
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| 140 |
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| 141 | (test buchberger-cyclic-5
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| 142 | "Buchberger algorithm - cyclic 5"
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| 143 | (with-fixture buchberger-cyclic-5-context ()
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| 144 | (is-true (grobner-test gb fl))
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| 145 | ;; NOTE: Cannot compare using SET-EXCLUSIVE-OR, as the Grobner basis
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| 146 | ;; FL was computed using "sugar" strategy and is different from
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| 147 | ;; the one obtained with BUCHBERGER, which uses the "normal" strategy.
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| 148 | (is (grobner-equal (buchberger fl) gb))
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| 149 | ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
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| 150 | )
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| 151 | )
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| 152 |
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| 153 | ;; A tough example learned from Cox
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| 154 | ;; poly_grobner([x^5+y^4+z^3-1,x^3+y^3+z^2-1], [x,y,z]);
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| 155 | ;; Note that the Grobner basis in the test is reduced, obtained with
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| 156 | ;; poly_reduced_grobner([x^5+y^4+z^3-1,x^3+y^3+z^2-1], [x,y,z]);
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| 157 | (def-fixture buchberger-cox-tough-context ()
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| 158 | (let ((fl (cdr (string->poly "[x^5+y^4+z^3-1,x^3+y^3+z^2-1]" '(x y z))))
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| 159 | (gb (cdr (string->poly "[z^2+y^3+x^3-1,z^3-x^2*z^2+y^4-x^2*y^3+x^2-1,
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| 160 | (-z^4)-x*z^3-2*y^3*z^2+2*z^2-y^6-x*y^4+2*y^3+x-1,
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| 161 | (-z^10)+z^9-5*y^3*z^8+5*z^8-10*y^6*z^6+3*y^4*z^6+20*y^3*z^6-13*z^6
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| 162 | -10*y^9*z^4+30*y^6*z^4-30*y^3*z^4+10*z^4+3*y^8*z^3-6*y^4*z^3
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| 163 | +3*z^3-5*y^12*z^2+20*y^9*z^2-30*y^6*z^2+20*y^3*z^2-5*z^2-y^15
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| 164 | +6*y^12-10*y^9-3*y^8+10*y^6+3*y^4-5*y^3,
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| 165 | (-44425*z^21)-44425*x*z^20-193795*z^20-88850*y^3*z^19+266550*y*z^19
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| 166 | -327070*x*z^19-1274354*z^19+44425*y^4*z^18-32190*y^3*z^18
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| 167 | +444250*y^2*z^18+451970*y*z^18-1278214*x*z^18-3527528*z^18
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| 168 | -44425*y^6*z^17+1526545*y^4*z^17-1842423*y^3*z^17
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| 169 | +1227150*y^2*z^17-1140996*y*z^17-2698855*x*z^17
