示例#1
0
ex
ex_collect_to_ex(const ex_collect_t& ec, const exvector& vars)
{
	exvector ev;
	ev.reserve(ec.size());
	for (std::size_t i = 0; i < ec.size(); ++i) {
		exvector tv;
		tv.reserve(vars.size() + 1);
		for (std::size_t j = 0; j < vars.size(); ++j) {
			const exp_vector_t& exp_vector(ec[i].first);

			bug_on(exp_vector.size() != vars.size(),
				"expected " << vars.size() << " variables, "
				"expression has " << exp_vector.size() << " instead");

			if (exp_vector[j] != 0)
				tv.push_back(pow(vars[j], exp_vector[j]));
		}
		tv.push_back(ec[i].second);
		ex tmp = dynallocate<mul>(tv);
		ev.push_back(tmp);
	}
	ex ret = dynallocate<add>(ev);
	return ret;
}
static ex make_divide_expr(const exvector& args)
{
	exvector rest_args;
	rest_args.reserve(args.size() - 1);
	std::copy(args.begin() + 1, args.end(), std::back_inserter(rest_args));
	ex rest_base = (new mul(rest_args))->setflag(status_flags::dynallocated);
	ex rest = pow(rest_base, *_num_1_p);
	return (new mul(args[0], rest))->setflag(status_flags::dynallocated);
}
示例#3
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exp_vector_t degree_vector(ex e, const exvector& vars)
{
	e = e.expand();
	exp_vector_t dvec(vars.size());
	for (std::size_t i = vars.size(); i-- != 0; ) {
		const int deg_i = e.degree(vars[i]);
		e = e.coeff(vars[i], deg_i);
		dvec[i] = deg_i;
	}
	return dvec;
}
示例#4
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/**
 * Compute the primitive part and the content of a modular multivariate
 * polynomial e \in Z_p[x_n][x_0, \ldots, x_{n-1}], i.e. e is considered
 * a polynomial in variables x_0, \ldots, x_{n-1} with coefficients being
 * modular polynomials Z_p[x_n]
 * @param e polynomial to operate on
 * @param pp primitive part of @a e, will be computed by this function
 * @param c content (in the sense described above) of @a e, will be
 *        computed by this function
 * @param vars variables x_0, \ldots, x_{n-1}, x_n
 * @param p modulus
 */
void primpart_content(ex& pp, ex& c, ex e, const exvector& vars,
		      const long p)
{
	static const ex ex1(1);
	static const ex ex0(0);
	e = e.expand();
	if (e.is_zero()) {
		pp = ex0;
		c = ex1;
		return;
	}
	exvector rest_vars = vars;
	rest_vars.pop_back();
	ex_collect_t ec;
	collect_vargs(ec, e, rest_vars);

	if (ec.size() == 1) {
		// the input polynomial factorizes into 
		// p_1(x_n) p_2(x_0, \ldots, x_{n-1})
		c = ec.rbegin()->second;
		ec.rbegin()->second = ex1;
		pp = ex_collect_to_ex(ec, rest_vars).expand().smod(numeric(p));
		return;
	}

	// Start from the leading coefficient (which is stored as a last
	// element of the terms array)
	auto i = ec.rbegin();
	ex g = i->second;
	// there are at least two terms, so it's safe to...
	++i;
	while (i != ec.rend() && !g.is_equal(ex1)) {
		g = euclid_gcd(i->second, g, vars.back(), p);
		++i;
	}
	if (g.is_equal(ex1)) {
		pp = e;
		c = ex1;
		return;
	}
	exvector mainvar;
	mainvar.push_back(vars.back());
	for (i = ec.rbegin(); i != ec.rend(); ++i) {
		ex tmp(0);
		if (!divide_in_z_p(i->second, g, tmp, mainvar, p))
			throw std::logic_error(std::string(__func__) +
					": bogus division failure");
		i->second = tmp;
	}

	pp = ex_collect_to_ex(ec, rest_vars).expand().smod(numeric(p));
	c = g;
}
示例#5
0
static unsigned check_factorization(const exvector& factors)
{
	ex e = (new mul(factors))->setflag(status_flags::dynallocated);
	ex ef = factor(e.expand());
	if (ef.nops() != factors.size()) {
		clog << "wrong number of factors, expected " << factors.size() <<
			", got " << ef.nops();
		return 1;
	}
	for (size_t i = 0; i < ef.nops(); ++i) {
		if (find(factors.begin(), factors.end(), ef.op(i)) == factors.end()) {
			clog << "wrong factorization: term not found: " << ef.op(i);
			return 1;
		}
	}
	return 0;
}
示例#6
0
static void
collect_term(ex_collect_priv_t& ec, const ex& e, const exvector& vars)
{
	if (e.is_zero())
		return;
	static const ex ex1(1);
	exp_vector_t key(vars.size());
	ex pre_coeff = e;
	for (std::size_t i = 0; i < vars.size(); ++i) {
		const int var_i_pow = pre_coeff.degree(vars[i]);
		key[i] = var_i_pow;
		pre_coeff = pre_coeff.coeff(vars[i], var_i_pow);
	}
	auto i = ec.find(key);
	if (i != ec.end())
		i->second += pre_coeff;
	else
		ec.insert(ex_collect_priv_t::value_type(key, pre_coeff));
}
示例#7
0
 GinacConstFunction::GinacConstFunction( const exvector& exs, const lst& params) 
     : Function( exs.size(), 0, params.nops()),
     exs_(exs), params_(params) {
         if(print__all){
         //std::cerr << "GinacConstFunction = ";					/**/
         //for(unsigned int i = 0; i < exs_.size(); i++ ){     /**/
         //    std::cerr << "[f("<<i<<") ="<<exs_[i] << "] " ; /**/
         //}													/**/
         //std::cerr << std::endl;								/**/
     	//}
     }
     
