* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2004 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 <numeric>
#include <stdexcept>
#include "pseries.h"
#include "mul.h"
#include "power.h"
#include "relational.h"
+#include "operators.h"
#include "symbol.h"
-#include "print.h"
#include "archive.h"
#include "utils.h"
-#include "debugmsg.h"
namespace GiNaC {
-GINAC_IMPLEMENT_REGISTERED_CLASS(pseries, basic)
+GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(pseries, basic,
+ print_func<print_context>(&pseries::do_print).
+ print_func<print_latex>(&pseries::do_print_latex).
+ print_func<print_tree>(&pseries::do_print_tree).
+ print_func<print_python>(&pseries::do_print_python).
+ print_func<print_python_repr>(&pseries::do_print_python_repr))
/*
- * Default ctor, dtor, copy ctor, assignment operator and helpers
+ * Default constructor
*/
-pseries::pseries() : basic(TINFO_pseries)
-{
- debugmsg("pseries default ctor", LOGLEVEL_CONSTRUCT);
-}
-
-void pseries::copy(const pseries &other)
-{
- inherited::copy(other);
- seq = other.seq;
- var = other.var;
- point = other.point;
-}
-
-DEFAULT_DESTROY(pseries)
+pseries::pseries() : inherited(TINFO_pseries) { }
/*
/** 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();
}
* Archiving
*/
-pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
+pseries::pseries(const archive_node &n, 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;
// functions overriding virtual functions from base classes
//////////
-void pseries::print(const print_context & c, unsigned level) const
+void pseries::print_series(const print_context & c, const char *openbrace, const char *closebrace, const char *mul_sym, const char *pow_sym, unsigned level) const
{
- debugmsg("pseries print", LOGLEVEL_PRINT);
+ if (precedence() <= level)
+ c.s << '(';
+
+ // objects of type pseries must not have any zero entries, so the
+ // trivial (zero) pseries needs a special treatment here:
+ if (seq.empty())
+ c.s << '0';
- if (is_a<print_tree>(c)) {
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
- c.s << std::string(level, ' ') << class_name()
- << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
- << std::endl;
- unsigned delta_indent = static_cast<const print_tree &>(c).delta_indent;
- unsigned num = seq.size();
- for (unsigned i=0; i<num; ++i) {
- seq[i].rest.print(c, level + delta_indent);
- seq[i].coeff.print(c, level + delta_indent);
- c.s << std::string(level + delta_indent, ' ') << "-----" << std::endl;
- }
- var.print(c, level + delta_indent);
- point.print(c, level + delta_indent);
+ // print a sign, if needed
+ if (i != seq.begin())
+ c.s << '+';
- } else {
+ if (!is_order_function(i->rest)) {
- if (precedence() <= level)
- c.s << "(";
-
- std::string par_open = is_a<print_latex>(c) ? "{(" : "(";
- std::string par_close = is_a<print_latex>(c) ? ")}" : ")";
-
- // objects of type pseries must not have any zero entries, so the
- // trivial (zero) pseries needs a special treatment here:
- if (seq.empty())
- c.s << '0';
- epvector::const_iterator i = seq.begin(), end = seq.end();
