source: branches/f4grobner/5am-tests.lisp

;;; -*-  Mode: Lisp -*- 
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;;;  Copyright (C) 1999, 2002, 2009, 2015 Marek Rychlik <rychlik@u.arizona.edu>          
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;;;  This program is free software; you can redistribute it and/or modify        
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;;
;; Run tests using 5am unit testing framework
;;
;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;

;; We assume that QuickLisp package manager is installed.
;; See :
;;      https://www.quicklisp.org/beta/
;;

;; The following is unnecessary after running:
;; * (ql:add-to-init-file)
;; at lisp prompt:
;;(load "~/quicklisp/setup")

(ql:quickload :fiveam)

(load "ngrobner.asd")
(asdf:load-system :ngrobner)

(defpackage #:ngrobner-tests
  (:use :cl :it.bese.fiveam 
        :ngrobner :priority-queue :monom
        :utils :order :ring :term :ring-and-order 
        :termlist :polynomial
        :priority-queue 
        :division
        :grobner-wrap
        )
  )

(in-package :ngrobner-tests)

(def-suite ngrobner-suite 
    :description "New Groebner Package Suite")

(in-suite ngrobner-suite)

#+nil
(test dummy-test
  "Makelist"
  (is (= (+ 2 2)) "2 plus 2 wasn't equal to 4 (using #'= to test equality)")
  (is (= 0 (+ -1 1)))
  (signals
      (error "Trying to add 4 to FOO didn't signal an error")
    (+ 'foo 4))
  (is (= 0 (+ 1 1)) "this should have failed"))

(test makelist-1 
  "makelist-1 test"
  (is (equal (makelist-1 (* 2 i) i 0 10) '(0 2 4 6 8 10 12 14 16 18 20)))
  (is (equal (makelist-1 (* 2 i) i 0 10 3) '(0 6 12 18))))

(test makelist
  "makelist"
  (is (equal (makelist (+ (* i i) (* j j)) (i 1 4) (j 1 i)) '(2 5 8 10 13 18 17 20 25 32)))
  (is (equal (makelist (list i j '---> (+ (* i i) (* j j))) (i 1 4) (j 1 i))
             '((1 1 ---> 2) (2 1 ---> 5) (2 2 ---> 8) (3 1 ---> 10) (3 2 ---> 13)
               (3 3 ---> 18) (4 1 ---> 17) (4 2 ---> 20) (4 3 ---> 25) (4 4 ---> 32)))))

(test summation
  "summation"
  (is (= (summation i (i 0 100)) 5050)))

(test inner-product
  "summation"
  (is (= (inner-product '(1 2 3) '(4 5 6)) 32)))

(test monom
  "monom"
  (is (every #'= (make-monom :dimension 3) '(0 0 0)) "Trivial monomial is a vector of 0's")
  (is (every #'= (make-monom :initial-exponents '(1 2 3)) '(1 2 3)) "Monomial with powers 1,2,3")
  (let ((p (make-monom :initial-exponents '(1 2 3))))
    (is (every #'= (monom-map (lambda (x) x) p) '(1 2 3)))))

  
(test order
  "order"
  (let ((p (make-monom :initial-exponents '(1 3 2)))
        (q (make-monom :initial-exponents '(1 2 3))))
    (is-true (lex>  p q)) 
    (is-true (grlex>  p q)) 
    (is-true (revlex>  p q)) 
    (is-true (grevlex>  p q)) 
    (is-false (invlex>  p q))))

(test elim-order
  "elimination order"
  (let* ((p (make-monom :initial-exponents '(1 2 3)))
         (q (make-monom :initial-exponents '(4 5 6)))
         (elim-order-factory (make-elimination-order-factory))
         (elim-order-1 (funcall elim-order-factory 1))
         (elim-order-2 (funcall elim-order-factory 2)))
    (is-false (funcall elim-order-1 p q))
    (is-false (funcall elim-order-2 p q))))

(test term
  "term"
  (let* ((m1 (make-monom :initial-exponents '(1 2 3)))
         (m2 (make-monom :initial-exponents '(3 5 2)))
         (m3 (monom-mul m1 m2))
         (t1 (make-term :monom m1 :coeff 7))
         (t2 (make-term :monom m2 :coeff 9))
         (t3 (make-term :monom m3 :coeff (* 7 9))))
    (is (equalp (term-mul +ring-of-integers+ t1 t2) t3))))