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| 170 | -1109995*z^17+88850*y^7*z^16+783555*y^6*z^16
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| 171 | +1954700*y^5*z^16+4467129*y^4*z^16-9605029*y^3*z^16
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| 172 | -752630*y^2*z^16-2972806*y*z^16-2572042*x*z^16
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| 173 | +13565093*z^16-44425*y^8*z^15+2697690*y^7*z^15
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| 174 | +456911*y^6*z^15+7105380*y^5*z^15+2647468*y^4*z^15
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| 175 | -10602997*y^3*z^15-7006014*y^2*z^15+1218640*y*z^15
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| 176 | +2619449*x*z^15+22302653*z^15+44425*y^10*z^14
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| 177 | +888500*y^9*z^14+2915955*y^8*z^14+9160898*y^7*z^14
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| 178 | -7506655*y^6*z^14+5800536*y^5*z^14-3245086*y^4*z^14
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| 179 | +20587543*y^3*z^14-8783974*y^2*z^14+3837574*y*z^14
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| 180 | +10650408*x*z^14-7954033*z^14-88850*y^11*z^13
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| 181 | +1881945*y^10*z^13+1921200*y^9*z^13+11847046*y^8*z^13
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| 182 | +9782204*y^7*z^13-12668822*y^6*z^13-10997536*y^5*z^13
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| 183 | +1090138*y^4*z^13+54430174*y^3*z^13-1436450*y^2*z^13
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| 184 | -11018460*y*z^13+11493837*x*z^13-56030677*z^13
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| 185 | +266550*y^12*z^12+1744810*y^11*z^12+6728289*y^10*z^12
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| 186 | -187950*y^9*z^12+15235952*y^8*z^12-505866*y^7*z^12
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| 187 | +10778914*y^6*z^12-25975004*y^5*z^12+899768*y^4*z^12
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| 188 | +13274582*y^3*z^12+4950830*y^2*z^12-21334144*y*z^12
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| 189 | -2616810*x*z^12-42908546*z^12-44425*y^14*z^11
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| 190 | +444250*y^13*z^11+718520*y^12*z^11+7686377*y^11*z^11
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| 191 | +9990070*y^10*z^11-1596036*y^9*z^11-1342215*y^8*z^11
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| 192 | -8841150*y^7*z^11+40955979*y^6*z^11-24957052*y^5*z^11
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| 193 | -36144372*y^4*z^11-82735585*y^3*z^11+13378064*y^2*z^11
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| 194 | +12799086*y*z^11-16744470*x*z^11+42041860*z^11
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| 195 | +339305*y^14*z^10+1671400*y^13*z^10+910274*y^12*z^10
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| 196 | +11626231*y^11*z^10+7801347*y^10*z^10+7831314*y^9*z^10
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| 197 | -26096155*y^8*z^10-16474014*y^7*z^10+11243399*y^6*z^10
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| 198 | -17808216*y^5*z^10-61462426*y^4*z^10-89174777*y^3*z^10
