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Simplify RCF C API. Add Z3_rcf_mk_roots (C API) and MkRoots (Python API). Implement basic root isolation support.

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2013-01-07 12:25:28 -08:00
parent 3c1f1a3b65
commit 09b5724d82
6 changed files with 216 additions and 118 deletions
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78
src/math/realclosure/realclosure.cpp
View file

@ -1082,10 +1082,86 @@ namespace realclosure {
}
}
void isolate_roots(unsigned n, numeral const * as, numeral_vector & roots) {
/**
\brief Root isolation for polynomials that are
- nonlinear (degree > 2)
- zero is not a root
- square free
- nonconstant
*/
void nl_nz_sqf_isolate_roots(unsigned n, value * const * as, numeral_vector & roots) {
SASSERT(n > 2);
SASSERT(!is_zero(as[0]));
SASSERT(!is_zero(as[n-1]));
// TODO
}
/**
\brief Root isolation for polynomials that are
- zero is not a root
- square free
- nonconstant
*/
void nz_sqf_isolate_roots(unsigned n, value * const * as, numeral_vector & roots) {
SASSERT(n > 1);
SASSERT(!is_zero(as[0]));
SASSERT(!is_zero(as[n-1]));
if (n == 2) {
// we don't need a field extension for linear polynomials.
numeral r;
value_ref neg_as_0(*this);
neg_as_0 = neg(as[0]);
set(r, div(neg_as_0, as[1]));
roots.push_back(r);
}
else {
nl_nz_sqf_isolate_roots(n, as, roots);
}
}
/**
\brief Root isolation for polynomials where 0 is not a root.
*/
void nz_isolate_roots(unsigned n, value * const * as, numeral_vector & roots) {
SASSERT(n > 0);
SASSERT(!is_zero(as[0]));
SASSERT(!is_zero(as[n-1]));
if (n == 1) {
// constant polynomial
return;
}
value_ref_buffer sqf(*this);
square_free(n, as, sqf);
nz_sqf_isolate_roots(sqf.size(), sqf.c_ptr(), roots);
}
/**
\brief Root isolation entry point.
*/
void isolate_roots(unsigned n, numeral const * as, numeral_vector & roots) {
SASSERT(n > 0);
SASSERT(!is_zero(as[n-1]));
if (n == 1) {
// constant polynomial
return;
}
unsigned i = 0;
for (; i < n; i++) {
if (!is_zero(as[i]))
break;
}
SASSERT(i < n);
SASSERT(!is_zero(as[i]));
ptr_buffer<value> as_values;
for (; i < n; i++)
as_values.push_back(as[i].m_value);
nz_isolate_roots(as_values.size(), as_values.c_ptr(), roots);
if (as_values.size() < n) {
// zero is a root
roots.push_back(numeral());
}
}
void reset(numeral & a) {
del(a);
SASSERT(is_zero(a));

4
src/math/realclosure/realclosure.h
View file

@ -278,6 +278,10 @@ namespace realclosure {
value * m_value;
public:
num():m_value(0) {}
// Low level functions for implementing the C API
void * c_ptr() { return m_value; }
static num mk(void * ptr) { num r; r.m_value = reinterpret_cast<value*>(ptr); return r; }
};
};