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source: branches/f4grobner/5am-symbolic-poly.lisp@ 4264

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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;; Unless NGROBNER system loaded by ASDF,
41;; load the dependencies directly
42#-ngrobner
43(progn
44 (require :utils "utils")
45 (require :copy "copy")
46 (require :monom "monom")
47 (require :polynomial "polynomial")
48 (require :infix "infix")
49 (require :symbolic-polynomial "symbolic-polynomial"))
50
51(defpackage #:5am-symbolic-poly
52 (:use :cl :it.bese.fiveam :monom :polynomial :infix :symbolic-polynomial))
53
54(in-package :5am-symbolic-poly)
55
56(def-suite symbolic-poly-suite
57 :description "Symbolic polynomial package suite")
58
59(in-suite symbolic-poly-suite)
60
61(test read-infix-form
62 "Infix form reader"
63 (is (equalp (with-input-from-string (s "X^2-Y^2+(-4/3)*U^2*W^3-5") (read-infix-form :stream s))
64 '(+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))))
65 (is (equalp (poly->string (string->poly "1" '(x y u w))) "1"))
66 (is (equalp (->sexp (string->poly "X^2-Y^2+(-4/3)*U^2*W^3-5" '(x y u w)))
67 '(+ (EXPT X 2) (* -1 (EXPT Y 2)) (* -4/3 (EXPT U 2) (EXPT W 3)) -5))))
68
69
70(def-fixture sym-poly-context ()
71 (let ((p (make-instance 'poly))
72 (p-symbolic (make-instance 'symbolic-poly :vars '(x))))
73 (dolist (x '( ((2) . 22) ((4) . 44) ((5) . 55) ((8) . 88) ((9) . 99) ))
74 (poly-insert-term p (make-instance 'term :exponents (car x) :coeff (cdr x)))
75 (poly-insert-term p-symbolic (make-instance 'term :exponents (car x) :coeff (cdr x))))
76 (&body)))
77
78(test sym-poly
79 "Symbolic polynomial"
80 (with-fixture sym-poly-context ()
81 (is (universal-equalp (change-class p 'symbolic-poly :vars '(x)) p-symbolic )))
82 (with-fixture sym-poly-context ()
83 (signals
84 (error "Number of variables does not equal dimension.")
85 (universal-equalp (change-class p 'symbolic-poly :vars '(x y)) p-symbolic ))))
86
87;; The following example uses the Grobner basis obtained with Maxima
88;; Grobner package
89;;
90;; 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]);
91;;
92;; The Maxima output is placed in the string STR-1. The string STR-1
93;; is parsed STRING->POLY to a polynomial list GB-1. Then we take GB-1 and apply
94;; POLY->STRING to it. Then we feed the string STR-2 into Maxima as
95;; input and format according to Maxima rules. The resulting string is
96;; STR-3. We parse it with STRING->POLY to a polynomial list GB-2.
97;; Obviously, we should have equality GB-1 and GB-2. This is the test.