- while (i != end) {
- // print a sign, if needed
- if (i != seq.begin())
- c.s << '+';
- if (!is_order_function(i->rest)) {
- // print 'rest', i.e. the expansion coefficient
- if (i->rest.info(info_flags::numeric) &&
- i->rest.info(info_flags::positive)) {
- i->rest.print(c);
- } else {
- c.s << par_open;
- i->rest.print(c);
- c.s << par_close;
- }
- // print 'coeff', something like (x-1)^42
- if (!i->coeff.is_zero()) {
- if (is_a<print_latex>(c))
- c.s << ' ';
- else
- c.s << '*';
- if (!point.is_zero()) {
- c.s << par_open;
- (var-point).print(c);
- c.s << par_close;
+ // print 'rest', i.e. the expansion coefficient
+ if (i->rest.info(info_flags::numeric) &&
+ i->rest.info(info_flags::positive)) {
+ i->rest.print(c);
+ } else {
+ c.s << openbrace << '(';
+ i->rest.print(c);
+ c.s << ')' << closebrace;
+ }
+
+ // print 'coeff', something like (x-1)^42
+ if (!i->coeff.is_zero()) {
+ c.s << mul_sym;
+ if (!point.is_zero()) {
+ c.s << openbrace << '(';
+ (var-point).print(c);
+ c.s << ')' << closebrace;
+ } else
+ var.print(c);
+ if (i->coeff.compare(_ex1)) {
+ c.s << pow_sym;
+ c.s << openbrace;
+ if (i->coeff.info(info_flags::negative)) {
+ c.s << '(';
+ i->coeff.print(c);
+ c.s << ')';
} else
- var.print(c);
- if (i->coeff.compare(_ex1())) {
- c.s << '^';
- if (i->coeff.info(info_flags::negative)) {
- c.s << par_open;
- i->coeff.print(c);
- c.s << par_close;
- } else {
- if (is_a<print_latex>(c)) {
- c.s << '{';
- i->coeff.print(c);
- c.s << '}';
- } else
- i->coeff.print(c);
- }
- }
+ i->coeff.print(c);
+ c.s << closebrace;
}
- } else
- Order(power(var-point,i->coeff)).print(c);
- ++i;
- }
+ }
+ } else
+ Order(power(var-point,i->coeff)).print(c);
+ ++i;
+ }
+
+ if (precedence() <= level)
+ c.s << ')';
+}
+
+void pseries::do_print(const print_context & c, unsigned level) const
+{
+ print_series(c, "", "", "*", "^", level);
+}
- if (precedence() <= level)
- c.s << ")";
+void pseries::do_print_latex(const print_latex & c, unsigned level) const
+{
+ print_series(c, "{", "}", " ", "^", level);
+}
+
+void pseries::do_print_python(const print_python & c, unsigned level) const
+{
+ print_series(c, "", "", "*", "**", level);
+}
+
+void pseries::do_print_tree(const print_tree & c, unsigned level) const
+{
+ c.s << std::string(level, ' ') << class_name() << " @" << this
+ << std::hex << ", hash=0x" << hashvalue << ", flags=0x" << flags << std::dec
+ << std::endl;
+ size_t num = seq.size();
+ for (size_t i=0; i<num; ++i) {
+ seq[i].rest.print(c, level + c.delta_indent);
+ seq[i].coeff.print(c, level + c.delta_indent);
+ c.s << std::string(level + c.delta_indent, ' ') << "-----" << std::endl;
}
+ var.print(c, level + c.delta_indent);
+ point.print(c, level + c.delta_indent);
+}
+
+void pseries::do_print_python_repr(const print_python_repr & c, unsigned level) const
+{
+ c.s << class_name() << "(relational(";
+ var.print(c);
+ c.s << ',';
+ point.print(c);
+ c.s << "),[";
+ size_t num = seq.size();
+ for (size_t 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 << "])";
}
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...
