* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2003 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
*/
+#include <iostream>
#include <stdexcept>
#include "pseries.h"
#include "print.h"
#include "archive.h"
#include "utils.h"
-#include "debugmsg.h"
namespace GiNaC {
* Default ctor, dtor, copy ctor, assignment operator and helpers
*/
-pseries::pseries() : basic(TINFO_pseries)
-{
- debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT);
-}
+pseries::pseries() : inherited(TINFO_pseries) { }
void pseries::copy(const pseries &other)
{
/** Construct pseries from a vector of coefficients and powers.
* expair.rest holds the coefficient, expair.coeff holds the power.
* The powers must be integers (positive or negative) and in ascending order;
- * the last coefficient can be Order(_ex1()) to represent a truncated,
+ * the last coefficient can be Order(_ex1) to represent a truncated,
* non-terminating series.
*
* @param rel_ expansion variable and point (must hold a relational)
* @return newly constructed pseries */
pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_)
{
- debugmsg("pseries ctor from ex,epvector", LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(is_exactly_a<relational>(rel_));
- GINAC_ASSERT(is_exactly_a<symbol>(rel_.lhs()));
+ GINAC_ASSERT(is_a<relational>(rel_));
+ GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
point = rel_.rhs();
var = rel_.lhs();
}
pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
{
- debugmsg("pseries ctor from archive_node", LOGLEVEL_CONSTRUCT);
for (unsigned int i=0; true; ++i) {
ex rest;
ex coeff;
void pseries::print(const print_context & c, unsigned level) const
{
- debugmsg("pseries print", LOGLEVEL_PRINT);
-
if (is_a<print_tree>(c)) {
c.s << std::string(level, ' ') << class_name()
var.print(c, level + delta_indent);
point.print(c, level + delta_indent);
+ } else if (is_a<print_python_repr>(c)) {
+ c.s << class_name() << "(relational(";
+ var.print(c);
+ c.s << ',';
+ point.print(c);
+ c.s << "),[";
+ unsigned num = seq.size();
+ for (unsigned i=0; i<num; ++i) {
+ if (i)
+ c.s << ',';
+ c.s << '(';
+ seq[i].rest.print(c);
+ c.s << ',';
+ seq[i].coeff.print(c);
+ c.s << ')';
+ }
+ c.s << "])";
} else {
if (precedence() <= level)
c.s << par_close;
} else
var.print(c);
- if (i->coeff.compare(_ex1())) {
- c.s << '^';
+ if (i->coeff.compare(_ex1)) {
+ if (is_a<print_python>(c))
+ c.s << "**";
+ else
+ c.s << '^';
if (i->coeff.info(info_flags::negative)) {
c.s << par_open;
i->coeff.print(c);
int pseries::compare_same_type(const basic & other) const
{
- GINAC_ASSERT(is_of_type(other, pseries));
+ GINAC_ASSERT(is_a<pseries>(other));
const pseries &o = static_cast<const pseries &>(other);
// first compare the lengths of the series...
{
if (var.is_equal(s)) {
if (seq.empty())
- return _ex0();
+ return _ex0;
// Binary search in sequence for given power
numeric looking_for = numeric(n);
throw(std::logic_error("pseries::coeff: compare() didn't return -1, 0 or 1"));
}
}
- return _ex0();
+ return _ex0;
} else
return convert_to_poly().coeff(s, n);
}
->setflag(status_flags::dynallocated | (options == 0 ? status_flags::expanded : 0));
}
-/** Implementation of ex::diff() for a power series. It treats the series as a
- * polynomial.
+/** Implementation of ex::diff() for a power series.
* @see ex::diff */
ex pseries::derivative(const symbol & s) const
{
+ epvector new_seq;
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+
if (s == var) {
- epvector new_seq;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
// FIXME: coeff might depend on var
while (it != itend) {
}
++it;
}
- return pseries(relational(var,point), new_seq);
+
} else {
- return *this;
+
+ while (it != itend) {
+ if (is_order_function(it->rest)) {
+ new_seq.push_back(*it);
+ } else {
+ ex c = it->rest.diff(s);
+ if (!c.is_zero())
+ new_seq.push_back(expair(c, it->coeff));
+ }
+ ++it;
+ }
}
+
+ return pseries(relational(var,point), new_seq);
}
ex pseries::convert_to_poly(bool no_order) const
ex basic::series(const relational & r, int order, unsigned options) const
{
epvector seq;
- numeric fac(1);
+ numeric fac = 1;
ex deriv = *this;
ex coeff = deriv.subs(r);
const symbol &s = ex_to<symbol>(r.lhs());
if (!coeff.is_zero())
- seq.push_back(expair(coeff, _ex0()));
+ seq.push_back(expair(coeff, _ex0));
int n;
for (n=1; n<order; ++n) {
// Higher-order terms, if present
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
