/** @file series.cpp
*
* Implementation of class for extended truncated power-series and
- * methods for series expansion.
- *
+ * methods for series expansion. */
+
+/*
* GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
#include "power.h"
#include "relational.h"
#include "symbol.h"
+#include "debugmsg.h"
+#ifndef NO_GINAC_NAMESPACE
+namespace GiNaC {
+#endif // ndef NO_GINAC_NAMESPACE
/*
* Default constructor, destructor, copy constructor, assignment operator and helpers
: basic(TINFO_series), seq(ops_), var(var_), point(point_)
{
debugmsg("series constructor from ex,ex,epvector", LOGLEVEL_CONSTRUCT);
- ASSERT(is_ex_exactly_of_type(var_, symbol));
+ GINAC_ASSERT(is_ex_exactly_of_type(var_, symbol));
}
{
if (level == 1)
return this->hold();
-
+
// Construct a new series with evaluated coefficients
epvector new_seq;
new_seq.reserve(seq.size());
return (new series(var, point, new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
+/** Evaluate numerically. The order term is dropped. */
ex series::evalf(int level) const
{
return convert_to_poly().evalf(level);
}
-
/*
* Construct expression (polynomial) out of series
*/
{
ex e;
epvector::const_iterator it = seq.begin(), itend = seq.end();
-
+
while (it != itend) {
if (is_order_function(it->rest)) {
if (!no_order)
ex coeff = deriv.subs(s == point);
if (!coeff.is_zero())
seq.push_back(expair(coeff, numeric(0)));
-
+
int n;
for (n=1; n<order; n++) {
fac = fac.mul(numeric(n));
if (!coeff.is_zero())
seq.push_back(expair(coeff, numeric(n)));
}
-
+
// Higher-order terms, if present
deriv = deriv.diff(s);
if (!deriv.is_zero())
nul.push_back(expair(Order(exONE()), exZERO()));
return series(var, point, nul);
}
-
+
// Series addition
epvector new_seq;
epvector::const_iterator a = seq.begin();
break;
} else
pow_a = ex_to_numeric((*a).coeff).to_int();
-
+
// If b is empty, fill up with elements from a and stop
if (b == b_end) {
while (a != a_end) {
break;
} else
pow_b = ex_to_numeric((*b).coeff).to_int();
-
+
// a and b are non-empty, compare powers
if (pow_a < pow_b) {
// a has lesser power, get coefficient from a
ex add::series(symbol const & s, ex const & point, int order) const
{
ex acc; // Series accumulator
-
+
// Get first term from overall_coeff
acc = overall_coeff.series(s,point,order);
-
+
// Add remaining terms
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
op = it->rest.series(s, point, order);
if (!it->coeff.is_equal(exONE()))
op = ex_to_series(op).mul_const(ex_to_numeric(it->coeff));
-
+
// Series addition
acc = ex_to_series(acc).add_series(ex_to_series(op));
}
{
epvector new_seq;
new_seq.reserve(seq.size());
-
+
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
if (!is_order_function(it->rest))
// Series multiplication
epvector new_seq;
-
+
const symbol *s = static_cast<symbol *>(var.bp);
int a_max = degree(*s);
int b_max = other.degree(*s);
int b_min = other.ldegree(*s);
int cdeg_min = a_min + b_min;
int cdeg_max = a_max + b_max;
-
+
int higher_order_a = INT_MAX;
int higher_order_b = INT_MAX;
if (is_order_function(coeff(*s, a_max)))
int higher_order_c = min(higher_order_a, higher_order_b);
if (cdeg_max >= higher_order_c)
cdeg_max = higher_order_c - 1;
-
+
for (int cdeg=cdeg_min; cdeg<=cdeg_max; cdeg++) {
ex co = exZERO();
// c(i)=a(0)b(i)+...+a(i)b(0)
}
-/** Implementation of ex::series() for product. This performs series multiplication when multiplying series.
- * @see ex::series */
/*
ex mul::series(symbol const & s, ex const & point, int order) const
{
}
*/
+/** Implementation of ex::series() for product. This performs series
+ * multiplication when multiplying series.
+ * @see ex::series */
ex mul::series(symbol const & s, ex const & point, int order) const
{
ex acc; // Series accumulator
-
+
// Get first term from overall_coeff
acc = overall_coeff.series(s, point, order);
-
+
// Multiply with remaining terms
epvector::const_iterator it = seq.begin();
epvector::const_iterator itend = seq.end();
int i;
const symbol *s = static_cast<symbol *>(var.bp);
int ldeg = ldegree(*s);
-
+
// Calculate coefficients of powered series
exvector co;
co.reserve(deg);
all_sums_zero = false;
co.push_back(co0 * sum / numeric(i));
}
-
+
// Construct new series (of non-zero coefficients)
epvector new_seq;
bool higher_order = false;
// Basis is not a series, may there be a singulary?
if (!exponent.info(info_flags::negint))
return basic::series(s, point, order);
-
+
// Expression is of type something^(-int), check for singularity
if (!basis.subs(s == point).is_zero())
return basic::series(s, point, order);
-
+
// Singularity encountered, expand basis into series
e = basis.series(s, point, order);
} else {
// Basis is a series
e = basis;
}
-
+
// Power e
return ex_to_series(e).power_const(ex_to_numeric(exponent), order);
}
* @return an expression holding a series object */
ex ex::series(symbol const &s, ex const &point, int order) const
{
- ASSERT(bp!=0);
+ GINAC_ASSERT(bp!=0);
return bp->series(s, point, order);
}
// Global constants
const series some_series;
type_info const & typeid_series = typeid(some_series);
+
+#ifndef NO_GINAC_NAMESPACE
+} // namespace GiNaC
+#endif // ndef NO_GINAC_NAMESPACE
git://www.ginac.de / ginac.git / blobdiff