}
/** Return the number of operands including a possible order term. */
-unsigned pseries::nops(void) const
+size_t pseries::nops() const
{
return seq.size();
}
/** Return the ith term in the series when represented as a sum. */
-ex pseries::op(int i) const
+ex pseries::op(size_t i) const
{
- if (i < 0 || unsigned(i) >= seq.size())
+ if (i >= seq.size())
throw (std::out_of_range("op() out of range"));
- return seq[i].rest * power(var - point, seq[i].coeff);
-}
-ex &pseries::let_op(int i)
-{
- throw (std::logic_error("let_op not defined for pseries"));
+ return seq[i].rest * power(var - point, seq[i].coeff);
}
/** Return degree of highest power of the series. This is usually the exponent
{
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);
}
return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
-ex pseries::subs(const lst & ls, const lst & lr, bool no_pattern) const
+ex pseries::conjugate() const
+{
+ epvector * newseq = conjugateepvector(seq);
+ ex newvar = var.conjugate();
+ ex newpoint = point.conjugate();
+
+ if (!newseq && are_ex_trivially_equal(newvar, var) && are_ex_trivially_equal(point, newpoint)) {
+ return *this;
+ }
+
+ ex result = (new pseries(newvar==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated);
+ if (newseq) {
+ delete newseq;
+ }
+ return result;
+}
+
+ex pseries::subs(const exmap & m, unsigned options) const
{
// If expansion variable is being substituted, convert the series to a
// polynomial and do the substitution there because the result might
// no longer be a power series
- if (ls.has(var))
- return convert_to_poly(true).subs(ls, lr, no_pattern);
+ if (m.find(var) != m.end())
+ return convert_to_poly(true).subs(m, options);
// Otherwise construct a new series with substituted coefficients and
// expansion point
newseq.reserve(seq.size());
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- newseq.push_back(expair(it->rest.subs(ls, lr, no_pattern), it->coeff));
+ newseq.push_back(expair(it->rest.subs(m, options), it->coeff));
++it;
}
- return (new pseries(relational(var,point.subs(ls, lr, no_pattern)), newseq))->setflag(status_flags::dynallocated);
+ return (new pseries(relational(var,point.subs(m, options)), newseq))->setflag(status_flags::dynallocated);
}
/** Implementation of ex::expand() for a power series. It expands all the
->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
return e;
}
-bool pseries::is_terminating(void) const
+bool pseries::is_terminating() const
{
return seq.empty() || !is_order_function((seq.end()-1)->rest);
}
ex basic::series(const relational & r, int order, unsigned options) const
{
epvector seq;
- 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()));
-
+
+ // default for order-values that make no sense for Taylor expansion
+ if ((order <= 0) && this->has(s)) {
+ seq.push_back(expair(Order(_ex1), order));
+ return pseries(r, seq);
+ }
+
+ // do Taylor expansion
+ numeric fac = 1;
+ ex deriv = *this;
+ ex coeff = deriv.subs(r, subs_options::no_pattern);
+
+ if (!coeff.is_zero()) {
+ seq.push_back(expair(coeff, _ex0));
+ }
+
int n;
for (n=1; n<order; ++n) {
- fac = fac.mul(numeric(n));
+ fac = fac.mul(n);
+ // We need to test for zero in order to see if the series terminates.
+ // The problem is that there is no such thing as a perfect test for
+ // zero. Expanding the term occasionally helps a little...
deriv = deriv.diff(s).expand();
- if (deriv.is_zero()) {
- // Series terminates
+ if (deriv.is_zero()) // Series terminates
return pseries(r, seq);
- }
- coeff = deriv.subs(r);
+
+ coeff = deriv.subs(r, subs_options::no_pattern);
if (!coeff.is_zero())
- seq.push_back(expair(fac.inverse() * coeff, numeric(n)));
+ seq.push_back(expair(fac.inverse() * coeff, n));
}
// Higher-order terms, if present
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
- seq.push_back(expair(Order(_ex1()), numeric(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);
}
{
pseries acc; // Series accumulator
- // Multiply with remaining terms
+ GINAC_ASSERT(is_a<symbol>(r.lhs()));
+ const ex& sym = r.lhs();
+
+ // holds ldegrees of the series of individual factors
+ std::vector<int> ldegrees;
+
+ // find minimal degrees
const epvector::const_iterator itbeg = seq.begin();
