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add power axioms to arith_solver

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This commit is contained in:
Nikolaj Bjorner 2025-04-23 10:48:29 -07:00
parent d73d104ded
commit 579ba8bd70
3 changed files with 32 additions and 0 deletions
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25
src/sat/smt/arith_axioms.cpp
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@ -65,6 +65,31 @@ namespace arith {
add_clause(eq, eq_internalize(t, a.mk_numeral(rational(1), a.is_int(t))));
}
// t = n^p
void solver::mk_power_axiom(expr* p, expr* x, expr* y) {
if (a.is_zero(y)) {
mk_power0_axioms(to_app(p), to_app(x));
return;
}
rational r;
// r > 0 => r^y > 0
if (a.is_extended_numeral(x, r) && r > 0) {
expr_ref zero(a.mk_real(0), m);
add_clause(~mk_literal(a.mk_le(p, zero)));
}
if (a.is_extended_numeral(y, r) && r > 0) {
// r is m/n then x >= 0 => x^m = p^n
if (denominator(r) > 1) {
expr_ref x_ge_0(a.mk_ge(x, a.mk_real(0)), m);
expr_ref x(m);
if (numerator(r) > 1)
x = a.mk_power(x, a.mk_real(numerator(r)));
expr_ref x_eq_pn(a.mk_eq(x, a.mk_power(p, a.mk_real(denominator(r)))), m);
add_clause(~mk_literal(x_ge_0), mk_literal(x_eq_pn));
}
}
}
// is_int(x) <=> to_real(to_int(x)) = x
void solver::mk_is_int_axiom(expr* n) {
expr* x = nullptr;