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fix unsoundness bug

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Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>
This commit is contained in:
Nikolaj Bjorner 2024-05-01 14:45:15 -07:00
parent 869643a551
commit 04c55c34e5
2 changed files with 32 additions and 4 deletions
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21
src/math/polynomial/polynomial.cpp
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@ -6317,6 +6317,27 @@ namespace polynomial {
return R.mk();
}
// x*q = p
//
// md = degree of x in p
// P = m0 + ...
// m0 = x^dm*m1
// m1 * p^dm * q^{md - dm}
// P' = m1 + ...
// property would be that x*q = p => P > 0 <=> P' > 0
// requires that q > 0
// Reasoning:
// P > 0
// <=> { since q > 0 }
// q^md * P > 0
// <=>
// q^md*x^dm*m0 + .. > 0
// <=>
// q^{md-dm}*(xq)^dm*m0 + ... > 0
// <=>
// q^{md-dm}*p^dm + .. > 0
// <=>
// P' > 0
void substitute(polynomial const* r, var x, polynomial const* p, polynomial const* q, polynomial_ref& result) {
unsigned md = degree(r, x);
if (md == 0) {