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correct ordered lemmas

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Signed-off-by: Lev Nachmanson <levnach@hotmail.com>
This commit is contained in:
Lev Nachmanson 2020-04-28 20:23:50 -07:00
parent 56690d16da
commit 7cfd16c7f9
2 changed files with 53 additions and 0 deletions
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50
src/math/lp/nla_order_lemmas.cpp
View file

@ -212,7 +212,24 @@ bool order::order_lemma_on_ac_and_bc(const monic& rm_ac,
// We try to find a monic n = cd, such that |b| = |d| // We try to find a monic n = cd, such that |b| = |d|
// and get a lemma m R n & |b| = |d| => ab/|b| R cd /|d|, where R is a relation // and get a lemma m R n & |b| = |d| => ab/|b| R cd /|d|, where R is a relation
void order::order_lemma_on_factorization(const monic& m, const factorization& ab) { void order::order_lemma_on_factorization(const monic& m, const factorization& ab) {
bool sign = m.rsign();
for (factor f: ab)
sign ^= _().canonize_sign(f);
const rational rsign = sign_to_rat(sign);
const rational fv = val(var(ab[0])) * val(var(ab[1]));
const rational mv = rsign * var_val(m);
TRACE("nla_solver",
tout << "ab.size()=" << ab.size() << "\n";
tout << "we should have sign*var_val(m):" << mv << "=(" << rsign << ")*(" << var_val(m) <<") to be equal to " << " val(var(ab[0]))*val(var(ab[1])):" << fv << "\n";);
TRACE("nla_solver", tout << "m="; _().print_monic_with_vars(m, tout); tout << "\nfactorization="; _().print_factorization(ab, tout);); TRACE("nla_solver", tout << "m="; _().print_monic_with_vars(m, tout); tout << "\nfactorization="; _().print_factorization(ab, tout););
if (mv != fv) {
bool gt = mv > fv;
for (unsigned j = 0, k = 1; j < 2; j++, k--) {
order_lemma_on_ab(m, rsign, var(ab[k]), var(ab[j]), gt);
explain(ab); explain(m);
TRACE("nla_solver", _().print_lemma(tout););
}
}
for (unsigned j = 0, k = 1; j < 2; j++, k--) { for (unsigned j = 0, k = 1; j < 2; j++, k--) {
order_lemma_on_ac_explore(m, ab, j == 1); order_lemma_on_ac_explore(m, ab, j == 1);
} }
@ -316,5 +333,38 @@ bool order::order_lemma_on_ac_and_bc_and_factors(const monic& ac,
} }
return false; return false;
} }
/*
given: sign * m = ab
lemma b != val(b) || sign 0 m <= a*val(b)
*/
void order::order_lemma_on_ab_gt(const monic& m, const rational& sign, lpvar a, lpvar b) {
SASSERT(sign * var_val(m) > val(a) * val(b));
add_lemma();
// negate b == val(b)
mk_ineq(b, llc::NE, val(b));
// ab <= val(b)a
mk_ineq(sign, m.var(), -val(b), a, llc::LE);
}
/*
given: sign * m = ab
lemma b != val(b) || sign*m >= a*val(b)
*/
void order::order_lemma_on_ab_lt(const monic& m, const rational& sign, lpvar a, lpvar b) {
TRACE("nla_solver", tout << "sign = " << sign << ", m = "; c().print_monic(m, tout) << ", a = "; c().print_var(a, tout) <<
", b = "; c().print_var(b, tout) << "\n";);
SASSERT(sign * var_val(m) < val(a) * val(b));
add_lemma();
// negate b == val(b)
mk_ineq(b, llc::NE, val(b));
// ab >= val(b)a
mk_ineq(sign, m.var(), -val(b), a, llc::GE);
}
void order::order_lemma_on_ab(const monic& m, const rational& sign, lpvar a, lpvar b, bool gt) {
if (gt)
order_lemma_on_ab_gt(m, sign, a, b);
else
order_lemma_on_ab_lt(m, sign, a, b);
}
} }

3
src/math/lp/nla_order_lemmas.h
View file

@ -48,6 +48,9 @@ private:
void order_lemma_on_factorization(const monic& rm, const factorization& ab); void order_lemma_on_factorization(const monic& rm, const factorization& ab);
void order_lemma_on_ab_gt(const monic& m, const rational& sign, lpvar a, lpvar b);
void order_lemma_on_ab_lt(const monic& m, const rational& sign, lpvar a, lpvar b);
void order_lemma_on_ab(const monic& m, const rational& sign, lpvar a, lpvar b, bool gt); void order_lemma_on_ab(const monic& m, const rational& sign, lpvar a, lpvar b, bool gt);
void order_lemma_on_factor_binomial_explore(const monic& m, bool k); void order_lemma_on_factor_binomial_explore(const monic& m, bool k);
void order_lemma_on_factor_binomial_rm(const monic& ac, bool k, const monic& bd); void order_lemma_on_factor_binomial_rm(const monic& ac, bool k, const monic& bd);