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