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);
}
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;
}
/**
* 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;
}
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;
}
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));
}
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));
}
}
/**
* 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;
}
static ex lst_reader(const exvector& ev)
{
return GiNaC::lst(ev.begin(), ev.end());
}