* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2000 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 <iostream>
#include <stdexcept>
#include "pseries.h"
#include "add.h"
-#include "inifcns.h"
+#include "inifcns.h" // for Order function
#include "lst.h"
#include "mul.h"
#include "power.h"
#include "relational.h"
+#include "operators.h"
#include "symbol.h"
#include "archive.h"
#include "utils.h"
-#include "debugmsg.h"
-#ifndef NO_NAMESPACE_GINAC
namespace GiNaC {
-#endif // ndef NO_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 constructor, destructor, copy constructor, assignment operator and helpers
+ * Default constructor
*/
-pseries::pseries() : basic(TINFO_pseries)
-{
- debugmsg("pseries default constructor", LOGLEVEL_CONSTRUCT);
-}
-
-pseries::~pseries()
-{
- debugmsg("pseries destructor", LOGLEVEL_DESTRUCT);
- destroy(false);
-}
-
-pseries::pseries(const pseries &other)
-{
- debugmsg("pseries copy constructor", LOGLEVEL_CONSTRUCT);
- copy(other);
-}
-
-const pseries &pseries::operator=(const pseries & other)
-{
- debugmsg("pseries operator=", LOGLEVEL_ASSIGNMENT);
- if (this != &other) {
- destroy(true);
- copy(other);
- }
- return *this;
-}
-
-void pseries::copy(const pseries &other)
-{
- inherited::copy(other);
- seq = other.seq;
- var = other.var;
- point = other.point;
-}
-
-void pseries::destroy(bool call_parent)
-{
- if (call_parent)
- inherited::destroy(call_parent);
-}
+pseries::pseries() : inherited(TINFO_pseries) { }
/*
- * Other constructors
+ * Other ctors
*/
/** 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)
* @param ops_ vector of {coefficient, power} pairs (coefficient must not be zero)
* @return newly constructed pseries */
-pseries::pseries(const ex &rel_, const epvector &ops_)
- : basic(TINFO_pseries), seq(ops_)
+pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_)
{
- debugmsg("pseries constructor from ex,epvector", LOGLEVEL_CONSTRUCT);
- GINAC_ASSERT(is_ex_exactly_of_type(rel_, relational));
- GINAC_ASSERT(is_ex_exactly_of_type(rel_.lhs(),symbol));
- point = rel_.rhs();
- var = *static_cast<symbol *>(rel_.lhs().bp);
+ GINAC_ASSERT(is_a<relational>(rel_));
+ GINAC_ASSERT(is_a<symbol>(rel_.lhs()));
+ point = rel_.rhs();
+ var = rel_.lhs();
}
* Archiving
*/
-/** Construct object from archive_node. */
-pseries::pseries(const archive_node &n, const lst &sym_lst) : inherited(n, sym_lst)
-{
- debugmsg("pseries constructor from archive_node", LOGLEVEL_CONSTRUCT);
- for (unsigned int i=0; true; ++i) {
- ex rest;
- ex coeff;
- if (n.find_ex("coeff", rest, sym_lst, i) && n.find_ex("power", coeff, sym_lst, i))
- seq.push_back(expair(rest, coeff));
- else
- break;
- }
- n.find_ex("var", var, sym_lst);
- n.find_ex("point", point, sym_lst);
-}
-
-/** Unarchive the object. */
-ex pseries::unarchive(const archive_node &n, const lst &sym_lst)
+pseries::pseries(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
{
- return (new pseries(n, sym_lst))->setflag(status_flags::dynallocated);
+ for (unsigned int i=0; true; ++i) {
+ ex rest;
+ ex coeff;
+ if (n.find_ex("coeff", rest, sym_lst, i) && n.find_ex("power", coeff, sym_lst, i))
+ seq.push_back(expair(rest, coeff));
+ else
+ break;
+ }
+ n.find_ex("var", var, sym_lst);
+ n.find_ex("point", point, sym_lst);
}
-/** Archive the object. */
void pseries::archive(archive_node &n) const
{
- inherited::archive(n);
- epvector::const_iterator i = seq.begin(), iend = seq.end();
- while (i != iend) {
- n.add_ex("coeff", i->rest);
- n.add_ex("power", i->coeff);
- ++i;
- }
- n.add_ex("var", var);
- n.add_ex("point", point);
+ inherited::archive(n);
+ epvector::const_iterator i = seq.begin(), iend = seq.end();
+ while (i != iend) {
+ n.add_ex("coeff", i->rest);
+ n.add_ex("power", i->coeff);
+ ++i;
+ }
+ n.add_ex("var", var);
+ n.add_ex("point", point);
}
