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Z3 sources
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
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Leonardo de Moura
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241
lib/polynomial_cmds.cpp
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241
lib/polynomial_cmds.cpp
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/*++
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Copyright (c) 2011 Microsoft Corporation
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Module Name:
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polynomial_cmds.cpp
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Abstract:
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Commands for debugging polynomial module.
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Author:
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Leonardo (leonardo) 2011-12-23
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Notes:
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--*/
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#include<sstream>
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#include"cmd_context.h"
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#include"cmd_util.h"
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#include"scoped_timer.h"
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#include"scoped_ctrl_c.h"
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#include"cancel_eh.h"
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#include"ast_smt2_pp.h"
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#include"expr2polynomial.h"
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#include"parametric_cmd.h"
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#include"mpq.h"
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#include"algebraic_numbers.h"
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#include"pp.h"
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#include"pp_params.h"
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#include"polynomial_var2value.h"
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#include"expr2var.h"
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static void to_poly(cmd_context & ctx, expr * t) {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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default_expr2polynomial expr2poly(ctx.m(), pm);
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polynomial::polynomial_ref p(pm);
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polynomial::scoped_numeral d(nm);
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if (!expr2poly.to_polynomial(t, p, d)) {
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throw cmd_exception("expression is not a polynomial");
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}
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expr_ref r(ctx.m());
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expr2poly.to_expr(p, true, r);
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if (!nm.is_one(d))
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ctx.regular_stream() << "(* " << nm.to_string(d) << " ";
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ctx.display(ctx.regular_stream(), r);
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if (!nm.is_one(d))
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ctx.regular_stream() << ")";
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ctx.regular_stream() << std::endl;
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}
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static void factor(cmd_context & ctx, expr * t, polynomial::factor_params const & ps) {
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polynomial::numeral_manager nm;
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polynomial::manager pm(nm);
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default_expr2polynomial expr2poly(ctx.m(), pm);
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polynomial::polynomial_ref p(pm);
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polynomial::scoped_numeral d(nm);
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if (!expr2poly.to_polynomial(t, p, d)) {
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throw cmd_exception("expression is not a polynomial");
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}
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polynomial::factors fs(pm);
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factor(p, fs, ps);
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ctx.regular_stream() << "(factors";
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rational f0(fs.get_constant());
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f0 = f0 / rational(d);
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ctx.regular_stream() << std::endl << f0;
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unsigned num_factors = fs.distinct_factors();
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expr_ref f(ctx.m());
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for (unsigned i = 0; i < num_factors; i++) {
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ctx.regular_stream() << std::endl;
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if (fs.get_degree(i) > 1)
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ctx.regular_stream() << "(^ ";
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expr2poly.to_expr(fs[i], true, f);
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ctx.display(ctx.regular_stream(), f);
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if (fs.get_degree(i) > 1)
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ctx.regular_stream() << " " << fs.get_degree(i) << ")";
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}
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ctx.regular_stream() << ")" << std::endl;
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}
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class poly_isolate_roots_cmd : public cmd {
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struct context {
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arith_util m_util;
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unsynch_mpq_manager m_qm;
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polynomial::manager m_pm;
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algebraic_numbers::manager m_am;
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polynomial_ref m_p;
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default_expr2polynomial m_expr2poly;
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polynomial::var m_var;
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typedef polynomial::simple_var2value<algebraic_numbers::manager> x2v;
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x2v m_x2v;
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context(ast_manager & m):
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m_util(m),
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m_pm(m_qm),
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m_am(m_qm),
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m_p(m_pm),
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m_expr2poly(m, m_pm),
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m_var(polynomial::null_var),
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m_x2v(m_am) {
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}
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void set_next_arg(cmd_context & ctx, expr * arg) {
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if (m_p.get() == 0) {
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scoped_mpz d(m_qm);
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if (!m_expr2poly.to_polynomial(arg, m_p, d))
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throw cmd_exception("expression is not a polynomial");
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}
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else if (m_var == polynomial::null_var) {
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if (!m_expr2poly.is_var(arg))
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throw cmd_exception("invalid assignment, argument is not a variable in the given polynomial");
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m_var = m_expr2poly.get_mapping().to_var(arg);
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}
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else {