(test termlist
  "termlist"
  (let* ((t1 (make-term  :monom (make-monom :initial-exponents '(1 2 3)) :coeff 7))
         (t2 (make-term  :monom (make-monom :initial-exponents '(3 5 2)) :coeff 9))
         (t11 (make-term :monom (make-monom :initial-exponents '(2 4 6)) :coeff 49))
         (t12 (make-term :monom (make-monom :initial-exponents '(4 7 5)) :coeff 126))
         (t22 (make-term :monom (make-monom :initial-exponents '(6 10 4)) :coeff 81))
         (p (list t2 t1))
         (p-sq (list t22 t12 t11))
         (ring-and-order (make-ring-and-order))
         (q (termlist-expt ring-and-order p 2)))
    (is-true (equalp q p-sq))))

(test poly
  "poly"
  (let* ((t1 (make-term  :monom (make-monom :initial-exponents '(1 2 3)) :coeff 7))
         (t2 (make-term  :monom (make-monom :initial-exponents '(3 5 2)) :coeff 9))
         (t11 (make-term :monom (make-monom :initial-exponents '(2 4 6)) :coeff 49))
         (t12 (make-term :monom (make-monom :initial-exponents '(4 7 5)) :coeff 126))
         (t22 (make-term :monom (make-monom :initial-exponents '(6 10 4)) :coeff 81))
         (p (make-poly-from-termlist (list t2 t1)))
         (p-sq (make-poly-from-termlist (list t22 t12 t11)))
         (ring-and-order (make-ring-and-order))
         (q (poly-expt ring-and-order p 2)))
    (is-true (equalp q p-sq))))


(test coerce-to-infix
  "Conversion to infix form"
  (is (equal 
       (coerce-to-infix :term (make-term-variable +ring-of-integers+ 5 3) '(x y z w u v))
       '(* 1 (EXPT X 0) (EXPT Y 0) (EXPT Z 0) (EXPT W 1) (EXPT U 0)))))

(test priority-queue
  "Priority queue"
  (let ((q (make-priority-queue)))
    (priority-queue-insert q 7)
    (priority-queue-insert q 8)
    (is (= (priority-queue-size q) 3) "Note that there is always a dummy element in the queue.")
    (is (equalp (priority-queue-heap q) #(0 7 8)))
    (is (= (priority-queue-remove q) 7))
    (is (= (priority-queue-remove q) 8))
    (is-true (priority-queue-empty-p q))
    (signals
        (error "Empty queue.")
      (priority-queue-remove q))))

;;
;; Currently parser cannot be tested, as it relies on many maxima functions
;; to parse a polynomial expression.
;;
#|
(test parser
  "Parser"
  (let (($f '((MLIST SIMP) ((MPLUS SIMP) $X ((MTIMES SIMP) -1 $Y)) ((MPLUS SIMP) $X $Y)))
        ($v '((MLIST SIMP) $X $Y)))
    (is-true (parse-poly-list $f $v))))
|#

(test infix-print 
  "Infix printer"
  (is (string= (infix-print '(+ x y) nil) "X+Y"))
  (is (string= (infix-print '(expt x 3) nil) "X^3"))
  (is (string= (infix-print '(+ 1 (expt x 3)) nil) "1+(X^3)"))
  (is (string= (infix-print '(* x y) nil) "X*Y"))
  (is (string= (infix-print '(* x (expt y 2)) nil) "X*(Y^2)")))

(test infix
  "Infix parser"
  (is (equal '#I( x^2 + y^2 ) '(+ (expt x 2) (expt y 2))))
  (is (equal '#I( [ x, y ] ) '(:[ X Y)))
  (is (equal '#I( x + y) '(+ x y)))
  (is (equal '#I( x^3 ) '(expt x 3)))
  (is (equal '#I( 1 + x^3) '(+ 1 (expt x 3))))
  (is (equal '#I( x * y^2 ) '(* x (expt y 2)))))

(test poly-reader
  "Polynomial reader"
  (is (equalp (with-input-from-string (s "X^2-Y^2+(-4/3)*U^2*W^3-5")
                (read-infix-form :stream s))
              '(+ (- (EXPT X 2) (EXPT Y 2)) (* (- (/ 4 3)) (EXPT U 2) (EXPT W 3)) (- 5))))
  (is (equalp (string->alist "X^2-Y^2+(-4/3)*U^2*W^3-5" '(x y u w))
              '(((2 0 0 0) . 1)
                ((0 2 0 0) . -1) 
                ((0 0 2 3) . -4/3)
                ((0 0 0 0) . -5))))
  (is (equalp (string->alist "[x^2-y^2+(-4/3)*u^2*w^3-5,y]" '(x y u w))
              '(:[ 
                (((2 0 0 0) . 1) ((0 2 0 0) . -1) ((0 0 2 3) . -4/3) ((0 0 0 0) . -5))
                (((0 1 0 0) . 1)))))
  (let ((p (make-poly-from-termlist (list (make-term :monom (make-monom :initial-exponents '(2 0)) :coeff 1)
                                          (make-term :monom (make-monom :initial-exponents '(0 2)) :coeff 2)))))
    (is (equalp (with-input-from-string (s "x^2+2*y^2") 
                  (read-poly '(x y) :stream s))
                p))
    (is (equalp (string->poly "x^2+2*y^2" '(x y)) p))))

