Module Subst

Jan Burse, created Sep 15. 2018
* This module provides symbolic substitution. The substitution
* operator subst/3 takes an original reduced expression, a replacement
* variable and a replacement expression. It will re-execute the
* constructors in the original reduced expression and replace every
* occurrence of the replacement variable by the replacement expression.
* Example:
* ?- X is A^2-B*A+B^2, Y is subst(X,A,2).
* X is A^2-A*B+B^2,
* Y is 4-2*B+B^2
* Since the constructors of the original expression are re-executed
* the substitution operator might cause new partial evaluations or
* simplifications. At the moment we provide substitution only for
* elements, substitution for vectors and matrices has not yet been
* implemented. Accordingly we do not yet support some special functions.
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* no liability that any problems might be solved with the information
* provided by XLOG Technologies GmbH.
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* for execution provided this comment remains unchanged.
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* functionality to the library. Not to be distributed with additional
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:- package(library(jekmin/frequent/leibniz)).
:- use_package(library(jekmin/frequent/groebner)).
:- use_package(library(jekmin/frequent/gauss)).
:- module(subst, []).
:- use_module(../groebner/polynom).
:- use_module(../groebner/generic).
/* Substitution */
* subst(P, X, R, Q):
* The predicate succeeds in Q with the substitution P[X/R].
% ordered:subst(+Ordered, +Variable, +Internal, -Ordered)
:- public ordered:subst/4.
ordered:subst(X, _, _, X).
* subst(P, X, R, Q):
* The predicate succeeds in Q with the substitution P[X/R].
% variable:subst(+Variable, +Variable, +Internal, -Internal)
:- public variable:subst/4.
variable:subst(X, X, R, S) :- !,
S = R.
variable:subst(X, _, _, X).
* subst(P, X, R, Q):
* The predicate succeeds in Q with the substitution P[X/R].
% polynom:subst(+Polynom, +Variable, +Internal, -Internal)
:- public polynom:subst/4.
polynom:subst(polynom(A, [N-B|L]), X, R, S) :- A @> X, !,
H is subst(B, X, R),
sys_coeff_subst(L, N, H, A, X, R, S).
polynom:subst(polynom(X, [N-A|L]), X, R, S) :- !,
sys_poly_subst(L, N, A, R, S).
polynom:subst(X, _, _, X).
% sys_poly_subst(+Map, +Integer, +Internal, +Internal, -Internal)
:- private sys_poly_subst/5.
sys_poly_subst([M-B|L], N, A, R, S) :-
user: -(N, M, K),
H is R^K*A+B,
sys_poly_subst(L, M, H, R, S).
sys_poly_subst([], N, A, R, S) :-
S is R^N*A.
% sys_coeff_subst(+Map, +Integer, +Internal, +Variable, +Variable, +Internal, -Internal)
:- private sys_coeff_subst/7.
sys_coeff_subst([M-B|L], N, C, A, X, R, S) :-
user: -(N, M, K),
H is A^K*C+subst(B, X, R),
sys_coeff_subst(L, M, H, A, X, R, S).
sys_coeff_subst([], N, C, A, _, _, S) :-
S is A^N*C.
* subst(P, X, R, Q):
* The predicate succeeds in Q with the substitution P[X/R].
% fraction:subst(+Polynom, +Variable, +Internal, -Internal)
:- public fraction:subst/4.
fraction:subst(fraction(A, B), X, R, S) :-
S is subst(A, X, R)/subst(B, X, R).