mirror of
https://github.com/Z3Prover/z3
synced 2025-04-08 10:25:18 +00:00
added polynomial evaluation at algebraic point
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
parent
bf2340850a
commit
0d230375be
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@ -22,6 +22,9 @@ Notes:
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#include"api_log_macros.h"
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#include"api_context.h"
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#include"algebraic_numbers.h"
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#include"expr2polynomial.h"
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#include"cancel_eh.h"
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#include"scoped_timer.h"
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extern "C" {
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@ -318,6 +321,34 @@ extern "C" {
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return !Z3_algebraic_eq(c, a, b);
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}
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static bool to_anum_vector(Z3_context c, unsigned n, Z3_ast a[], scoped_anum_vector & as) {
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algebraic_numbers::manager & _am = am(c);
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scoped_anum tmp(_am);
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for (unsigned i = 0; i < n; i++) {
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if (is_rational(c, a[i])) {
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_am.set(tmp, get_rational(c, a[i]).to_mpq());
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as.push_back(tmp);
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}
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else if (is_irrational(c, a[i])) {
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as.push_back(get_irrational(c, a[i]));
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}
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else {
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return false;
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}
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}
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return true;
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}
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class vector_var2anum : public polynomial::var2anum {
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scoped_anum_vector const & m_as;
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public:
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vector_var2anum(scoped_anum_vector & as):m_as(as) {}
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virtual ~vector_var2anum() {}
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virtual algebraic_numbers::manager & m() const { return m_as.m(); }
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virtual bool contains(polynomial::var x) const { return static_cast<unsigned>(x) < m_as.size(); }
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virtual algebraic_numbers::anum const & operator()(polynomial::var x) const { return m_as.get(x); }
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};
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Z3_ast_vector Z3_API Z3_algebraic_roots(Z3_context c, Z3_ast p, unsigned n, Z3_ast a[]) {
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Z3_TRY;
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LOG_Z3_algebraic_roots(c, p, n, a);
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@ -331,8 +362,30 @@ extern "C" {
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Z3_TRY;
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LOG_Z3_algebraic_eval(c, p, n, a);
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RESET_ERROR_CODE();
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// TODO
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return 0;
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polynomial::manager & pm = mk_c(c)->pm();
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polynomial_ref _p(pm);
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polynomial::scoped_numeral d(pm.m());
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expr2polynomial converter(mk_c(c)->m(), pm, 0, true);
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if (!converter.to_polynomial(to_expr(p), _p, d)) {
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SET_ERROR_CODE(Z3_INVALID_ARG);
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return 0;
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}
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algebraic_numbers::manager & _am = am(c);
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scoped_anum_vector as(_am);
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if (!to_anum_vector(c, n, a, as)) {
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SET_ERROR_CODE(Z3_INVALID_ARG);
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return 0;
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}
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{
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cancel_eh<algebraic_numbers::manager> eh(_am);
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api::context::set_interruptable(*(mk_c(c)), eh);
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scoped_timer timer(mk_c(c)->params().m_timeout, &eh);
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vector_var2anum v2a(as);
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int r = _am.eval_sign_at(_p, v2a);
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if (r > 0) return 1;
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else if (r < 0) return -1;
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else return 0;
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}
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Z3_CATCH_RETURN(0);
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}
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@ -32,6 +32,7 @@ Revision History:
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#include"event_handler.h"
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#include"tactic_manager.h"
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#include"context_params.h"
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#include"api_polynomial.h"
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namespace smtlib {
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class parser;
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@ -81,6 +82,8 @@ namespace api {
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Z3_ast_print_mode m_print_mode;
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event_handler * m_interruptable; // Reference to an object that can be interrupted by Z3_interrupt
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pmanager m_pmanager;
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public:
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// Scoped obj for setting m_interruptable
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class set_interruptable {
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@ -167,6 +170,13 @@ namespace api {
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void check_sorts(ast * n);
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// ------------------------
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//
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// Polynomial manager & caches
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//
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// -----------------------
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polynomial::manager & pm() { return m_pmanager.pm(); }
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// ------------------------
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//
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// Solver interface for backward compatibility
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34
src/api/api_polynomial.cpp
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34
src/api/api_polynomial.cpp
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@ -0,0 +1,34 @@
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/*++
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Copyright (c) 2012 Microsoft Corporation
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Module Name:
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api_polynomial.cpp
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Abstract:
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Polynomial manager and caches for the external API.