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| 199 | +30957924*y^2*z^10+55234262*y*z^10-12049440*x*z^10
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| 200 | +91874913*z^10+1628711*y^14*z^9+3140020*y^13*z^9
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| 201 | +1263518*y^12*z^9+4404103*y^11*z^9+2153415*y^10*z^9
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| 202 | +19135710*y^9*z^9-40336258*y^8*z^9-39769140*y^7*z^9
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| 203 | -68036522*y^6*z^9+12529572*y^5*z^9+7525711*y^4*z^9
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| 204 | +37559804*y^3*z^9+21952328*y^2*z^9+29962348*y*z^9
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| 205 | +4801407*x*z^9+31327296*z^9+3000105*y^14*z^8
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| 206 | +4046756*y^13*z^8+3116408*y^12*z^8-11359143*y^11*z^8
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| 207 | -9140507*y^10*z^8+5385232*y^9*z^8-38148698*y^8*z^8
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| 208 | -41664378*y^7*z^8-80668677*y^6*z^8+73310048*y^5*z^8
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| 209 | +103064435*y^4*z^8+127272309*y^3*z^8-30170622*y^2*z^8
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| 210 | -39724286*y*z^8+8854766*x*z^8-57432520*z^8
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| 211 | +2743338*y^14*z^7+3960482*y^13*z^7+5071808*y^12*z^7
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| 368 | -72824464*y^5*z^4-73097103*y^4*z^4-55627499*y^3*z^4
|
|---|
| 369 | +28155166*y^2*z^4+28220776*y*z^4+23328*x^2*z^4+9720*x*z^4
|
|---|
| 370 | +27941326*z^4-11437557*y^14*z^3-11328236*y^13*z^3
|
|---|
| 371 | -11280880*y^12*z^3+47780995*y^11*z^3+47175827*y^10*z^3
|
|---|
| 372 | +46880484*y^9*z^3-29152980*y^8*z^3-62322100*y^7*z^3
|
|---|
| 373 | -61589201*y^6*z^3-4522320*y^5*z^3-5850743*y^4*z^3
|
|---|
| 374 | +27747047*y^3*z^3+8893592*y^2*z^3+9356264*y*z^3
|
|---|
| 375 | -23328*x^2*z^3+5832*x*z^3+9673136*z^3-6849778*y^14*z^2
|
|---|
| 376 | -6905668*y^13*z^2-6894490*y^12*z^2+33943290*y^11*z^2
|
|---|
| 377 | +34193580*y^10*z^2+34174626*y^9*z^2-33299528*y^8*z^2
|
|---|
| 378 | -54131228*y^7*z^2-54345068*y^6*z^2+12452276*y^5*z^2
|
|---|
| 379 | +13044224*y^4*z^2+33736442*y^3*z^2+538394*y^2*z^2
|
|---|
| 380 | +247766*y*z^2-23328*x^2*z^2+95162*z^2-1891498*y^14*z
|
|---|
| 381 | -1884694*y^13*z-1910938*y^12*z+9409862*y^11*z
|
|---|
| 382 | +9408890*y^10*z+9573158*y^9*z-9206714*y^8*z-15072692*y^7*z
|
|---|
| 383 | -15315692*y^6*z+3496256*y^5*z+3690656*y^4*z+54432*x*y^3*z
|
|---|
| 384 | +9648974*y^3*z-93312*x*y^2*z+93312*y^2*z+7776*x^2*y*z
|
|---|
| 385 | -7776*y*z-7776*x^2*z+38880*x*z-31104*z-67438*y^14
|
|---|
| 386 | -78130*y^13-55774*y^12+373154*y^11+393566*y^10+248738*y^9
|
|---|
| 387 | -541310*y^8-571580*y^7-359684*y^6+386624*y^5+200000*y^4
|
|---|
| 388 | -54432*x*y^3+126266*y^3+93312*x*y^2-93312*y^2-7776*x^2*y
|
|---|
| 389 | +7776*y+7776*x^2-38880*x+31104,
|
|---|
| 390 | 62197*z^21+62197*x*z^20+291088*z^20+124394*y^3*z^19-373182*y*z^19
|
|---|
| 391 | +477679*x*z^19+1878962*z^19-62197*y^4*z^18+84600*y^3*z^18
|
|---|
| 392 | -621970*y^2*z^18-751376*y*z^18+1943665*x*z^18+5547434*z^18
|
|---|
| 393 | +62197*y^6*z^17-2156998*y^4*z^17+2610963*y^3*z^17
