Tests Simplify

Jan Burse, erstellt 15. Sep 2018
/**
* Prolog test cases for the symbolic fractions simplification.
*
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:- use_package(library(jekdev/reference/testing)).
:- multifile runner:ref/4.
:- discontiguous runner:ref/4.
:- multifile runner:case/4.
:- discontiguous runner:case/4.
:- use_module(library(groebner/generic)).
:- use_module(library(misc/residue)).
% simp_neg/2
runner:ref(simp_neg, 2, groebner_simplify, 'groebner 0.9.1, 3.1').
runner:case(simp_neg, 2, groebner_simplify, 'groebner 0.9.1, 3.1, XLOG 1') :-
X is -A,
printable(X, Y),
Y == -A.
runner:case(simp_neg, 2, groebner_simplify, 'groebner 0.9.1, 3.1, XLOG 2') :-
X is - (A^2-3*A+4),
printable(X, Y),
Y == -4+3*A-A^2.
runner:case(simp_neg, 2, groebner_simplify, 'groebner 0.9.1, 3.1, XLOG 3') :-
X is - (A-7)/(B-3),
printable(X, Y),
Y == - (7-A)/(3-B).
runner:case(simp_neg, 2, groebner_simplify, 'groebner 0.9.2, 3.1, XLOG 4') :-
X is A/(sqrt(2)-sqrt(3)),
printable(X, Y),
Y == - (sqrt(2)+sqrt(3))*A.
% simp_add/3
runner:ref(simp_add, 3, groebner_simplify, 'groebner 0.9.1, 3.2').
runner:case(simp_add, 3, groebner_simplify, 'groebner 0.9.1, 3.2, XLOG 1') :-
X is 2*A+A,
printable(X, Y),
Y == 3*A.
runner:case(simp_add, 3, groebner_simplify, 'groebner 0.9.1, 3.2, XLOG 2') :-
X is A+B,
printable(X, Y),
Y == A+B.
runner:case(simp_add, 3, groebner_simplify, 'groebner 0.9.1, 3.2, XLOG 3') :-
X is A+B/A,
printable(X, Y),
Y == A+B/A.
runner:case(simp_add, 3, groebner_simplify, 'groebner 0.9.1, 3.2, XLOG 4') :-
X is A*(B-1)+B*(A+2),
printable(X, Y),
Y == -A+(2+2*A)*B.
runner:case(simp_add, 3, groebner_simplify, 'groebner 0.9.1, 3.2, XLOG 5') :-
X is 7/(B-3)+(B+2)/5,
printable(X, Y),
Y == 2/5+1/5*B-7/(3-B).
runner:case(simp_add, 3, groebner_simplify, 'groebner 0.9.2, 3.2, XLOG 6') :-
X is (A+sqrt(2))*(A+sqrt(8)),
printable(X, Y),
Y == 4+sqrt(18)*A+A^2.
% simp_sub/3
runner:ref(simp_sub, 3, groebner_simplify, 'groebner 0.9.1, 3.3').
runner:case(simp_sub, 3, groebner_simplify, 'groebner 0.9.1, 3.3, XLOG 1') :-
X is A-2*A,
printable(X, Y),
Y == -A.
runner:case(simp_sub, 3, groebner_simplify, 'groebner 0.9.1, 3.3, XLOG 2') :-
X is A-B,
printable(X, Y),
Y == A-B.
runner:case(simp_sub, 3, groebner_simplify, 'groebner 0.9.1, 3.3, XLOG 3') :-
X is A-A/B,
printable(X, Y),
Y == A-A/B.
runner:case(simp_sub, 3, groebner_simplify, 'groebner 0.9.1, 3.3, XLOG 4') :-
X is A*(B-1)-B*(A+2),
printable(X, Y),
Y == -A-2*B.
runner:case(simp_sub, 3, groebner_simplify, 'groebner 0.9.1, 3.3, XLOG 5') :-
X is 7/(B-3)-(B+2)/5,
printable(X, Y),
Y == -2/5-1/5*B-7/(3-B).
runner:case(simp_sub, 3, groebner_simplify, 'groebner 0.9.2, 3.3, XLOG 6') :-
X is (A-sqrt(2))*(A-sqrt(8)),
printable(X, Y),
Y == 4-sqrt(18)*A+A^2.
