[1201] | 1 | ;;; -*- Mode: Lisp -*-
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[302] | 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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[309] | 22 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 23 | ;;
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[355] | 24 | ;; Run tests using 5am unit testing framework
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[309] | 25 | ;;
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| 26 | ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;
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| 27 |
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[342] | 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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[286] | 38 | (ql:quickload :fiveam)
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[301] | 39 |
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[292] | 40 | (load "ngrobner.asd")
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[291] | 41 | (asdf:load-system :ngrobner)
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[1326] | 42 |
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[367] | 43 | (defpackage #:ngrobner-tests
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[604] | 44 | (:use :cl :it.bese.fiveam
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| 45 | :ngrobner :priority-queue :monomial
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[957] | 46 | :utils :order :ring :term :ring-and-order
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[1069] | 47 | :termlist :polynomial
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[1024] | 48 | :priority-queue
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[1175] | 49 | :division
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[1364] | 50 | :grobner-wrap
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[604] | 51 | )
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| 52 | )
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[286] | 53 |
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[1251] | 54 | (in-package :ngrobner-tests)
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[287] | 55 |
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[367] | 56 | (def-suite ngrobner-suite
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[368] | 57 | :description "New Groebner Package Suite")
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[281] | 58 |
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[367] | 59 | (in-suite ngrobner-suite)
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[287] | 60 |
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[312] | 61 | #+nil
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[289] | 62 | (test dummy-test
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[281] | 63 | "Makelist"
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| 64 | (is (= (+ 2 2)) "2 plus 2 wasn't equal to 4 (using #'= to test equality)")
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| 65 | (is (= 0 (+ -1 1)))
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| 66 | (signals
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| 67 | (error "Trying to add 4 to FOO didn't signal an error")
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| 68 | (+ 'foo 4))
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| 69 | (is (= 0 (+ 1 1)) "this should have failed"))
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[289] | 70 |
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[293] | 71 | (test makelist-1
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[303] | 72 | "makelist-1 test"
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[597] | 73 | (is (equal (makelist-1 (* 2 i) i 0 10) '(0 2 4 6 8 10 12 14 16 18 20)))
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| 74 | (is (equal (makelist-1 (* 2 i) i 0 10 3) '(0 6 12 18))))
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[294] | 75 |
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[303] | 76 | (test makelist
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[314] | 77 | "makelist"
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[598] | 78 | (is (equal (makelist (+ (* i i) (* j j)) (i 1 4) (j 1 i)) '(2 5 8 10 13 18 17 20 25 32)))
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| 79 | (is (equal (makelist (list i j '---> (+ (* i i) (* j j))) (i 1 4) (j 1 i))
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[303] | 80 | '((1 1 ---> 2) (2 1 ---> 5) (2 2 ---> 8) (3 1 ---> 10) (3 2 ---> 13)
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| 81 | (3 3 ---> 18) (4 1 ---> 17) (4 2 ---> 20) (4 3 ---> 25) (4 4 ---> 32)))))
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[290] | 82 |
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[1414] | 83 | (test summation
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| 84 | "summation"
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| 85 | (is (= (summation i (i 0 100)) 5050)))
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| 86 |
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[1415] | 87 | (test inner-product
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| 88 | "summation"
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| 89 | (is (= (inner-product '(1 2 3) '(4 5 6)) 32)))
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| 90 |
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[314] | 91 | (test monom
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| 92 | "monom"
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[885] | 93 | (is (every #'= (make-monom :dimension 3) '(0 0 0)) "Trivial monomial is a vector of 0's")
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| 94 | (is (every #'= (make-monom :initial-exponents '(1 2 3)) '(1 2 3)) "Monomial with powers 1,2,3")
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[867] | 95 | (let ((p (make-monom :initial-exponents '(1 2 3))))
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[885] | 96 | (is (every #'= (monom-map (lambda (x) x) p) '(1 2 3)))))
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[867] | 97 |
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[303] | 98 |
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[347] | 99 | (test order
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| 100 | "order"
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[948] | 101 | (let ((p (make-monom :initial-exponents '(1 3 2)))
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| 102 | (q (make-monom :initial-exponents '(1 2 3))))
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[600] | 103 | (is-true (lex> p q))
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| 104 | (is-true (grlex> p q))
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| 105 | (is-true (revlex> p q))
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| 106 | (is-true (grevlex> p q))
