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source: branches/f4grobner/5am-buchberger.lisp@ 4551

Last change on this file since 4551 was 4542, checked in by Marek Rychlik, 9 years ago

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1;;; -*- Mode: Lisp -*-
2;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
3;;;
4;;; Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>
5;;;
6;;; This program is free software; you can redistribute it and/or modify
7;;; it under the terms of the GNU General Public License as published by
8;;; the Free Software Foundation; either version 2 of the License, or
9;;; (at your option) any later version.
10;;;
11;;; This program is distributed in the hope that it will be useful,
12;;; but WITHOUT ANY WARRANTY; without even the implied warranty of
13;;; MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
14;;; GNU General Public License for more details.
15;;;
16;;; You should have received a copy of the GNU General Public License
17;;; along with this program; if not, write to the Free Software
18;;; Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA.
19;;;
20;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
21
22;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
23;;
24;; Run tests using 5am unit testing framework
25;;
26;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
27
28;; We assume that QuickLisp package manager is installed.
29;; See :
30;; https://www.quicklisp.org/beta/
31;;
32
33;; The following is unnecessary after running:
34;; * (ql:add-to-init-file)
35;; at lisp prompt:
36;;(load "~/quicklisp/setup")
37
38(ql:quickload :fiveam)
39
40(defpackage #:5am-buchberger
41 (:use :cl :it.bese.fiveam :monom :polynomial :infix :symbolic-polynomial :division :priority-queue :buchberger :grobner-debug))
42
43(in-package :5am-buchberger)
44
45(def-suite buchberger-suite
46 :description "Buchberger algorithm suite")
47
48(in-suite buchberger-suite)
49
50(def-fixture buchberger-context ()
51 (let ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
52 (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y)))))
53 (&body)))
54
55
56(test buchberger
57 "Buchberger algorithm"
58 (with-fixture buchberger-context ()
59 (is-true (grobner-test gb fl))
60 (is (every #'universal-equalp (buchberger fl) gb))
61 ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
62 )
63 )
64
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]);
66(def-fixture buchberger-enneper-surface-context ()
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))))
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,
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,
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,
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,
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,
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
74 -1296*v^2*z-1944*z-243*v^2*y^2-648*y^2+243*v^2*x^2+648*x^2,
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,
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
77 +81*y^3+81*v*y^2-81*x^2*y-81*v*x^2,
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
79 -216*y*z^3+6912*v*z^3+81*y^3*z^2-9720*v*y^2*z^2
80 -1539*x^2*y*z^2+31104*y*z^2+62208*v*z^2+8505*y^3*z
81 +46656*v*y^2*z-8505*x^2*y*z-93312*y*z+729*v*y^4-23328*y^3
82 -1458*v*x^2*y^2-23328*v*y^2+23328*x^2*y+729*v*x^4
83 +23328*v*x^2,
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
85 +5832*z^3+972*y^2*z^2+17496*v*y*z^2-2430*x^2*z^2+8748*v*y^3*z
86 -19683*y^2*z+2187*x^2*z-5103*y^4-4374*v*y^3+5832*x^2*y^2
87 +4374*v*x^2*y-729*x^4,
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
89 +3888*z^4+81*y^2*z^3+17496*v*y*z^3-2997*x^2*z^3+17496*z^3
90 +8748*v*y^3*z^2-16767*y^2*z^2+17496*v*y*z^2-5103*x^2*z^2
91 -5103*y^4*z+5832*x^2*y^2*z-6561*y^2*z-729*x^4*z+6561*x^2*z
92 -2187*y^4+4374*x^2*y^2-2187*x^4,
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
94 +419904*z^5+174960*y^2*z^4-174960*x^2*z^4-10935*y^4*z^3
95 -56862*x^2*y^2*z^3+314928*y^2*z^3-10935*x^4*z^3+314928*x^2*z^3
96 +118098*y^4*z^2-118098*x^4*z^2+59049*y^4*z-118098*x^2*y^2*z
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)))))
98 (&body)))
99
100
101(test buchberger-enneper-surface
102 "Buchberger algorithm - Enneper surface"
103 (with-fixture buchberger-enneper-surface-context ()
104 (is-true (grobner-test gb fl))
105 ;; NOTE: Cannot compare using SET-EXCLUSIVE-OR, as the Grobner basis
106 ;; FL was computed using "sugar" strategy and is different from
107 ;; the one obtained with BUCHBERGER, which uses the "normal" strategy.