% simp_mul/3
runner:ref(simp_mul, 3, groebner_simplify, 'groebner 0.9.1, 3.4').
runner:case(simp_mul, 3, groebner_simplify, 'groebner 0.9.1, 3.4, XLOG 1') :-
X is A^2*A,
printable(X, Y),
Y == A^3.
runner:case(simp_mul, 3, groebner_simplify, 'groebner 0.9.1, 3.4, XLOG 2') :-
X is A*(A+1),
printable(X, Y),
Y == A+A^2.
runner:case(simp_mul, 3, groebner_simplify, 'groebner 0.9.1, 3.4, XLOG 3') :-
X is A*B/A,
printable(X, Y),
Y == B.
runner:case(simp_mul, 3, groebner_simplify, 'groebner 0.9.1, 3.4, XLOG 4') :-
X is (B-1)*(A*B+A),
printable(X, Y),
Y == - (1-B^2)*A.
runner:case(simp_mul, 3, groebner_simplify, 'groebner 0.9.1, 3.4, XLOG 5') :-
X is (B-1)/A*((B+1)/A),
printable(X, Y),
Y == - (1-B^2)/A^2.
runner:case(simp_mul, 3, groebner_simplify, 'groebner 0.9.2, 3.4, XLOG 6') :-
X is sqrt(1/5)*(sqrt(10)/A+sqrt(15)/B),
printable(X, Y),
Y == (sqrt(3)*A+sqrt(2)*B)/(A*B).
runner:case(simp_mul, 3, groebner_simplify, 'groebner 0.9.2, 3.4, XLOG 7') :-
X is (6+sqrt(18)*A+3*A^2)*(sqrt(6)-sqrt(3)*A),
printable(X, Y),
Y == sqrt(216)-sqrt(27)*A^3.
% simp_slash/3
runner:ref(simp_slash, 3, groebner_simplify, 'groebner 0.9.1, 3.5').
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.1, 3.5, XLOG 1') :-
X is 0/(1+_),
printable(X, Y),
Y == 0.
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.1, 3.5, XLOG 2') :-
X is A/A^2,
printable(X, Y),
Y == 1/A.
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.1, 3.5, XLOG 3') :-
X is A/(A+1),
printable(X, Y),
Y == 1-1/(1+A).
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.1, 3.5, XLOG 4') :-
X is A/(A/B),
printable(X, Y),
Y == B.
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.1, 3.5, XLOG 5') :-
X is (B^2-1)/(A*B+A),
printable(X, Y),
Y == - (1-B)/A.
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.1, 3.5, XLOG 6') :-
X is (B^2-1)/A/((A*B+A)/A),
printable(X, Y),
Y == - (1-B)/A.
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.2, 3.5, XLOG 7') :-
X is (sqrt(10)/A+sqrt(15)/B)/sqrt(5),
printable(X, Y),
Y == (sqrt(3)*A+sqrt(2)*B)/(A*B).
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.2, 3.5, XLOG 8') :-
X is (sqrt(216)-sqrt(27)*A^3)/(sqrt(6)-sqrt(3)*A),
printable(X, Y),
Y == 6+sqrt(18)*A+3*A^2.
runner:case(simp_slash, 3, groebner_simplify, 'groebner 0.9.2, 3.5, XLOG 9') :-
catch(_ is _/0, error(E,_), true),
E == evaluation_error(zero_divisor).
% simp_int_pow/3
runner:ref(simp_int_pow, 3, groebner_simplify, 'groebner 0.9.1, 3.6').
runner:case(simp_int_pow, 3, groebner_simplify, 'groebner 0.9.1, 3.6, XLOG 1') :-
X is A^2,
printable(X, Y),
Y == A^2.
runner:case(simp_int_pow, 3, groebner_simplify, 'groebner 0.9.1, 3.6, XLOG 2') :-
X is (1+A)^5,
printable(X, Y),
Y == 1+5*A+10*A^2+10*A^3+5*A^4+A^5.
runner:case(simp_int_pow, 3, groebner_simplify, 'groebner 0.9.1, 3.6, XLOG 3') :-
X is ((1-A)/(1+A))^3,
printable(X, Y),
Y == -1+(2+6*A^2)/(1+3*A+3*A^2+A^3).
runner:case(simp_int_pow, 3, groebner_simplify, 'groebner 0.9.2, 3.6, XLOG 4') :-
X is (1+sqrt(2)+A)^2,
printable(X, Y),
Y == 3+sqrt(8)+(2+sqrt(8))*A+A^2.
runner:case(simp_int_pow, 3, groebner_simplify, 'groebner 0.9.2, 3.6, XLOG 5') :-
X is (sqrt(3)*A*B-sqrt(2))*A,
Y is (sqrt(3)*A*B-sqrt(2))*B,
Z is (X/Y)^2,
printable(Z, T),
T == A^2/B^2.

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