- seq.push_back(expair(Order(_ex1()), n));
+ seq.push_back(expair(Order(_ex1), n));
return pseries(r, seq);
}
{
epvector seq;
const ex point = r.rhs();
- GINAC_ASSERT(is_exactly_a<symbol>(r.lhs()));
+ GINAC_ASSERT(is_a<symbol>(r.lhs()));
if (this->is_equal_same_type(ex_to<symbol>(r.lhs()))) {
if (order > 0 && !point.is_zero())
- seq.push_back(expair(point, _ex0()));
+ seq.push_back(expair(point, _ex0));
if (order > 1)
- seq.push_back(expair(_ex1(), _ex1()));
+ seq.push_back(expair(_ex1, _ex1));
else
- seq.push_back(expair(Order(_ex1()), numeric(order)));
+ seq.push_back(expair(Order(_ex1), numeric(order)));
} else
- seq.push_back(expair(*this, _ex0()));
+ seq.push_back(expair(*this, _ex0));
return pseries(r, seq);
}
// results in an empty (constant) series
if (!is_compatible_to(other)) {
epvector nul;
- nul.push_back(expair(Order(_ex1()), _ex0()));
+ nul.push_back(expair(Order(_ex1), _ex0));
return pseries(relational(var,point), nul);
}
} else {
// Add coefficient of a and b
if (is_order_function((*a).rest) || is_order_function((*b).rest)) {
- new_seq.push_back(expair(Order(_ex1()), (*a).coeff));
+ new_seq.push_back(expair(Order(_ex1), (*a).coeff));
break; // Order term ends the sequence
} else {
ex sum = (*a).rest + (*b).rest;
epvector::const_iterator itend = seq.end();
for (; it!=itend; ++it) {
ex op;
- if (is_ex_exactly_of_type(it->rest, pseries))
+ if (is_exactly_a<pseries>(it->rest))
op = it->rest;
else
op = it->rest.series(r, order, options);
- if (!it->coeff.is_equal(_ex1()))
+ if (!it->coeff.is_equal(_ex1))
op = ex_to<pseries>(op).mul_const(ex_to<numeric>(it->coeff));
// Series addition
// results in an empty (constant) series
if (!is_compatible_to(other)) {
epvector nul;
- nul.push_back(expair(Order(_ex1()), _ex0()));
+ nul.push_back(expair(Order(_ex1), _ex0));
return pseries(relational(var,point), nul);
}
cdeg_max = higher_order_c - 1;
for (int cdeg=cdeg_min; cdeg<=cdeg_max; ++cdeg) {
- ex co = _ex0();
+ ex co = _ex0;
// c(i)=a(0)b(i)+...+a(i)b(0)
for (int i=a_min; cdeg-i>=b_min; ++i) {
ex a_coeff = coeff(var, i);
new_seq.push_back(expair(co, numeric(cdeg)));
}
if (higher_order_c < INT_MAX)
- new_seq.push_back(expair(Order(_ex1()), numeric(higher_order_c)));
+ new_seq.push_back(expair(Order(_ex1), numeric(higher_order_c)));
return pseries(relational(var, point), new_seq);
}
co.push_back(power(coeff(var, ldeg), p));
bool all_sums_zero = true;
for (int i=1; i<deg; ++i) {
- ex sum = _ex0();
+ ex sum = _ex0;
for (int j=1; j<=i; ++j) {
ex c = coeff(var, j + ldeg);
if (is_order_function(c)) {
- co.push_back(Order(_ex1()));
+ co.push_back(Order(_ex1));
break;
} else
sum += (p * j - (i - j)) * co[i - j] * c;
}
}
if (!higher_order && !all_sums_zero)
- new_seq.push_back(expair(Order(_ex1()), p * ldeg + deg));
+ new_seq.push_back(expair(Order(_ex1), p * ldeg + deg));
return pseries(relational(var,point), new_seq);
}
ex power::series(const relational & r, int order, unsigned options) const
{
// If basis is already a series, just power it
- if (is_ex_exactly_of_type(basis, pseries))
+ if (is_exactly_a<pseries>(basis))
return ex_to<pseries>(basis).power_const(ex_to<numeric>(exponent), order);
// Basis is not a series, may there be a singularity?
if (basis.is_equal(r.lhs() - r.rhs())) {
epvector new_seq;
if (ex_to<numeric>(exponent).to_int() < order)
- new_seq.push_back(expair(_ex1(), exponent));
+ new_seq.push_back(expair(_ex1, exponent));
else
- new_seq.push_back(expair(Order(_ex1()), exponent));
+ new_seq.push_back(expair(Order(_ex1), exponent));
return pseries(r, new_seq);
}
ex pseries::series(const relational & r, int order, unsigned options) const
{
const ex p = r.rhs();
- GINAC_ASSERT(is_exactly_a<symbol>(r.lhs()));
+ GINAC_ASSERT(is_a<symbol>(r.lhs()));
const symbol &s = ex_to<symbol>(r.lhs());
if (var.is_equal(s) && point.is_equal(p)) {
while (it != itend) {
int o = ex_to<numeric>(it->coeff).to_int();
if (o >= order) {
- new_seq.push_back(expair(Order(_ex1()), o));
+ new_seq.push_back(expair(Order(_ex1), o));
break;
}
new_seq.push_back(*it);
ex e;
relational rel_;
- if (is_ex_exactly_of_type(r,relational))
+ if (is_exactly_a<relational>(r))
rel_ = ex_to<relational>(r);
- else if (is_ex_exactly_of_type(r,symbol))
- rel_ = relational(r,_ex0());
+ else if (is_a<symbol>(r))
+ rel_ = relational(r,_ex0);
else
throw (std::logic_error("ex::series(): expansion point has unknown type"));
git://www.ginac.de / ginac.git / blobdiff