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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(load "ngrobner.asd")
41(asdf:load-system :ngrobner)
42
43(defpackage #:ngrobner-tests
44 (:use :cl :it.bese.fiveam
45 :ngrobner :priority-queue :monomial
46 :utils :order :ring :term :ring-and-order
47 :termlist :polynomial
48 :priority-queue
49 :division
50 :grobner-wrap
51 )
52 )
53
54(in-package :ngrobner-tests)
55
56(def-suite ngrobner-suite
57 :description "New Groebner Package Suite")
58
59(in-suite ngrobner-suite)
60
61#+nil
62(test dummy-test
63 "Makelist"
64 (is (= (+ 2 2)) "2 plus 2 wasn't equal to 4 (using #'= to test equality)")
65 (is (= 0 (+ -1 1)))
66 (signals
67 (error "Trying to add 4 to FOO didn't signal an error")
68 (+ 'foo 4))
69 (is (= 0 (+ 1 1)) "this should have failed"))
70
71(test makelist-1
72 "makelist-1 test"
73 (is (equal (makelist-1 (* 2 i) i 0 10) '(0 2 4 6 8 10 12 14 16 18 20)))
74 (is (equal (makelist-1 (* 2 i) i 0 10 3) '(0 6 12 18))))
75
76(test makelist
77 "makelist"
78 (is (equal (makelist (+ (* i i) (* j j)) (i 1 4) (j 1 i)) '(2 5 8 10 13 18 17 20 25 32)))
79 (is (equal (makelist (list i j '---> (+ (* i i) (* j j))) (i 1 4) (j 1 i))
80 '((1 1 ---> 2) (2 1 ---> 5) (2 2 ---> 8) (3 1 ---> 10) (3 2 ---> 13)
81 (3 3 ---> 18) (4 1 ---> 17) (4 2 ---> 20) (4 3 ---> 25) (4 4 ---> 32)))))
82
83(test monom
84 "monom"
85 (is (every #'= (make-monom :dimension 3) '(0 0 0)) "Trivial monomial is a vector of 0's")
86 (is (every #'= (make-monom :initial-exponents '(1 2 3)) '(1 2 3)) "Monomial with powers 1,2,3")
87 (let ((p (make-monom :initial-exponents '(1 2 3))))
88 (is (every #'= (monom-map (lambda (x) x) p) '(1 2 3)))))
89
90
91(test order
92 "order"
93 (let ((p (make-monom :initial-exponents '(1 3 2)))
94 (q (make-monom :initial-exponents '(1 2 3))))
95 (is-true (lex> p q))
96 (is-true (grlex> p q))
97 (is-true (revlex> p q))
98 (is-true (grevlex> p q))
99 (is-false (invlex> p q))))
100
101(test elim-order
102 "elimination order"
103 (let* ((p (make-monom :initial-exponents '(1 2 3)))
104 (q (make-monom :initial-exponents '(4 5 6)))
105 (elim-order-factory (make-elimination-order-factory))
106 (elim-order-1 (funcall elim-order-factory 1))
107 (elim-order-2 (funcall elim-order-factory 2)))
108 (is-false (funcall elim-order-1 p q))
109 (is-false (funcall elim-order-2 p q))))
110
111(test term
112 "term"
113 (let* ((m1 (make-monom :initial-exponents '(1 2 3)))
114 (m2 (make-monom :initial-exponents '(3 5 2)))
115 (m3 (monom-mul m1 m2))
116 (t1 (make-term m1 7))
117 (t2 (make-term m2 9))
118 (t3 (make-term m3 (* 7 9))))
119 (is (equalp (term-mul *ring-of-integers* t1 t2) t3))))
120
121(test termlist
122 "termlist"
123 (let* ((t1 (make-term (make-monom :initial-exponents '(1 2 3)) 7))
124 (t2 (make-term (make-monom :initial-exponents '(3 5 2)) 9))
125 (t11 (make-term (make-monom :initial-exponents '(2 4 6)) 49))
126 (t12 (make-term (make-monom :initial-exponents '(4 7 5)) 126))
127 (t22 (make-term (make-monom :initial-exponents '(6 10 4)) 81))
128 (p (list t2 t1))
129 (p-sq (list t22 t12 t11))
130 (ring-and-order (make-ring-and-order))
131 (q (termlist-expt ring-and-order p 2)))
132 (is-true (equalp q p-sq))))
133
134(test poly