98;;
99(def-fixture big-poly-list-context ()
100 (let* ((vars '(u v x y z))
101 (str-1 "[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,
102 (-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,
103 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,
104 (-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,
105 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,
106 (-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
107 -1296*v^2*z-1944*z-243*v^2*y^2-648*y^2+243*v^2*x^2+648*x^2,
108 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,
109 (-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
110 +81*y^3+81*v*y^2-81*x^2*y-81*v*x^2,
111 (-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
112 -216*y*z^3+6912*v*z^3+81*y^3*z^2-9720*v*y^2*z^2
113 -1539*x^2*y*z^2+31104*y*z^2+62208*v*z^2+8505*y^3*z
114 +46656*v*y^2*z-8505*x^2*y*z-93312*y*z+729*v*y^4-23328*y^3
115 -1458*v*x^2*y^2-23328*v*y^2+23328*x^2*y+729*v*x^4
116 +23328*v*x^2,
117 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
118 +5832*z^3+972*y^2*z^2+17496*v*y*z^2-2430*x^2*z^2+8748*v*y^3*z
119 -19683*y^2*z+2187*x^2*z-5103*y^4-4374*v*y^3+5832*x^2*y^2
120 +4374*v*x^2*y-729*x^4,
121 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
122 +3888*z^4+81*y^2*z^3+17496*v*y*z^3-2997*x^2*z^3+17496*z^3
123 +8748*v*y^3*z^2-16767*y^2*z^2+17496*v*y*z^2-5103*x^2*z^2
124 -5103*y^4*z+5832*x^2*y^2*z-6561*y^2*z-729*x^4*z+6561*x^2*z
125 -2187*y^4+4374*x^2*y^2-2187*x^4,
126 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
127 +419904*z^5+174960*y^2*z^4-174960*x^2*z^4-10935*y^4*z^3
128 -56862*x^2*y^2*z^3+314928*y^2*z^3-10935*x^4*z^3+314928*x^2*z^3
129 +118098*y^4*z^2-118098*x^4*z^2+59049*y^4*z-118098*x^2*y^2*z
130 +59049*x^4*z+19683*y^6-59049*x^2*y^4+59049*x^4*y^2-19683*x^6]")
131 ;; Parse STR-1 to polynomial list GB-1
132 (gb-1 (string->poly str-1 vars))
133 ;; Format GB-1 as a string STR-2
134 (str-2 (poly->string gb-1))
135 ;; Here STR-3 is a Maxima-postprocessed STR-2"
136 (str-3 "[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,
137 (-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,
138 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,
139 (-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,
140 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,
141 (-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
142 -1296*V^2*Z-1944*Z-243*V^2*Y^2-648*Y^2+243*V^2*X^2+648*X^2,
143 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,
144 (-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
145 +81*Y^3+81*V*Y^2-81*X^2*Y-81*V*X^2,
146 (-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
147 -216*Y*Z^3+6912*V*Z^3+81*Y^3*Z^2-9720*V*Y^2*Z^2
148 -1539*X^2*Y*Z^2+31104*Y*Z^2+62208*V*Z^2+8505*Y^3*Z
149 +46656*V*Y^2*Z-8505*X^2*Y*Z-93312*Y*Z+729*V*Y^4-23328*Y^3
150 -1458*V*X^2*Y^2-23328*V*Y^2+23328*X^2*Y+729*V*X^4
151 +23328*V*X^2,
152 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
153 +5832*Z^3+972*Y^2*Z^2+17496*V*Y*Z^2-2430*X^2*Z^2+8748*V*Y^3*Z
154 -19683*Y^2*Z+2187*X^2*Z-5103*Y^4-4374*V*Y^3+5832*X^2*Y^2
155 +4374*V*X^2*Y-729*X^4,
156 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
157 +3888*Z^4+81*Y^2*Z^3+17496*V*Y*Z^3-2997*X^2*Z^3+17496*Z^3
158 +8748*V*Y^3*Z^2-16767*Y^2*Z^2+17496*V*Y*Z^2-5103*X^2*Z^2
159 -5103*Y^4*Z+5832*X^2*Y^2*Z-6561*Y^2*Z-729*X^4*Z+6561*X^2*Z
160 -2187*Y^4+4374*X^2*Y^2-2187*X^4,
161 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
162 +419904*Z^5+174960*Y^2*Z^4-174960*X^2*Z^4-10935*Y^4*Z^3
163 -56862*X^2*Y^2*Z^3+314928*Y^2*Z^3-10935*X^4*Z^3+314928*X^2*Z^3
164 +118098*Y^4*Z^2-118098*X^4*Z^2+59049*Y^4*Z-118098*X^2*Y^2*Z
165 +59049*X^4*Z+19683*Y^6-59049*X^2*Y^4+59049*X^4*Y^2-19683*X^6]")
166 ;; Finally, obtain a polynomial list GB-2 by parsing STR-3
167 (gb-2 (string->poly str-3 vars)))
168 ;; Discart STR-2
169 (declare (ignore str-2))
170 (&body)))
171
172(test big-poly-list
173 "Big polynomial list"
174 (with-fixture big-poly-list-context ()
175 (is (universal-equalp gb-1 gb-2))))
176
177
178(run! 'symbolic-poly-suite)
179(format t "All tests done!~%")
180
181
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