64 lines
1.7 KiB
Prolog
64 lines
1.7 KiB
Prolog
removeElement([_|Tail], 0, Tail).
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removeElement([Head|Tail], J, [Head|X]) :-
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J_2 is J - 1,
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removeElement(Tail, J_2, X).
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removeColumn([], _, []).
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removeColumn([Matrix_head|Matrix_tail], J, [X|Y]) :-
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removeElement(Matrix_head, J, X),
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removeColumn(Matrix_tail, J, Y).
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removeRow([_|Matrix_tail], 0, Matrix_tail).
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removeRow([Matrix_head|Matrix_tail], I, [Matrix_head|X]) :-
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I_2 is I - 1,
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removeRow(Matrix_tail, I_2, X).
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cofactor(Matrix, I, J, X) :-
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removeRow(Matrix, I, Matrix_2),
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removeColumn(Matrix_2, J, Matrix_3),
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det(Matrix_3, Y),
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X is (-1) ** (I + J) * Y.
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det_summand(_, _, [], 0).
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det_summand(Matrix, J, B, X) :-
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B = [B_head|B_tail],
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cofactor(Matrix, 0, J, Z),
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J_2 is J + 1,
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det_summand(Matrix, J_2, B_tail, Y),
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X is B_head * Z + Y.
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det([[X]], X).
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det(Matrix, X) :-
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Matrix = [Matrix_head|_],
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det_summand(Matrix, 0, Matrix_head, X).
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replaceElement([_|Tail], 0, New, [New|Tail]).
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replaceElement([Head|Tail], J, New, [Head|Y]) :-
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J_2 is J - 1,
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replaceElement(Tail, J_2, New, Y).
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replaceColumn([], _, _, []).
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replaceColumn([Matrix_head|Matrix_tail], J, [Column_head|Column_tail], [X|Y]) :-
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replaceElement(Matrix_head, J, Column_head, X),
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replaceColumn(Matrix_tail, J, Column_tail, Y).
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cramerElements(_, B, L, []) :- length(B, L).
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cramerElements(A, B, J, [X_J|Others]) :-
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replaceColumn(A, J, B, A_J),
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det(A_J, Det_A_J),
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det(A, Det_A),
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X_J is Det_A_J / Det_A,
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J_2 is J + 1,
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cramerElements(A, B, J_2, Others).
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cramer(A, B, X) :- cramerElements(A, B, 0, X).
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results(X) :-
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A = [
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[2, -1, 5, 1],
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[3, 2, 2, -6],
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[1, 3, 3, -1],
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[5, -2, -3, 3]
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],
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B = [-3, -32, -47, 49],
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cramer(A, B, X).
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