108 (is (grobner-equal (buchberger fl) gb))
109 ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
110 )
111 )
112
113;; Cyclic roots of degree 5
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]);
115(def-fixture buchberger-cyclic-5-context ()
116 (let ((fl
117 (cdr (string->poly
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]"
119 '(u v x y z))))
120 (gb (cdr (string->poly "[z+y+x+v+u,
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,
122 z^15+122*z^10-122*z^5-1,
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
124 -1650*y^5*z^2-179073*z^2-550*y^6*z-69019*y*z-825*v*z-275*y^2
125 -275*v^2,(-z^11)-143*z^6-55*v*z^5+144*z+55*v,
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
127 +440*y^5*z^2+42124*z^2+110*y^6*z+15106*y*z+275*v*z-275*v*y,
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
129 -1045*y^5*z^2-105873*z^2-330*y^6*z-40726*y*z+550*x*z-275*v*z
130 -550*y^2+275*x^2+275*v*x,
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
132 +69307*z^3+275*y^6*z^2+28018*y*z^2-550*x*z^2+550*y^2*z
133 +550*x^2*z+275*x^3,(-z^11)-143*z^6-55*x*z^5+144*z+55*x,
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
135 -136674*z^2-440*y^6*z-53913*y*z+275*x*z-275*y^2-275*x*y,
136 1042*z^12+398*y*z^11+127116*z^7+48554*y*z^6-55*y^5*z^2-128103*z^2
137 -165*y^6*z-48787*y*z-55*y^7+55*y^2]" '(u v x y z)))))
138 (&body)))
139
140
141(test buchberger-cyclic-5
142 "Buchberger algorithm - cyclic 5"
143 (with-fixture buchberger-cyclic-5-context ()
144 (is-true (grobner-test gb fl))
145 ;; NOTE: Cannot compare using SET-EXCLUSIVE-OR, as the Grobner basis
146 ;; FL was computed using "sugar" strategy and is different from
147 ;; the one obtained with BUCHBERGER, which uses the "normal" strategy.
148 (is (grobner-equal (buchberger fl) gb))
149 ;;(is (every #'universal-equalp (parallel-buchberger fl) gb))
150 )
151 )
152
153;; A tough example learned from Cox
154;; poly_grobner([x^5+y^4+z^3-1,x^3+y^3+z^2-1], [x,y,z]);
155;; Note that the Grobner basis in the test is reduced, obtained with
156;; poly_reduced_grobner([x^5+y^4+z^3-1,x^3+y^3+z^2-1], [x,y,z]);
157(def-fixture buchberger-cox-tough-context ()
158 (let ((fl (cdr (string->poly "[x^5+y^4+z^3-1,x^3+y^3+z^2-1]" '(x y z))))
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,
160 (-z^4)-x*z^3-2*y^3*z^2+2*z^2-y^6-x*y^4+2*y^3+x-1,
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
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
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
164 +6*y^12-10*y^9-3*y^8+10*y^6+3*y^4-5*y^3,
165 (-44425*z^21)-44425*x*z^20-193795*z^20-88850*y^3*z^19+266550*y*z^19