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[948] | 107 | (is-false (invlex> p q))))
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| 108 |
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| 109 | (test elim-order
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| 110 | "elimination order"
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| 111 | (let* ((p (make-monom :initial-exponents '(1 2 3)))
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| 112 | (q (make-monom :initial-exponents '(4 5 6)))
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| 113 | (elim-order-factory (make-elimination-order-factory))
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| 114 | (elim-order-1 (funcall elim-order-factory 1))
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| 115 | (elim-order-2 (funcall elim-order-factory 2)))
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[949] | 116 | (is-false (funcall elim-order-1 p q))
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| 117 | (is-false (funcall elim-order-2 p q))))
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[347] | 118 |
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[381] | 119 | (test term
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| 120 | "term"
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[855] | 121 | (let* ((m1 (make-monom :initial-exponents '(1 2 3)))
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| 122 | (m2 (make-monom :initial-exponents '(3 5 2)))
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[602] | 123 | (m3 (monom-mul m1 m2))
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| 124 | (t1 (make-term m1 7))
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| 125 | (t2 (make-term m2 9))
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| 126 | (t3 (make-term m3 (* 7 9))))
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| 127 | (is (equalp (term-mul *ring-of-integers* t1 t2) t3))))
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[381] | 128 |
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[950] | 129 | (test termlist
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| 130 | "termlist"
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[968] | 131 | (let* ((t1 (make-term (make-monom :initial-exponents '(1 2 3)) 7))
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[966] | 132 | (t2 (make-term (make-monom :initial-exponents '(3 5 2)) 9))
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[967] | 133 | (t11 (make-term (make-monom :initial-exponents '(2 4 6)) 49))
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[963] | 134 | (t12 (make-term (make-monom :initial-exponents '(4 7 5)) 126))
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| 135 | (t22 (make-term (make-monom :initial-exponents '(6 10 4)) 81))
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| 136 | (p (list t2 t1))
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| 137 | (p-sq (list t22 t12 t11))
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[956] | 138 | (ring-and-order (make-ring-and-order))
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| 139 | (q (termlist-expt ring-and-order p 2)))
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[969] | 140 | (is-true (equalp q p-sq))))
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[950] | 141 |
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[970] | 142 | (test poly
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| 143 | "poly"
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| 144 | (let* ((t1 (make-term (make-monom :initial-exponents '(1 2 3)) 7))
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| 145 | (t2 (make-term (make-monom :initial-exponents '(3 5 2)) 9))
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| 146 | (t11 (make-term (make-monom :initial-exponents '(2 4 6)) 49))
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| 147 | (t12 (make-term (make-monom :initial-exponents '(4 7 5)) 126))
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| 148 | (t22 (make-term (make-monom :initial-exponents '(6 10 4)) 81))
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| 149 | (p (make-poly-from-termlist (list t2 t1)))
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| 150 | (p-sq (make-poly-from-termlist (list t22 t12 t11)))
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| 151 | (ring-and-order (make-ring-and-order))
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[1027] | 152 | (q (poly-expt ring-and-order p 2)))
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[972] | 153 | (is-true (equalp q p-sq))))
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[950] | 154 |
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| 155 |
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[381] | 156 | (test coerce-to-infix
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[582] | 157 | "Conversion to infix form"
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| 158 | (is (equal
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[605] | 159 | (coerce-to-infix :term (make-term-variable *ring-of-integers* 5 3) '(x y z w u v))
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[582] | 160 | '(* 1 (EXPT X 0) (EXPT Y 0) (EXPT Z 0) (EXPT W 1) (EXPT U 0)))))
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[381] | 161 |
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[584] | 162 | (test priority-queue
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| 163 | "Priority queue"
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[607] | 164 | (let ((q (make-priority-queue)))
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| 165 | (priority-queue-insert q 7)
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| 166 | (priority-queue-insert q 8)
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| 167 | (is (= (priority-queue-size q) 3) "Note that there is always a dummy element in the queue.")
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| 168 | (is (equalp (priority-queue-heap q) #(0 7 8)))
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| 169 | (is (= (priority-queue-remove q) 7))
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| 170 | (is (= (priority-queue-remove q) 8))
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[610] | 171 | (is-true (priority-queue-empty-p q))
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[613] | 172 | (signals
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| 173 | (error "Empty queue.")
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| 174 | (priority-queue-remove q))))
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[584] | 175 |
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[634] | 176 | ;;
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| 177 | ;; Currently parser cannot be tested, as it relies on many maxima functions
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| 178 | ;; to parse a polynomial expression.