 void GinacConstFunction::eval(bool do_f, bool do_g, bool do_H){
     
     lst argsAndParams;
     lst::const_iterator params_it = params_.begin();
     
     for( unsigned int i = 0; params_it != params_.end(); params_it++, i++ ){
         argsAndParams.append( ex_to<symbol>(*params_it) == p(i));
     }
     //std::cerr << "NEXT FUNC"<< std::endl;           /**/
     
     if (do_f){
         for(unsigned int i = 0; i < exs_.size(); i++ ){
             f(i) = ex_to<numeric>(exs_[i].subs( argsAndParams )).to_double();
             //std::cerr << "f("<<i<<") ="<<f(i)<< std::endl; /**/
         }
     }
     
     if (do_g){
         clear_g();
     }
     
     if (do_H){
         clear_h();
     }
 }
static ex make_binop_expr(const int binop, const exvector& args)
{
	switch (binop) {
		case '+':
			return (new add(args))->setflag(status_flags::dynallocated);
		case '-':
			return make_minus_expr(args);
		case '*':
			return (new mul(args))->setflag(status_flags::dynallocated);
		case '/':
			return make_divide_expr(args);
		case '^':
			if (args.size() != 2)
				throw std::invalid_argument(
						std::string(__func__) 
						+ ": power should have exactly 2 operands");
			return pow(args[0], args[1]);
		default:
			throw std::invalid_argument(
					std::string(__func__) 
					+ ": invalid binary operation: " 
					+ char(binop));
	}
}
示例#9
0
/** 
 * Exact polynomial division of a, b \in Z_p[x_0, \ldots, x_n]
 * It doesn't check whether the inputs are proper polynomials, so be careful
 * of what you pass in.
 *  
 * @param a  first multivariate polynomial (dividend)
 * @param b  second multivariate polynomial (divisor)
 * @param q  quotient (returned)
 * @param var variables X iterator to first element of vector of symbols
 *
 * @return "true" when exact division succeeds (the quotient is returned in
 *          q), "false" otherwise.
 * @note @a p = 0 means the base ring is Z
 */
bool divide_in_z_p(const ex &a, const ex &b, ex &q, const exvector& vars, const long p)
{
	static const ex _ex1(1);
	if (b.is_zero())
		throw(std::overflow_error("divide_in_z: division by zero"));
	if (b.is_equal(_ex1)) {
		q = a;
		return true;
	}
	if (is_exactly_a<numeric>(a)) {
		if (is_exactly_a<numeric>(b)) {
			// p == 0 means division in Z
			if (p == 0) {
				const numeric tmp = ex_to<numeric>(a/b);
				if (tmp.is_integer()) {
					q = tmp;
					return true;
				} else
					return false;
			} else {
				q = (a*recip(ex_to<numeric>(b), p)).smod(numeric(p));
				return true;
			}
		} else
			return false;
	}
	if (a.is_equal(b)) {
		q = _ex1;
		return true;
	}

	// Main symbol
	const ex &x = vars.back();

	// Compare degrees
	int adeg = a.degree(x), bdeg = b.degree(x);
	if (bdeg > adeg)
		return false;

	// Polynomial long division (recursive)
	ex r = a.expand();
	if (r.is_zero())
		return true;
	int rdeg = adeg;
	ex eb = b.expand();
	ex blcoeff = eb.coeff(x, bdeg);
	exvector v;
	v.reserve(std::max(rdeg - bdeg + 1, 0));
	exvector rest_vars(vars);
	rest_vars.pop_back();
	while (rdeg >= bdeg) {
		ex term, rcoeff = r.coeff(x, rdeg);
		if (!divide_in_z_p(rcoeff, blcoeff, term, rest_vars, p))
			break;
		term = (term*power(x, rdeg - bdeg)).expand();
		v.push_back(term);
		r = (r - term*eb).expand();
		if (p != 0)
			r = r.smod(numeric(p));
		if (r.is_zero()) {
			q = (new add(v))->setflag(status_flags::dynallocated);
			return true;
		}
		rdeg = r.degree(x);
	}
	return false;
}
示例#10
0
static ex lst_reader(const exvector& ev)
{
	return GiNaC::lst(ev.begin(), ev.end());
}