166 -327070*x*z^19-1274354*z^19+44425*y^4*z^18-32190*y^3*z^18
167 +444250*y^2*z^18+451970*y*z^18-1278214*x*z^18-3527528*z^18
168 -44425*y^6*z^17+1526545*y^4*z^17-1842423*y^3*z^17
169 +1227150*y^2*z^17-1140996*y*z^17-2698855*x*z^17
170 -1109995*z^17+88850*y^7*z^16+783555*y^6*z^16
171 +1954700*y^5*z^16+4467129*y^4*z^16-9605029*y^3*z^16
172 -752630*y^2*z^16-2972806*y*z^16-2572042*x*z^16
173 +13565093*z^16-44425*y^8*z^15+2697690*y^7*z^15
174 +456911*y^6*z^15+7105380*y^5*z^15+2647468*y^4*z^15
175 -10602997*y^3*z^15-7006014*y^2*z^15+1218640*y*z^15
176 +2619449*x*z^15+22302653*z^15+44425*y^10*z^14
177 +888500*y^9*z^14+2915955*y^8*z^14+9160898*y^7*z^14
178 -7506655*y^6*z^14+5800536*y^5*z^14-3245086*y^4*z^14
179 +20587543*y^3*z^14-8783974*y^2*z^14+3837574*y*z^14
180 +10650408*x*z^14-7954033*z^14-88850*y^11*z^13
181 +1881945*y^10*z^13+1921200*y^9*z^13+11847046*y^8*z^13
182 +9782204*y^7*z^13-12668822*y^6*z^13-10997536*y^5*z^13
183 +1090138*y^4*z^13+54430174*y^3*z^13-1436450*y^2*z^13
184 -11018460*y*z^13+11493837*x*z^13-56030677*z^13
185 +266550*y^12*z^12+1744810*y^11*z^12+6728289*y^10*z^12
186 -187950*y^9*z^12+15235952*y^8*z^12-505866*y^7*z^12
187 +10778914*y^6*z^12-25975004*y^5*z^12+899768*y^4*z^12
188 +13274582*y^3*z^12+4950830*y^2*z^12-21334144*y*z^12
189 -2616810*x*z^12-42908546*z^12-44425*y^14*z^11
190 +444250*y^13*z^11+718520*y^12*z^11+7686377*y^11*z^11
191 +9990070*y^10*z^11-1596036*y^9*z^11-1342215*y^8*z^11
192 -8841150*y^7*z^11+40955979*y^6*z^11-24957052*y^5*z^11
193 -36144372*y^4*z^11-82735585*y^3*z^11+13378064*y^2*z^11
194 +12799086*y*z^11-16744470*x*z^11+42041860*z^11
195 +339305*y^14*z^10+1671400*y^13*z^10+910274*y^12*z^10
196 +11626231*y^11*z^10+7801347*y^10*z^10+7831314*y^9*z^10
197 -26096155*y^8*z^10-16474014*y^7*z^10+11243399*y^6*z^10
198 -17808216*y^5*z^10-61462426*y^4*z^10-89174777*y^3*z^10
199 +30957924*y^2*z^10+55234262*y*z^10-12049440*x*z^10
200 +91874913*z^10+1628711*y^14*z^9+3140020*y^13*z^9
201 +1263518*y^12*z^9+4404103*y^11*z^9+2153415*y^10*z^9
202 +19135710*y^9*z^9-40336258*y^8*z^9-39769140*y^7*z^9
203 -68036522*y^6*z^9+12529572*y^5*z^9+7525711*y^4*z^9
204 +37559804*y^3*z^9+21952328*y^2*z^9+29962348*y*z^9
205 +4801407*x*z^9+31327296*z^9+3000105*y^14*z^8
206 +4046756*y^13*z^8+3116408*y^12*z^8-11359143*y^11*z^8
207 -9140507*y^10*z^8+5385232*y^9*z^8-38148698*y^8*z^8
208 -41664378*y^7*z^8-80668677*y^6*z^8+73310048*y^5*z^8
209 +103064435*y^4*z^8+127272309*y^3*z^8-30170622*y^2*z^8
210 -39724286*y*z^8+8854766*x*z^8-57432520*z^8
211 +2743338*y^14*z^7+3960482*y^13*z^7+5071808*y^12*z^7
212 -25510554*y^11*z^7-29133398*y^10*z^7-31118752*y^9*z^7