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| 179 | ;;
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[614] | 180 | #|
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| 181 | (test parser
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| 182 | "Parser"
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| 183 | (let (($f '((MLIST SIMP) ((MPLUS SIMP) $X ((MTIMES SIMP) -1 $Y)) ((MPLUS SIMP) $X $Y)))
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[620] | 184 | ($v '((MLIST SIMP) $X $Y)))
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| 185 | (is-true (parse-poly-list $f $v))))
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[633] | 186 | |#
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[614] | 187 |
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[691] | 188 | (test infix-print
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[694] | 189 | "Infix printer"
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[691] | 190 | (is (string= (infix-print '(+ x y) nil) "X+Y"))
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| 191 | (is (string= (infix-print '(expt x 3) nil) "X^3"))
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[693] | 192 | (is (string= (infix-print '(+ 1 (expt x 3)) nil) "1+(X^3)"))
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| 193 | (is (string= (infix-print '(* x y) nil) "X*Y"))
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| 194 | (is (string= (infix-print '(* x (expt y 2)) nil) "X*(Y^2)")))
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[832] | 195 |
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| 196 | (test infix
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| 197 | "Infix parser"
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[693] | 198 | (is (equal '#I( x^2 + y^2 ) '(+ (expt x 2) (expt y 2))))
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[831] | 199 | (is (equal '#I( [ x, y ] ) '(:[ X Y)))
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| 200 | (is (equal '#I( x + y) '(+ x y)))
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[864] | 201 | (is (equal '#I( x^3 ) '(expt x 3)))
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| 202 | (is (equal '#I( 1 + x^3) '(+ 1 (expt x 3))))
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| 203 | (is (equal '#I( x * y^2 ) '(* x (expt y 2)))))
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[691] | 204 |
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[1070] | 205 | (test poly-reader
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| 206 | "Polynomial reader"
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[1084] | 207 | (is (equalp (with-input-from-string (s "X^2-Y^2+(-4/3)*U^2*W^3-5")
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[1089] | 208 | (read-infix-form :stream s))
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[1083] | 209 | '(+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))))
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[1167] | 210 | (is (equalp (string->alist "X^2-Y^2+(-4/3)*U^2*W^3-5" '(x y u w))
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| 211 | '(((2 0 0 0) . 1)
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| 212 | ((0 2 0 0) . -1)
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| 213 | ((0 0 2 3) . -4/3)
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| 214 | ((0 0 0 0) . -5))))
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[1173] | 215 | (is (equalp (string->alist "[x^2-y^2+(-4/3)*u^2*w^3-5,y]" '(x y u w))
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| 216 | '(:[
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| 217 | (((2 0 0 0) . 1) ((0 2 0 0) . -1) ((0 0 2 3) . -4/3) ((0 0 0 0) . -5))
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| 218 | (((0 1 0 0) . 1)))))
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[1099] | 219 | (let ((p (make-poly-from-termlist (list (make-term (make-monom :initial-exponents '(2 0)) 1)
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| 220 | (make-term (make-monom :initial-exponents '(0 2)) 2)))))
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[1101] | 221 | (is (equalp (with-input-from-string (s "x^2+2*y^2")
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| 222 | (read-poly '(x y) :stream s))
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| 223 | p))
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[1103] | 224 | (is (equalp (string->poly "x^2+2*y^2" '(x y)) p))))
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[1023] | 225 |
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[1223] | 226 | ;; Manual calculation supporting the test below.
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| 227 | ;; We divide X^2 by [X+Y,X-2*Y] with LEX> as order.
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| 228 | ;; LM(X^2)=X^2 is divisible by LM(X+Y)=X so the first partial quotient is X.
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| 229 | ;; Next, X^2 - X*(X+Y) = -X*Y.
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[1224] | 230 | ;; LM(-X*Y)=X*Y is divibile by LM(X+Y)=X so the second partial quotient is -Y.
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[1281] | 231 | ;; Next, -X*Y-(-Y)*(X+Y) = Y^2.