const epvector::const_iterator itend = seq.end();
for (epvector::const_iterator it=itbeg; it!=itend; ++it) {
- ex op = recombine_pair_to_ex(*it).series(r, order, options);
+
+ ex expon = it->coeff;
+ int factor = 1;
+ ex buf;
+ if (expon.info(info_flags::integer)) {
+ buf = it->rest;
+ factor = ex_to<numeric>(expon).to_int();
+ } else {
+ buf = recombine_pair_to_ex(*it);
+ }
+
+ int real_ldegree = 0;
+ try {
+ real_ldegree = buf.expand().ldegree(sym-r.rhs());
+ } catch (std::runtime_error) {}
+
+ if (real_ldegree == 0) {
+ int orderloop = 0;
+ do {
+ orderloop++;
+ real_ldegree = buf.series(r, orderloop, options).ldegree(sym);
+ } while (real_ldegree == orderloop);
+ }
+
+ ldegrees.push_back(factor * real_ldegree);
+ }
+
+ int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0);
+
+ if (degsum >= order) {
+ epvector epv;
+ epv.push_back(expair(Order(_ex1), order));
+ return (new pseries(r, epv))->setflag(status_flags::dynallocated);
+ }
+
+ // Multiply with remaining terms
+ std::vector<int>::const_iterator itd = ldegrees.begin();
+ for (epvector::const_iterator it=itbeg; it!=itend; ++it, ++itd) {
+
+ // do series expansion with adjusted order
+ ex op = recombine_pair_to_ex(*it).series(r, order-degsum+(*itd), options);
// Series multiplication
- if (it==itbeg)
+ if (it == itbeg)
acc = ex_to<pseries>(op);
else
acc = ex_to<pseries>(acc.mul_series(ex_to<pseries>(op)));
}
+
return acc.mul_const(ex_to<numeric>(overall_coeff));
}
if (!(p*ldeg).is_integer())
throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series");
+ // adjust number of coefficients
+ deg = deg - (p*ldeg).to_int();
+
// O(x^n)^(-m) is undefined
if (seq.size() == 1 && is_order_function(seq[0].rest) && p.real().is_negative())
throw pole_error("pseries::power_const(): division by zero",1);
exvector co;
co.reserve(deg);
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 (!sum.is_zero())
- all_sums_zero = false;
co.push_back(sum / coeff(var, ldeg) / i);
}
break;
}
}
- if (!higher_order && !all_sums_zero)
- new_seq.push_back(expair(Order(_ex1()), p * ldeg + deg));
+ if (!higher_order)
+ 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?
bool must_expand_basis = false;
try {
- basis.subs(r);
+ basis.subs(r, subs_options::no_pattern);
} catch (pole_error) {
must_expand_basis = true;
}
-
+
// Is the expression of type something^(-int)?
- if (!must_expand_basis && !exponent.info(info_flags::negint))
+ if (!must_expand_basis && !exponent.info(info_flags::negint) && !is_a<add>(basis))
return basic::series(r, order, options);
-
+
// Is the expression of type 0^something?
- if (!must_expand_basis && !basis.subs(r).is_zero())
+ if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero() && !is_a<add>(basis))
return basic::series(r, order, options);
// Singularity encountered, is the basis equal to (var - point)?
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);
}
// No, expand basis into series
- ex e = basis.series(r, order, options);
- return ex_to<pseries>(e).power_const(ex_to<numeric>(exponent), order);
+
+ numeric numexp;
+ if (is_a<numeric>(exponent)) {
+ numexp = ex_to<numeric>(exponent);
+ } else {
+ numexp = 0;
+ }
+ const ex& sym = r.lhs();
+ // find existing minimal degree
+ int real_ldegree = basis.expand().ldegree(sym-r.rhs());
+ if (real_ldegree == 0) {
+ int orderloop = 0;
+ do {
+ orderloop++;
+ real_ldegree = basis.series(r, orderloop, options).ldegree(sym);
+ } while (real_ldegree == orderloop);
+ }
+
+ if (!(real_ldegree*numexp).is_integer())
+ throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series");
+ ex e = basis.series(r, (order + real_ldegree*(1-numexp)).to_int(), options);
+
+ ex result;
+ try {
+ result = ex_to<pseries>(e).power_const(numexp, order);
+ } catch (pole_error) {
+ epvector ser;
+ ser.push_back(expair(Order(_ex1), order));
+ result = pseries(r, ser);
+ }
+
+ return result;
}
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);
* @return an expression holding a pseries object */
ex ex::series(const ex & r, int order, unsigned options) const
{
- GINAC_ASSERT(bp!=0);
ex e;
relational rel_;
- if (is_ex_exactly_of_type(r,relational))
+ if (is_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