|
|---|
| 394 | -1915728*y^2*z^17+1344852*y*z^17+4414720*x*z^17+3387640*z^17
|
|---|
| 395 | -124394*y^7*z^16-1077246*y^6*z^16-2736668*y^5*z^16
|
|---|
| 396 | -6941979*y^4*z^16+14282032*y^3*z^16+421886*y^2*z^16
|
|---|
| 397 | +4556674*y*z^16+5079481*x*z^16-17694533*z^16+62197*y^8*z^15
|
|---|
| 398 | -3816420*y^7*z^15-979745*y^6*z^15-10817568*y^5*z^15
|
|---|
| 399 | -5993371*y^4*z^15+19475671*y^3*z^15+9863628*y^2*z^15
|
|---|
| 400 | -201616*y*z^15-1881863*x*z^15-36718052*z^15-62197*y^10*z^14
|
|---|
| 401 | -1243940*y^9*z^14-4062702*y^8*z^14-14043134*y^7*z^14
|
|---|
| 402 | +10159270*y^6*z^14-11660088*y^5*z^14+2355712*y^4*z^14
|
|---|
| 403 | -22068016*y^3*z^14+15450484*y^2*z^14-5236534*y*z^14
|
|---|
| 404 | -15324612*x*z^14-1299572*z^14+124394*y^11*z^13
|
|---|
| 405 | -2654574*y^10*z^13-3085092*y^9*z^13-17875228*y^8*z^13
|
|---|
| 406 | -18301298*y^7*z^13+20912123*y^6*z^13+11254696*y^5*z^13
|
|---|
| 407 | -998824*y^4*z^13-82420621*y^3*z^13+7344470*y^2*z^13
|
|---|
| 408 | +13720314*y*z^13-21069324*x*z^13+76544146*z^13
|
|---|
| 409 | -373182*y^12*z^12-2403280*y^11*z^12-10265835*y^10*z^12
|
|---|
| 410 | -763326*y^9*z^12-27161252*y^8*z^12-5672886*y^7*z^12
|
|---|
| 411 | -8030785*y^6*z^12+39489536*y^5*z^12-1373297*y^4*z^12
|
|---|
| 412 | -45846113*y^3*z^12-4006574*y^2*z^12+33940378*y*z^12
|
|---|
| 413 | -3669771*x*z^12+84649877*z^12+62197*y^14*z^11
|
|---|
| 414 | -621970*y^13*z^11-1124558*y^12*z^11-11520437*y^11*z^11
|
|---|
| 415 | -17348077*y^10*z^11+1861182*y^9*z^11-7471074*y^8*z^11
|
|---|
| 416 | +9874692*y^7*z^11-58997319*y^6*z^11+48089980*y^5*z^11
|
|---|
| 417 | +50094117*y^4*z^11+97789063*y^3*z^11-19868540*y^2*z^11
|
|---|
| 418 | -6467994*y*z^11+21506892*x*z^11-28651966*z^11
|
|---|
| 419 | -455276*y^14*z^10-2537698*y^13*z^10-1645616*y^12*z^10
|
|---|
| 420 | -20025700*y^11*z^10-16847943*y^10*z^10-10386480*y^9*z^10
|
|---|
| 421 | +33102991*y^8*z^10+26175312*y^7*z^10-35006123*y^6*z^10
|
|---|
| 422 | +41808924*y^5*z^10+101736412*y^4*z^10+154747355*y^3*z^10
|
|---|
| 423 | -49836054*y^2*z^10-77962850*y*z^10+23712288*x*z^10
|
|---|
| 424 | -134827431*z^10-2422655*y^14*z^9-5225662*y^13*z^9
|
|---|
| 425 | -2338550*y^12*z^9-12994009*y^11*z^9-9032604*y^10*z^9
|
|---|
| 426 | -29961138*y^9*z^9+66936577*y^8*z^9+64418844*y^7*z^9
|
|---|
| 427 | +81555203*y^6*z^9-2708652*y^5*z^9+24063602*y^4*z^9
|
|---|
| 428 | +1148833*y^3*z^9-47268530*y^2*z^9-67373776*y*z^9
|
|---|
| 429 | +1764237*x*z^9-88593549*z^9-4986216*y^14*z^8-7428554*y^13*z^8
|
|---|
| 430 | -5165504*y^12*z^8+10993230*y^11*z^8+9390554*y^10*z^8
|
|---|
| 431 | -17534260*y^9*z^8+76120232*y^8*z^8+79656150*y^7*z^8
|
|---|
| 432 | +137987784*y^6*z^8-101941496*y^5*z^8-132624275*y^4*z^8
|
|---|
| 433 | -172225566*y^3*z^8+25125354*y^2*z^8+30962138*y*z^8
|
|---|
| 434 | -11052938*x*z^8+46839364*z^8-5523915*y^14*z^7
|
|---|
| 435 | -8105042*y^13*z^7-8820386*y^12*z^7+38847465*y^11*z^7
|
|---|
| 436 | +43483352*y^10*z^7+36765466*y^9*z^7+29301146*y^8*z^7
|
|---|
| 437 | -1847500*y^7*z^7+21773417*y^6*z^7-135684168*y^5*z^7
|
|---|
| 438 | -158340584*y^4*z^7-125604427*y^3*z^7+80065726*y^2*z^7
|
|---|
| 439 | +87379542*y*z^7-3888*x^2*z^7-6288353*x*z^7+100799218*z^7
|
|---|
| 440 | -2561289*y^14*z^6-5335154*y^13*z^6-7823078*y^12*z^6
