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Add prem_gcd based on pseudo-remainder

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-01-12 19:36:07 -08:00
parent 13d5c3e07a
commit 7711146d23
1 changed files with 54 additions and 0 deletions
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54
src/math/realclosure/realclosure.cpp
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@ -2866,6 +2866,11 @@ namespace realclosure {
} }
} }
void prem(unsigned sz1, value * const * p1, unsigned sz2, value * const * p2, value_ref_buffer & r) {
unsigned d;
prem(sz1, p1, sz2, p2, d, r);
}
/** /**
\brief r <- -p \brief r <- -p
*/ */
@ -3386,6 +3391,55 @@ namespace realclosure {
} }
} }
void flip_sign_if_lc_neg(value_ref_buffer & r) {
unsigned sz = r.size();
if (sz == 0)
return;
if (sign(r[sz - 1]) < 0)
neg(r);
}
void prem_gcd(unsigned sz1, value * const * p1, unsigned sz2, value * const * p2, value_ref_buffer & r) {
INC_DEPTH();
TRACE("rcf_gcd", tout << "prem-GCD [" << m_exec_depth << "]\n";
display_poly(tout, sz1, p1); tout << "\n";
display_poly(tout, sz2, p2); tout << "\n";);
SASSERT(p1 != r.c_ptr());
SASSERT(p2 != r.c_ptr());
if (sz1 == 0) {
r.append(sz2, p2);
flip_sign_if_lc_neg(r);
}
else if (sz2 == 0) {
r.append(sz1, p1);
flip_sign_if_lc_neg(r);
}
else {
value_ref_buffer A(*this);
value_ref_buffer B(*this);
value_ref_buffer R(*this);
A.append(sz1, p1);
B.append(sz2, p2);
while (true) {
TRACE("rcf_gcd",
tout << "A: "; display_poly(tout, A.size(), A.c_ptr()); tout << "\n";
tout << "B: "; display_poly(tout, B.size(), B.c_ptr()); tout << "\n";);
if (B.empty()) {
normalize_int_coeffs(A);
flip_sign_if_lc_neg(A);
r = A;
TRACE("rcf_gcd",
tout << "gcd result: "; display_poly(tout, r.size(), r.c_ptr()); tout << "\n";);
return;
}
prem(A.size(), A.c_ptr(), B.size(), B.c_ptr(), R);
normalize_int_coeffs(R);
A = B;
B = R;
}
}
}
// --------------------------------- // ---------------------------------
// //
// Derivatives and Sturm-Tarski Sequences // Derivatives and Sturm-Tarski Sequences