;; Manual calculation supporting the test below.
;; We divide X^2 by [X+Y,X-2*Y] with LEX> as order.
;; LM(X^2)=X^2 is divisible by LM(X+Y)=X so the first partial quotient is X.
;; Next, X^2 - X*(X+Y) = -X*Y.
;; LM(-X*Y)=X*Y is divibile by LM(X+Y)=X so the second partial quotient is -Y.
;; Next, -X*Y-(-Y)*(X+Y) = Y^2.
;; LM(Y^2)=Y^2 is not divisible by LM(X+Y)=X or LM(X-2*Y)=X. Hence, division
;; ends. The list of quotients is [X-Y,0]. The remainder is Y^2
(test division
  "Division in polynomial ring"
  (let* ((f (string->poly "x^2" '(x y)))
         (y-sq (string->poly "y^2" '(x y)))
         (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (quotients (cdr (string->poly "[x-y,0]" '(x y)))))
    (is (equalp (multiple-value-list (normal-form ring-and-order f fl)) (list y-sq 1 2)))
    (is (equalp (multiple-value-list (poly-pseudo-divide ring-and-order f fl))
                (list quotients y-sq 1 2)))
    (is-false (buchberger-criterion ring-and-order fl)))
  (let* ((f (string->poly "x^2-4*y^2" '(x y)))
         (g (string->poly "x+2*y" '(x y)))
         (h (string->poly "x-2*y" '(x y)))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order)))
    (is (poly-equal-no-sugar-p (poly-exact-divide ring-and-order f g) h))))


(test buchberger
  "Buchberger algorithm"
  (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y)))))
    (is-true (grobner-test ring-and-order gb fl))
    (is (every #'poly-equal-no-sugar-p (buchberger ring-and-order fl) gb))
    (is (every #'poly-equal-no-sugar-p (parallel-buchberger ring-and-order fl) gb))))

(test gebauer-moeller
  "Gebauer-Moeller algorithm"
  (let* ((fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (gb (cdr (string->poly "[y,x-2*y]" '(x y)))))
    (is-true (grobner-test ring-and-order gb fl))
    (is (every #'poly-equal-no-sugar-p (gebauer-moeller ring-and-order fl) gb))))

(test reduction
  "Reduction algorithm"
  (let* ((fl (cdr (string->poly "[x^2,x+y,x-2*y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (gb (cdr (string->poly "[y,x-2*y]" '(x y))))
         (reduced-gb (cdr (string->poly "[y,x]" '(x y)))))
    (is-true (grobner-test ring-and-order gb fl))
    (is (poly-set-equal-no-sugar-p (reduction ring-and-order gb) reduced-gb))))

(test minimization
  "Minimization algorithm"
  (let* ((gb (cdr (string->poly "[x,y,x-2*y,x^2]" '(x y))))
         (minimal-gb (cdr (string->poly "[y,x-2*y]" '(x y)))))
    (is (equalp (minimization gb) minimal-gb))))

(test grobner-wrap
  "Grobner interface to many algorithms"
  (let* (($poly_grobner_algorithm :buchberger)
         (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (gb (cdr (string->poly "[x+y,x-2*y,y]" '(x y))))
         (reduced-gb (cdr (string->poly "[y,x]" '(x y)))))
    (is-true (grobner-test ring-and-order gb fl))
    (is (poly-set-equal-no-sugar-p (grobner ring-and-order fl) gb))
    (is (poly-set-equal-no-sugar-p (reduced-grobner ring-and-order fl) reduced-gb))))


(test elimination-ideal
  "Elimination ideal"
  (let* (($poly_grobner_algorithm :buchberger)
         (fl (cdr (string->poly "[x+y,x-2*y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (elim-1-fl (cdr (string->poly "[y]" '(x y)))))
    (is (poly-set-equal-no-sugar-p (elimination-ideal ring-and-order fl 1) elim-1-fl))
    (is (null (elimination-ideal ring-and-order fl 2)))))

(test colon-ideal
  "Colon ideal"
  (let* (($poly_grobner_algorithm :buchberger)
         (I (cdr (string->poly "[x^2*y,x*y^2]" '(x y))))
         (J (cdr (string->poly "[x,y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (I-colon-J (cdr (string->poly "[x*y]" '(x y)))))
    (is (poly-set-equal-no-sugar-p (colon-ideal ring-and-order I J) I-colon-J))))

(test poly-lcm
  "Polynomial LCM"
  (let* (($poly_grobner_algorithm :buchberger)
         (f (string->poly "x^2-y^2" '(x y)))
         (g (string->poly "(x+y)^2" '(x y)))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (lcm-f-and-g (string->poly "(x+y)^2*(x-y)" '(x y))))
    (is (poly-equal-no-sugar-p (poly-lcm ring-and-order f g) lcm-f-and-g))))