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| 232 | ;; LM(Y^2)=Y^2 is not divisible by LM(X+Y)=X or LM(X-2*Y)=X. Hence, division
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| 233 | ;; ends. The list of quotients is [X-Y,0]. The remainder is Y^2
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[1174] | 234 | (test division
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| 235 | "Division in polynomial ring"
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[1183] | 236 | (let* ((f (string->poly "x^2" '(x y)))
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[1186] | 237 | (y-sq (string->poly "y^2" '(x y)))
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[1183] | 238 | (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
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| 239 | (ring *ring-of-integers*)
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| 240 | (order #'lex>)
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[1194] | 241 | (ring-and-order (make-ring-and-order :ring ring :order order))
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| 242 | (quotients (cdr (string->poly "[x-y,0]" '(x y)))))
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[1250] | 243 | (is (equalp (multiple-value-list (normal-form ring-and-order f fl)) (list y-sq 1 2)))
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[1196] | 244 | (is (equalp (multiple-value-list (poly-pseudo-divide ring-and-order f fl))
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[1202] | 245 | (list quotients y-sq 1 2)))
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[1283] | 246 | (is-false (buchberger-criterion ring-and-order fl)))
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[1287] | 247 | (let* ((f (string->poly "x^2-4*y^2" '(x y)))
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| 248 | (g (string->poly "x+2*y" '(x y)))
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| 249 | (h (string->poly "x-2*y" '(x y)))
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[1286] | 250 | (ring *ring-of-integers*)
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| 251 | (order #'lex>)
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| 252 | (ring-and-order (make-ring-and-order :ring ring :order order)))
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[1285] | 253 | (is (equalp (poly-exact-divide ring-and-order f g) h))))
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[1174] | 254 |
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[1303] | 255 |
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| 256 | (test buchberger
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| 257 | "Buchberger algorithm"
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| 258 | (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
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| 259 | (ring *ring-of-integers*)
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| 260 | (order #'lex>)
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| 261 | (ring-and-order (make-ring-and-order :ring ring :order order))
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[1306] | 262 | (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y)))))
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[1324] | 263 | (is-true (grobner-test ring-and-order gb fl))
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[1311] | 264 | (is (equalp (buchberger ring-and-order fl) gb))
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| 265 | (is (equalp (parallel-buchberger ring-and-order fl) gb))))
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[1303] | 266 |
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[1318] | 267 | (test gebauer-moeller
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| 268 | "Gebauer-Moeller algorithm"
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| 269 | (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
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| 270 | (ring *ring-of-integers*)
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| 271 | (order #'lex>)
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| 272 | (ring-and-order (make-ring-and-order :ring ring :order order))
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[1322] | 273 | (gb (cdr (string->poly "[y,x-2*y]" '(x y)))))
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[1324] | 274 | (is-true (grobner-test ring-and-order gb fl))
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[1318] | 275 | (is (equalp (gebauer-moeller ring-and-order fl) gb))))
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[1303] | 276 |
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[1336] | 277 | (test gb-postprocessing
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[1338] | 278 | "Grobner basis postprocessing"
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[1336] | 279 | (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
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| 280 | (ring *ring-of-integers*)
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| 281 | (order #'lex>)
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| 282 | (ring-and-order (make-ring-and-order :ring ring :order order))
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[1337] | 283 | (gb (cdr (string->poly "[y,x-2*y]" '(x y))))
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[1339] | 284 | (reduced-gb (cdr (string->poly "[y,x]" '(x y)))))
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[1336] | 285 | (is-true (grobner-test ring-and-order gb fl))
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[1340] | 286 | (is (equalp (reduction ring-and-order gb) reduced-gb)))
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| 287 | (let* ((gb (cdr (string->poly "[x,y,x-2*y,x^2]" '(x y))))
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[1350] | 288 | (minimal-gb (cdr (string->poly "[y,x-2*y]" '(x y)))))
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[1340] | 289 | (is (equalp (minimization gb) minimal-gb))))
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[1303] | 290 |
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[1365] | 291 | (test grobner-wrap
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[1366] | 292 | "Grobner interface to many algorithms"
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[1368] | 293 | (let* (($poly_grobner_algorithm :buchberger)
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[1367] | 294 | (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
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[1365] | 295 | (ring *ring-of-integers*)
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| 296 | (order #'lex>)
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| 297 | (ring-and-order (make-ring-and-order :ring ring :order order))
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[1371] | 298 | (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y))))
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[1372] | 299 | (reduced-gb (cdr (string->poly "[y,x]" '(x y)))))
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[1365] | 300 | (is-true (grobner-test ring-and-order gb fl))
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[1370] | 301 | (is (equalp (grobner ring-and-order fl) gb))
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| 302 | (is (equalp (reduced-grobner ring-and-order fl) reduced-gb))))
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[1336] | 303 |
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[1365] | 304 |
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[367] | 305 | (run! 'ngrobner-suite)
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[346] | 306 | (format t "All tests done!~%")
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[345] | 307 |
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| 308 |
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