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Author:
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Leonardo de Moura (leonardo) 2012-12-08
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Notes:
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--*/
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#include"api_polynomial.h"
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namespace api {
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pmanager::pmanager():
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m_pm(m_nm) {
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}
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pmanager::~pmanager() {
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}
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void pmanager::set_cancel(bool f) {
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m_pm.set_cancel(f);
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}
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};
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39
src/api/api_polynomial.h
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39
src/api/api_polynomial.h
Normal file
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@ -0,0 +1,39 @@
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/*++
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Copyright (c) 2012 Microsoft Corporation
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Module Name:
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api_polynomial.h
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Abstract:
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Polynomial manager and caches for the external API.
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Author:
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Leonardo de Moura (leonardo) 2012-12-08
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Notes:
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--*/
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#ifndef _API_POLYNOMIAL_H_
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#define _API_POLYNOMIAL_H_
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#include"polynomial.h"
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namespace api {
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class pmanager {
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unsynch_mpz_manager m_nm;
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polynomial::manager m_pm;
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// TODO: add support for caching expressions -> polynomial and back
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public:
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pmanager();
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virtual ~pmanager();
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polynomial::manager & pm() { return m_pm; }
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void set_cancel(bool f);
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};
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};
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#endif
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@ -1126,6 +1126,27 @@ def Var(idx, s):
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_z3_assert(is_sort(s), "Z3 sort expected")
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return _to_expr_ref(Z3_mk_bound(s.ctx_ref(), idx, s.ast), s.ctx)
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def RealVar(idx, ctx=None):
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"""
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Create a real free variable. Free variables are used to create quantified formulas.
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They are also used to create polynomials.
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>>> RealVar(0)
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Var(0)
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"""
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return Var(idx, RealSort(ctx))
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def RealVarVector(n, ctx=None):
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"""
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Create a list of Real free variables.
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The variables have ids: 0, 1, ..., n-1
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>>> x0, x1, x2, x3 = RealVarVector(4)
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>>> x2
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Var(2)
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"""
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return [ RealVar(i, ctx) for i in range(n) ]
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#########################################
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#
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# Booleans
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@ -481,6 +481,30 @@ class Numeral:
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def ctx_ref(self):
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return self.ctx.ref()
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def eval_sign_at(p, vs):
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"""
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Evaluate the sign of the polynomial `p` at `vs`. `p` is a Z3
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Expression containing arithmetic operators: +, -, *, ^k where k is
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an integer; and free variables x that is_var(x) is True. Moreover,
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all variables must be real.
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The result is 1 if the polynomial is positive at the given point,
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-1 if negative, and 0 if zero.