135 "poly"
136 (let* ((t1 (make-term (make-monom :initial-exponents '(1 2 3)) 7))
137 (t2 (make-term (make-monom :initial-exponents '(3 5 2)) 9))
138 (t11 (make-term (make-monom :initial-exponents '(2 4 6)) 49))
139 (t12 (make-term (make-monom :initial-exponents '(4 7 5)) 126))
140 (t22 (make-term (make-monom :initial-exponents '(6 10 4)) 81))
141 (p (make-poly-from-termlist (list t2 t1)))
142 (p-sq (make-poly-from-termlist (list t22 t12 t11)))
143 (ring-and-order (make-ring-and-order))
144 (q (poly-expt ring-and-order p 2)))
145 (is-true (equalp q p-sq))))
146
147
148(test coerce-to-infix
149 "Conversion to infix form"
150 (is (equal
151 (coerce-to-infix :term (make-term-variable *ring-of-integers* 5 3) '(x y z w u v))
152 '(* 1 (EXPT X 0) (EXPT Y 0) (EXPT Z 0) (EXPT W 1) (EXPT U 0)))))
153
154(test priority-queue
155 "Priority queue"
156 (let ((q (make-priority-queue)))
157 (priority-queue-insert q 7)
158 (priority-queue-insert q 8)
159 (is (= (priority-queue-size q) 3) "Note that there is always a dummy element in the queue.")
160 (is (equalp (priority-queue-heap q) #(0 7 8)))
161 (is (= (priority-queue-remove q) 7))
162 (is (= (priority-queue-remove q) 8))
163 (is-true (priority-queue-empty-p q))
164 (signals
165 (error "Empty queue.")
166 (priority-queue-remove q))))
167
168;;
169;; Currently parser cannot be tested, as it relies on many maxima functions
170;; to parse a polynomial expression.
171;;
172#|
173(test parser
174 "Parser"
175 (let (($f '((MLIST SIMP) ((MPLUS SIMP) $X ((MTIMES SIMP) -1 $Y)) ((MPLUS SIMP) $X $Y)))
176 ($v '((MLIST SIMP) $X $Y)))
177 (is-true (parse-poly-list $f $v))))
178|#
179
180(test infix-print
181 "Infix printer"
182 (is (string= (infix-print '(+ x y) nil) "X+Y"))
183 (is (string= (infix-print '(expt x 3) nil) "X^3"))
184 (is (string= (infix-print '(+ 1 (expt x 3)) nil) "1+(X^3)"))
185 (is (string= (infix-print '(* x y) nil) "X*Y"))
186 (is (string= (infix-print '(* x (expt y 2)) nil) "X*(Y^2)")))
187
188(test infix
189 "Infix parser"
190 (is (equal '#I( x^2 + y^2 ) '(+ (expt x 2) (expt y 2))))
191 (is (equal '#I( [ x, y ] ) '(:[ X Y)))
192 (is (equal '#I( x + y) '(+ x y)))
193 (is (equal '#I( x^3 ) '(expt x 3)))
194 (is (equal '#I( 1 + x^3) '(+ 1 (expt x 3))))
195 (is (equal '#I( x * y^2 ) '(* x (expt y 2)))))
196
197(test poly-reader
198 "Polynomial reader"
199 (is (equalp (with-input-from-string (s "X^2-Y^2+(-4/3)*U^2*W^3-5")
200 (read-infix-form :stream s))
201 '(+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))))
202 (is (equalp (string->alist "X^2-Y^2+(-4/3)*U^2*W^3-5" '(x y u w))
203 '(((2 0 0 0) . 1)
204 ((0 2 0 0) . -1)
205 ((0 0 2 3) . -4/3)
206 ((0 0 0 0) . -5))))
207 (is (equalp (string->alist "[x^2-y^2+(-4/3)*u^2*w^3-5,y]" '(x y u w))
208 '(:[
209 (((2 0 0 0) . 1) ((0 2 0 0) . -1) ((0 0 2 3) . -4/3) ((0 0 0 0) . -5))
210 (((0 1 0 0) . 1)))))
211 (let ((p (make-poly-from-termlist (list (make-term (make-monom :initial-exponents '(2 0)) 1)
212 (make-term (make-monom :initial-exponents '(0 2)) 2)))))
213 (is (equalp (with-input-from-string (s "x^2+2*y^2")
214 (read-poly '(x y) :stream s))
215 p))
216 (is (equalp (string->poly "x^2+2*y^2" '(x y)) p))))
217
218;; Manual calculation supporting the test below.