(test grobner-member
  "Ideal membership"
  (let* (($poly_grobner_algorithm :buchberger)
         (f (string->poly "y" '(x y)))
         (fl (cdr (string->poly "[x-y,x+y,y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order)))
    (is-true (buchberger-criterion ring-and-order fl))
    (is-true (grobner-member ring-and-order f fl))))

(test grobner-equal
  "Equality of ideal generated by Groebner bases"
  (let* (($poly_grobner_algorithm :buchberger)
         (fl (cdr (string->poly "[x,x-y,y]" '(x y))))
         (gl (cdr (string->poly "[x-y,x+2*y,y]" '(x y))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order)))
    (is-true (buchberger-criterion ring-and-order fl))
    (is-true (buchberger-criterion ring-and-order gl))
    (is-true (grobner-equal ring-and-order fl gl))))

;; Calculates [F, U*P-1]
(test saturation-extension-1
  "Saturation extension with 1 polynomial"
  (let* ((F-str "[x^3,x^2*y]")
         (F (cdr (string->poly F-str '(x y))))
         (P (string->poly "x^2" '(x y)))
         (ring +ring-of-integers+)
         (F-sat (append (cdr (string->poly F-str '(u x y)))
                        (cdr (string->poly "[u*x^2-1]" '(u x y))))))
    (is (poly-set-equal-no-sugar-p   (saturation-extension-1 ring F p) F-sat))))

;; Calculate [F, U1*P1+U2*P2+...+UK*PK-1], where PLIST=[P1,P2,...,PK]. It destructively modifies F.
(test polysaturation-extension
  "Polysaturation extension"
  (let* ((F-str "[x^3,x^2*y]")
         (F (cdr (string->poly F-str '(x y))))
         (P (cdr (string->poly "[x^2,x*y]" '(x y))))
         (ring +ring-of-integers+)
         (F-sat (append (cdr (string->poly F-str '(u1 u2 x y)))
                        (cdr (string->poly "[u1*(x^2) + u2*(x*y)-1]" '(u1 u2 x y))))))
    (is (poly-set-equal-no-sugar-p (polysaturation-extension ring F P) F-sat))))

;; Calculate F : p^inf
(test ideal-saturation-1
  "Ideal saturation with 1 polynomial"
  (let* (($poly_grobner_algorithm :buchberger)
         (F (cdr (string->poly "[x^3*(y+z^2),x^2*(y-z^2)]" '(x y z))))
         (p (string->poly "x" '(x y z)))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (G (cdr (string->poly "[y,z^2]" '(x y z)))))
    (is (poly-set-equal-no-sugar-p (ideal-saturation-1 ring-and-order F p) G))))

;; Calculate F : p1^inf : p2^inf : ... : ps^inf
(test ideal-polysaturation-1
  "Ideal polysaturation one-by-one with 2 polynomials"
  (let* (($poly_grobner_algorithm :buchberger)
         (F (cdr (string->poly "[x^3*z*y,x*z*y^2]" '(x y z))))
         (P (cdr (string->poly "[x,z]" '(x y z))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (G (cdr (string->poly "[y]" '(x y z)))))
    (is (poly-set-equal-no-sugar-p (ideal-polysaturation-1 ring-and-order F p) G))))

;; Calculate F : P^inf
(test ideal-saturation
  "Ideal saturation"
  (let* (($poly_grobner_algorithm :buchberger)
         (F (cdr (string->poly "[x^3*(y+z^2),x^2*(y-z^2)]" '(x y z))))
         (P (cdr (string->poly "[x]" '(x y z))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (G (cdr (string->poly "[y,z^2]" '(x y z)))))
    (is (poly-set-equal-no-sugar-p (ideal-saturation ring-and-order F P) G))))

;; Calculate F : P1^inf : P2^inf : ... : Ps^inf where Pi are ideals
(test ideal-polysaturation
  "Ideal polysaturation"
  (let* (($poly_grobner_algorithm :buchberger)
         (F (cdr (string->poly "[x^3*z*y,x*z*y^2]" '(x y z))))
         (P1 (cdr (string->poly "[x]" '(x y z))))
         (P2 (cdr (string->poly "[z]" '(x y z))))
         (ring +ring-of-integers+)
         (order #'lex>)
         (ring-and-order (make-ring-and-order :ring ring :order order))
         (G (cdr (string->poly "[y]" '(x y z)))))
    (is (poly-set-equal-no-sugar-p (ideal-polysaturation ring-and-order F (list P1 P2)) G))))

(run! 'ngrobner-suite)
(format t "All tests done!~%")