213 -1947773*y^8*z^7+21330064*y^7*z^7+18392944*y^6*z^7
214 +73580532*y^5*z^7+82980083*y^4*z^7+49867042*y^3*z^7
215 -52627432*y^2*z^7-56881602*y*z^7+1892306*x*z^7
216 -63266461*z^7+437586*y^14*z^6+1782242*y^13*z^6
217 +3440132*y^12*z^6-28425462*y^11*z^6-36482669*y^10*z^6
218 -46554784*y^9*z^6+58365386*y^8*z^6+86946000*y^7*z^6
219 +105699982*y^6*z^6-21170564*y^5*z^6-28598633*y^4*z^6
220 -74430398*y^3*z^6-9384858*y^2*z^6-8218528*y*z^6
221 -1980847*x*z^6-5375344*z^6-3228714*y^14*z^5
222 -2836264*y^13*z^5-2194496*y^12*z^5-9426528*y^11*z^5
223 -11662110*y^10*z^5-15507324*y^9*z^5+63744949*y^8*z^5
224 +61819454*y^7*z^5+68420946*y^6*z^5-74140892*y^5*z^5
225 -75995106*y^4*z^5-79475920*y^3*z^5+26513908*y^2*z^5
226 +26664768*y*z^5+17496*x*z^5+27268337*z^5-6067476*y^14*z^4
227 -6324094*y^13*z^4-6620078*y^12*z^4+21880364*y^11*z^4
228 +22936006*y^10*z^4+24599634*y^9*z^4+662692*y^8*z^4
229 -20296984*y^7*z^4-23355948*y^6*z^4-25675184*y^5*z^4
230 -25336908*y^4*z^4-1372204*y^3*z^4+15113990*y^2*z^4
231 +15232088*y*z^4-34992*x*z^4+14641598*z^4-5393667*y^14*z^3
232 -5404156*y^13*z^3-5499938*y^12*z^3+29810057*y^11*z^3
233 +29956543*y^10*z^3+30284550*y^9*z^3-35221464*y^8*z^3
234 -53124800*y^7*z^3-52987825*y^6*z^3+18268092*y^5*z^3
235 +18247517*y^4*z^3+36291181*y^3*z^3-2001554*y^2*z^3
236 -2010302*y*z^3+17496*x*z^3-1214234*z^3-1569800*y^14*z^2
237 -1661654*y^13*z^2-1622288*y^12*z^2+10350756*y^11*z^2
238 +10775034*y^10*z^2+10578204*y^9*z^2-15349894*y^8*z^2
239 -20474824*y^7*z^2-20457328*y^6*z^2+10504900*y^5*z^2
240 +10793584*y^4*z^2+15564220*y^3*z^2-2374910*y^2*z^2
241 +69984*x*y*z^2-2436146*y*z^2-69984*x*z^2-2619854*z^2
242 +632812*y^14*z+685300*y^13*z+632812*y^12*z-3181556*y^11*z
243 -3478988*y^10*z-3111572*y^9*z+3269036*y^8*z+5569880*y^7*z
244 +4905032*y^6*z-1388096*y^5*z-1738016*y^4*z-2796644*y^3*z
245 -139968*x*y*z+139968*y*z+139968*x*z-139968*z+501226*y^14
246 +474982*y^13+501226*y^12-2497382*y^11-2348666*y^10
247 -2532374*y^9+2453642*y^8+3756116*y^7+4088540*y^6
248 -941216*y^5-766256*y^4-2689838*y^3+69984*x*y-69984*y
249 -69984*x+69984,
250 z^22+x*z^21+6*z^21+2*y^3*z^20-6*y*z^20+9*x*z^20+37*z^20-y^4*z^19
251 +4*y^3*z^19-10*y^2*z^19-20*y*z^19+42*x*z^19+132*z^19+y^6*z^18
252 -36*y^4*z^18+45*y^3*z^18-44*y^2*z^18+2*y*z^18+117*x*z^18+191*z^18
253 -2*y^7*z^17-16*y^6*z^17-44*y^5*z^17-158*y^4*z^17+286*y^3*z^17
254 -40*y^2*z^17+94*y*z^17+195*x*z^17-156*z^17+y^8*z^16-64*y^7*z^16
255 -38*y^6*z^16-232*y^5*z^16-265*y^4*z^16+642*y^3*z^16+148*y^2*z^16
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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
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