219;; We divide X^2 by [X+Y,X-2*Y] with LEX> as order.
220;; LM(X^2)=X^2 is divisible by LM(X+Y)=X so the first partial quotient is X.
221;; Next, X^2 - X*(X+Y) = -X*Y.
222;; LM(-X*Y)=X*Y is divibile by LM(X+Y)=X so the second partial quotient is -Y.
223;; Next, -X*Y-(-Y)*(X+Y) = Y^2.
224;; LM(Y^2)=Y^2 is not divisible by LM(X+Y)=X or LM(X-2*Y)=X. Hence, division
225;; ends. The list of quotients is [X-Y,0]. The remainder is Y^2
226(test division
227 "Division in polynomial ring"
228 (let* ((f (string->poly "x^2" '(x y)))
229 (y-sq (string->poly "y^2" '(x y)))
230 (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
231 (ring *ring-of-integers*)
232 (order #'lex>)
233 (ring-and-order (make-ring-and-order :ring ring :order order))
234 (quotients (cdr (string->poly "[x-y,0]" '(x y)))))
235 (is (equalp (multiple-value-list (normal-form ring-and-order f fl)) (list y-sq 1 2)))
236 (is (equalp (multiple-value-list (poly-pseudo-divide ring-and-order f fl))
237 (list quotients y-sq 1 2)))
238 (is-false (buchberger-criterion ring-and-order fl)))
239 (let* ((f (string->poly "x^2-4*y^2" '(x y)))
240 (g (string->poly "x+2*y" '(x y)))
241 (h (string->poly "x-2*y" '(x y)))
242 (ring *ring-of-integers*)
243 (order #'lex>)
244 (ring-and-order (make-ring-and-order :ring ring :order order)))
245 (is (equalp (poly-exact-divide ring-and-order f g) h))))
246
247
248(test buchberger
249 "Buchberger algorithm"
250 (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
251 (ring *ring-of-integers*)
252 (order #'lex>)
253 (ring-and-order (make-ring-and-order :ring ring :order order))
254 (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y)))))
255 (is-true (grobner-test ring-and-order gb fl))
256 (is (equalp (buchberger ring-and-order fl) gb))
257 (is (equalp (parallel-buchberger ring-and-order fl) gb))))
258
259(test gebauer-moeller
260 "Gebauer-Moeller algorithm"
261 (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
262 (ring *ring-of-integers*)
263 (order #'lex>)
264 (ring-and-order (make-ring-and-order :ring ring :order order))
265 (gb (cdr (string->poly "[y,x-2*y]" '(x y)))))
266 (is-true (grobner-test ring-and-order gb fl))
267 (is (equalp (gebauer-moeller ring-and-order fl) gb))))
268
269(test gb-postprocessing
270 "Grobner basis postprocessing"
271 (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
272 (ring *ring-of-integers*)
273 (order #'lex>)
274 (ring-and-order (make-ring-and-order :ring ring :order order))
275 (gb (cdr (string->poly "[y,x-2*y]" '(x y))))
276 (reduced-gb (cdr (string->poly "[y,x]" '(x y)))))
277 (is-true (grobner-test ring-and-order gb fl))
278 (is (equalp (reduction ring-and-order gb) reduced-gb)))
279 (let* ((gb (cdr (string->poly "[x,y,x-2*y,x^2]" '(x y))))
280 (minimal-gb (cdr (string->poly "[y,x-2*y]" '(x y)))))
281 (is (equalp (minimization gb) minimal-gb))))
282
283(test grobner-wrap
284 "Grobner interface to many algorithms"
285 (let* (($poly_grobner_algorithm :buchberger)
286 (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
287 (ring *ring-of-integers*)
288 (order #'lex>)
289 (ring-and-order (make-ring-and-order :ring ring :order order))
290 (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y))))
291 (reduced-gb (cdr (string->poly "[x,y]" '(x y)))))
292 (is-true (grobner-test ring-and-order gb fl))
293 (is (equalp (grobner ring-and-order fl) gb))
294 (is (equalp (reduced-grobner ring-and-order fl) reduced-gb))))
295
296
297(run! 'ngrobner-suite)
298(format t "All tests done!~%")
299
300
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