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>>> x0, x1, x2 = RealVarVector(3)
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>>> eval_sign_at(x0**2 + x1*x2 + 1, (Numeral(0), Numeral(1), Numeral(2)))
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1
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>>> eval_sign_at(x0**2 - 2, [ Numeral(Sqrt(2)) ])
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0
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>>> eval_sign_at((x0 + x1)*(x0 + x2), (Numeral(0), Numeral(Sqrt(2)), Numeral(Sqrt(3))))
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1
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"""
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num = len(vs)
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_vs = (Ast * num)()
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for i in range(num):
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_vs[i] = vs[i].ast
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return Z3_algebraic_eval(p.ctx_ref(), p.as_ast(), num, _vs)
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if __name__ == "__main__":
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import doctest
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@ -49,21 +49,24 @@ struct expr2polynomial::imp {
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polynomial::polynomial_ref_vector m_presult_stack;
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polynomial::scoped_numeral_vector m_dresult_stack;
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bool m_use_var_idxs;
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volatile bool m_cancel;
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imp(expr2polynomial & w, ast_manager & am, polynomial::manager & pm, expr2var * e2v):
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imp(expr2polynomial & w, ast_manager & am, polynomial::manager & pm, expr2var * e2v, bool use_var_idxs):
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m_wrapper(w),
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m_am(am),
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m_autil(am),
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m_pm(pm),
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m_expr2var(e2v == 0 ? alloc(expr2var, am) : e2v),
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m_expr2var_owner(e2v == 0),
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m_expr2var(e2v == 0 && !use_var_idxs ? alloc(expr2var, am) : e2v),
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m_expr2var_owner(e2v == 0 && !use_var_idxs),
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m_var2expr(am),
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m_cached_domain(am),
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m_cached_polynomials(pm),
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m_cached_denominators(pm.m()),
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m_presult_stack(pm),
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m_dresult_stack(pm.m()),
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m_use_var_idxs(use_var_idxs),
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m_cancel(false) {
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}
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cooperate("expr2polynomial");
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}
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void throw_not_polynomial() {
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throw default_exception("the given expression is not a polynomial");
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}
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void throw_no_int_var() {
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throw default_exception("integer variables are not allowed in the given polynomial");
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}
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void push_frame(app * t) {
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m_frame_stack.push_back(frame(t));
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}
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}
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void store_var_poly(expr * t) {
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polynomial::var x = m_expr2var->to_var(t);
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if (x == UINT_MAX) {
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bool is_int = m_autil.is_int(t);
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x = m_wrapper.mk_var(is_int);
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m_expr2var->insert(t, x);
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if (x >= m_var2expr.size())
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m_var2expr.resize(x+1, 0);
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m_var2expr.set(x, t);
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polynomial::var x;
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if (m_use_var_idxs) {
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SASSERT(::is_var(t));
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if (m_autil.is_int(t))
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throw_no_int_var();
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unsigned idx = to_var(t)->get_idx();
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while (idx >= m_pm.num_vars())
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m_pm.mk_var();
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x = static_cast<polynomial::var>(idx);
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}
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else {
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x = m_expr2var->to_var(t);
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if (x == UINT_MAX) {
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bool is_int = m_autil.is_int(t);
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x = m_wrapper.mk_var(is_int);
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m_expr2var->insert(t, x);
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if (x >= m_var2expr.size())
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m_var2expr.resize(x+1, 0);
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m_var2expr.set(x, t);
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}
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}
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polynomial::numeral one(1);
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store_result(t, pm().mk_polynomial(x), one);
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rational k;
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SASSERT(t->get_num_args() == 2);
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if (!m_autil.is_numeral(t->get_arg(1), k) || !k.is_int() || !k.is_unsigned()) {
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store_var_poly(t);
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if (m_use_var_idxs)
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throw_not_polynomial();
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else
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store_var_poly(t);
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return true;
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}
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push_frame(t);
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}
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default:
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// can't handle operator
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if (m_use_var_idxs)
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throw_not_polynomial();
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store_var_poly(t);
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return true;
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}
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@ -190,6 +218,8 @@ struct expr2polynomial::imp {
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SASSERT(is_app(t));
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if (!m_autil.is_arith_expr(t)) {
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if (m_use_var_idxs)