|
|---|
| 441 | +52680669*y^11*z^6+65292989*y^10*z^6+76413538*y^9*z^6
|
|---|
| 442 | -69509327*y^8*z^6-119457606*y^7*z^6-135926551*y^6*z^6
|
|---|
| 443 | -18081196*y^5*z^6-15863623*y^4*z^6+56776217*y^3*z^6
|
|---|
| 444 | +40208808*y^2*z^6+40930240*y*z^6-11664*x^2*z^6+343198*x*z^6
|
|---|
| 445 | +42613627*z^6+3518784*y^14*z^5+1983340*y^13*z^5
|
|---|
| 446 | +253010*y^12*z^5+31408200*y^11*z^5+38911488*y^10*z^5
|
|---|
| 447 | +47606934*y^9*z^5-110691688*y^8*z^5-125367140*y^7*z^5
|
|---|
| 448 | -139019436*y^6*z^5+93428348*y^5*z^5+95842332*y^4*z^5
|
|---|
| 449 | +125597464*y^3*z^5-21532348*y^2*z^5-20745570*y*z^5
|
|---|
| 450 | -19440*x^2*z^5-5832*x*z^5-21217046*z^5+9539685*y^14*z^4
|
|---|
| 451 | +9316858*y^13*z^4+9093788*y^12*z^4-18625895*y^11*z^4
|
|---|
| 452 | -17408485*y^10*z^4-16339548*y^9*z^4-39460090*y^8*z^4
|
|---|
| 453 | -16066196*y^7*z^4-17749911*y^6*z^4+66181556*y^5*z^4
|
|---|
| 454 | +66222615*y^4*z^4+45915757*y^3*z^4-26910314*y^2*z^4
|
|---|
| 455 | -27005570*y*z^4-11664*x*z^4-26735354*z^4+10740936*y^14*z^3
|
|---|
| 456 | +10658716*y^13*z^3+10641134*y^12*z^3-46816940*y^11*z^3
|
|---|
| 457 | -46335370*y^10*z^3-46176990*y^9*z^3+33130656*y^8*z^3
|
|---|
| 458 | +64709996*y^7*z^3+64170334*y^6*z^3-1268748*y^5*z^3
|
|---|
| 459 | +131590*y^4*z^3-32235268*y^3*z^3-6653686*y^2*z^3
|
|---|
| 460 | -7185370*y*z^3+19440*x^2*z^3-7526542*z^3+6000836*y^14*z^2
|
|---|
| 461 | +6064016*y^13*z^2+6053324*y^12*z^2-30408756*y^11*z^2
|
|---|
| 462 | -30703272*y^10*z^2-30698412*y^9*z^2+31174168*y^8*z^2
|
|---|
| 463 | +49525624*y^7*z^2+49799728*y^6*z^2-12830488*y^5*z^2
|
|---|
| 464 | -13526440*y^4*z^2-31703908*y^3*z^2+133388*y^2*z^2
|
|---|
| 465 | +469700*y*z^2+15552*x^2*z^2+650492*z^2+1367102*y^14*z
|
|---|
| 466 | +1360298*y^13*z+1388486*y^12*z-6785938*y^11*z-6786910*y^10*z
|
|---|
| 467 | -6962842*y^9*z+6567238*y^8*z+10879468*y^7*z+11139964*y^6*z
|
|---|
| 468 | -2410528*y^5*z-2641864*y^4*z-69984*x*y^3*z-7044490*y^3*z
|
|---|
| 469 | +104976*x*y^2*z-104976*y^2*z-34992*x*z+34992*z-74500*y^14
|
|---|
| 470 | -64780*y^13-90052*y^12+331676*y^11+318068*y^10+479420*y^9
|
|---|
| 471 | -139220*y^8-559064*y^7-796232*y^6-148432*y^5+77072*y^4
|
|---|
| 472 | +69984*x*y^3+596060*y^3-104976*x*y^2+104976*y^2+34992*x
|
|---|
| 473 | -34992]" '(x y z)))))
|
|---|
| 474 | (&body)))
|
|---|
| 475 |
|
|---|
| 476 | (test buchberger-cox-tough
|
|---|
| 477 | "Buchberger algorithm - Cox tough example"
|
|---|
| 478 | (with-fixture buchberger-cox-tough-context ()
|
|---|
| 479 | (is-true (grobner-test gb fl))
|
|---|
| 480 | ;;
|
|---|
| 481 | ;; TODO: The following test runs out of memory with normal strategy, as expected.
|
|---|
| 482 | ;;
|
|---|
| 483 | ;; NOTE: Cannot compare using SET-EXCLUSIVE-OR, as the Grobner basis
|
|---|
| 484 | ;; FL was computed using "sugar" strategy and is different from
|
|---|
| 485 | ;; the one obtained with BUCHBERGER, which uses the "normal" strategy.
|
|---|
| 486 | ;; (is (grobner-equal (buchberger fl) gb))
|
|---|
| 487 | ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
|
|---|
| 488 | )
|
|---|
| 489 | )
|
|---|
| 490 |
|
|---|
| 491 |
|
|---|
| 492 | (run! 'buchberger-suite)
|
|---|
| 493 | (format t "All tests done!~%")
|
|---|
| 494 |
|
|---|
| 495 |
|
|---|