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rational k;
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scoped_anum v(m_am);
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if (m_util.is_numeral(arg, k)) {
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m_am.set(v, k.to_mpq());
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}
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else if (m_util.is_irrational_algebraic_numeral(arg)) {
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m_am.set(v, m_util.to_irrational_algebraic_numeral(arg));
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}
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else {
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throw cmd_exception("invalid assignment, argument is not a value");
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}
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m_x2v.push_back(m_var, v);
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m_var = polynomial::null_var;
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}
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}
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void execute(cmd_context & ctx) {
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if (m_p.get() == 0)
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throw cmd_exception("polynomial expected");
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polynomial::var_vector xs;
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m_pm.vars(m_p, xs);
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unsigned num_assigned = 0;
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for (unsigned i = 0; i < xs.size(); i++) {
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if (m_x2v.contains(xs[i]))
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num_assigned++;
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}
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if (num_assigned != xs.size() && num_assigned + 1 != xs.size())
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throw cmd_exception("given assignment is not sufficient to make the given polynomial univariate");
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scoped_anum_vector rs(m_am);
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m_am.isolate_roots(m_p, m_x2v, rs);
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ctx.regular_stream() << "(roots";
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for (unsigned i = 0; i < rs.size(); i++) {
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ctx.regular_stream() << std::endl;
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if (!get_pp_default_params().m_pp_decimal)
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m_am.display_root_smt2(ctx.regular_stream(), rs[i]);
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else
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m_am.display_decimal(ctx.regular_stream(), rs[i]);
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}
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ctx.regular_stream() << ")" << std::endl;
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}
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};
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scoped_ptr<context> m_ctx;
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public:
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poly_isolate_roots_cmd(char const * name = "poly/isolate-roots"):cmd(name), m_ctx(0) {}
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virtual char const * get_usage() const { return "<term> (<term> <value>)*"; }
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virtual char const * get_descr(cmd_context & ctx) const { return "isolate the roots a multivariate polynomial modulo an assignment"; }
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virtual unsigned get_arity() const { return VAR_ARITY; }
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virtual void prepare(cmd_context & ctx) {
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m_ctx = alloc(context, ctx.m());
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}
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virtual void finalize(cmd_context & ctx) {
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m_ctx = 0;
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}
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virtual void failure_cleanup(cmd_context & ctx) {
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m_ctx = 0;
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}
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virtual cmd_arg_kind next_arg_kind(cmd_context & ctx) const {
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return CPK_EXPR;
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}
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virtual void set_next_arg(cmd_context & ctx, expr * arg) {
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m_ctx->set_next_arg(ctx, arg);
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}
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virtual void execute(cmd_context & ctx) {
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m_ctx->execute(ctx);
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m_ctx = 0;
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}
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};
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UNARY_CMD(to_poly_cmd, "to-poly", "<term>", "convert expression into sum-of-monomials form", CPK_EXPR, expr *, to_poly(ctx, arg););
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class poly_factor_cmd : public parametric_cmd {
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expr * m_target;
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public:
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poly_factor_cmd(char const * name = "poly/factor"):parametric_cmd(name) {}
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virtual char const * get_usage() const { return "<term> (<keyword> <value>)*"; }
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virtual char const * get_main_descr() const {
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return "factor a polynomial";
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}
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virtual void init_pdescrs(cmd_context & ctx, param_descrs & p) {
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polynomial::factor_params::get_param_descrs(p);
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}
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virtual void prepare(cmd_context & ctx) {
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parametric_cmd::prepare(ctx);
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m_target = 0;
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}
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virtual cmd_arg_kind next_arg_kind(cmd_context & ctx) const {
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if (m_target == 0) return CPK_EXPR;
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return parametric_cmd::next_arg_kind(ctx);
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}
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virtual void set_next_arg(cmd_context & ctx, expr * arg) {
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m_target = arg;
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}
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virtual void execute(cmd_context & ctx) {
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polynomial::factor_params ps;
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ps.updt_params(m_params);
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factor(ctx, m_target, ps);
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}
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};
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void install_polynomial_cmds(cmd_context & ctx) {
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#ifndef _EXTERNAL_RELEASE
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ctx.insert(alloc(to_poly_cmd));
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ctx.insert(alloc(poly_factor_cmd));
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ctx.insert(alloc(poly_isolate_roots_cmd));
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#endif
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}
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