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throw_not_polynomial();
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store_var_poly(t);
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return true;
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}
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for (unsigned i = 0; i < sz; i++) {
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margs.reset();
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polynomial::monomial * m = pm().get_monomial(p, i);
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polynomial::monomial * _m = pm().get_monomial(p, i);
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polynomial::numeral const & a = pm().coeff(p, i);
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if (!nm().is_one(a)) {
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margs.push_back(m_autil.mk_numeral(rational(a), is_int));
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}
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unsigned msz = pm().size(m);
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unsigned msz = pm().size(_m);
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for (unsigned j = 0; j < msz; j++) {
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polynomial::var x = pm().get_var(m, j);
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expr * t = m_var2expr.get(x);
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if (m_wrapper.is_int(x) && !is_int) {
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t = m_autil.mk_to_real(t);
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polynomial::var x = pm().get_var(_m, j);
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expr * t;
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if (m_use_var_idxs) {
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t = m().mk_var(x, m_autil.mk_real());
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}
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unsigned d = pm().degree(m, j);
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else {
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t = m_var2expr.get(x);
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if (m_wrapper.is_int(x) && !is_int) {
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t = m_autil.mk_to_real(t);
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}
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}
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unsigned d = pm().degree(_m, j);
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if (use_power && d > 1) {
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margs.push_back(m_autil.mk_power(t, m_autil.mk_numeral(rational(d), is_int)));
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}
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}
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};
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expr2polynomial::expr2polynomial(ast_manager & am, polynomial::manager & pm, expr2var * e2v) {
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m_imp = alloc(imp, *this, am, pm, e2v);
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expr2polynomial::expr2polynomial(ast_manager & am, polynomial::manager & pm, expr2var * e2v, bool use_var_idxs) {
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m_imp = alloc(imp, *this, am, pm, e2v, use_var_idxs);
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}
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expr2polynomial::~expr2polynomial() {
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@ -451,10 +487,12 @@ void expr2polynomial::to_expr(polynomial::polynomial_ref const & p, bool use_pow
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}
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bool expr2polynomial::is_var(expr * t) const {
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SASSERT(!m_imp->m_use_var_idxs);
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return m_imp->m_expr2var->is_var(t);
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}
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expr2var const & expr2polynomial::get_mapping() const {
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SASSERT(!m_imp->m_use_var_idxs);
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return *(m_imp->m_expr2var);
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}
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@ -29,7 +29,24 @@ class expr2polynomial {
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struct imp;
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imp * m_imp;
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public:
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expr2polynomial(ast_manager & am, polynomial::manager & pm, expr2var * e2v);
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expr2polynomial(ast_manager & am,
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polynomial::manager & pm,
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expr2var * e2v,
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/*
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If true, the expressions converted into
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polynomials should only contain Z3 free variables.
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A Z3 variable x, with idx i, is converted into
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the variable i of the polynomial manager pm.
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An exception is thrown if there is a mismatch between
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the sorts x and the variable in the polynomial manager.
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The argument e2v is ignored when use_var_idxs is true.
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Moreover, only real variables are allowed.
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*/
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bool use_var_idxs = false
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);
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virtual ~expr2polynomial();
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ast_manager & m() const;
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@ -63,6 +80,8 @@ public:
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/**
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\brief Return the mapping from expressions to variables
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\pre the object was created using use_var_idxs = false.
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*/
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expr2var const & get_mapping() const;
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/**
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\brief Return true if the variable is associated with an expression of integer sort.
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*/
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virtual bool is_int(polynomial::var x) const = 0;
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virtual bool is_int(polynomial::var x) const { UNREACHABLE(); return false; }
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protected:
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virtual polynomial::var mk_var(bool is_int) = 0;
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virtual polynomial::var mk_var(bool is_int) { UNREACHABLE(); return polynomial::null_var; }
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};
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class default_expr2polynomial : public expr2polynomial {
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@ -64,6 +64,8 @@ namespace algebraic_numbers {
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static void collect_param_descrs(param_descrs & r) { get_param_descrs(r); }
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void set_cancel(bool f);
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void cancel() { set_cancel(true); }
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||||
void updt_params(params_ref const & p);
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||||
|
||||
|
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Loading…
Reference in a new issue