+DEFAULT_UNARCHIVE(pseries)
+
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
-basic *pseries::duplicate() const
-{
- debugmsg("pseries duplicate", LOGLEVEL_DUPLICATE);
- return new pseries(*this);
-}
-
-void pseries::print(std::ostream &os, unsigned upper_precedence) const
-{
- debugmsg("pseries print", LOGLEVEL_PRINT);
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
- // omit zero terms
- if (i->rest.is_zero())
- continue;
- // print a sign, if needed
- if (i!=seq.begin())
- os << '+';
- 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)) {
- os << i->rest;
- } else
- os << "(" << i->rest << ')';
- // print 'coeff', something like (x-1)^42
- if (!i->coeff.is_zero()) {
- os << '*';
- if (!point.is_zero())
- os << '(' << var-point << ')';
- else
- os << var;
- if (i->coeff.compare(_ex1())) {
- os << '^';
- if (i->coeff.info(info_flags::negative))
- os << '(' << i->coeff << ')';
- else
- os << i->coeff;
- }
- }
- } else {
- os << Order(power(var-point,i->coeff));
- }
- }
-}
-
-
-void pseries::printraw(std::ostream &os) const
-{
- debugmsg("pseries printraw", LOGLEVEL_PRINT);
- os << "pseries(" << var << ";" << point << ";";
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
- os << "(" << (*i).rest << "," << (*i).coeff << "),";
- }
- os << ")";
-}
-
-
-void pseries::printtree(std::ostream & os, unsigned indent) const
-{
- debugmsg("pseries printtree",LOGLEVEL_PRINT);
- os << std::string(indent,' ') << "pseries "
- << ", hash=" << hashvalue
- << " (0x" << std::hex << hashvalue << std::dec << ")"
- << ", flags=" << flags << std::endl;
- for (unsigned i=0; i<seq.size(); ++i) {
- seq[i].rest.printtree(os,indent+delta_indent);
- seq[i].coeff.printtree(os,indent+delta_indent);
- if (i!=seq.size()-1)
- os << std::string(indent+delta_indent,' ') << "-----" << std::endl;
- }
- var.printtree(os, indent+delta_indent);
- point.printtree(os, indent+delta_indent);
+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
+{
+ 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';
+
+ 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 << 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
+ i->coeff.print(c);
+ c.s << closebrace;
+ }
+ }
+ } 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);
+}
+
+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_a<pseries>(other));
+ const pseries &o = static_cast<const pseries &>(other);
+
+ // first compare the lengths of the series...
+ if (seq.size()>o.seq.size())
+ return 1;
+ if (seq.size()<o.seq.size())
+ return -1;
+
+ // ...then the expansion point...
+ int cmpval = var.compare(o.var);
+ if (cmpval)
+ return cmpval;
+ cmpval = point.compare(o.point);
+ if (cmpval)
+ return cmpval;
+
+ // ...and if that failed the individual elements
+ epvector::const_iterator it = seq.begin(), o_it = o.seq.begin();
+ while (it!=seq.end() && o_it!=o.seq.end()) {
+ cmpval = it->compare(*o_it);
+ if (cmpval)
+ return cmpval;
+ ++it;
+ ++o_it;
+ }
+
+ // so they are equal.
+ return 0;
}
/** Return the number of operands including a possible order term. */
-unsigned pseries::nops(void) const
+size_t pseries::nops() const
{
- return seq.size();
+ 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())
- throw (std::out_of_range("op() out of range"));
- return seq[i].rest * power(var - point, seq[i].coeff);
-}
+ if (i >= seq.size())
+ throw (std::out_of_range("op() out of range"));
-
-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
* of the Order term. If s is not the expansion variable of the series, the
* series is examined termwise. */
-int pseries::degree(const symbol &s) const
-{
- if (var.is_equal(s)) {
- // Return last exponent
- if (seq.size())
- return ex_to_numeric((*(seq.end() - 1)).coeff).to_int();
- else
- return 0;
- } else {
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- if (it == itend)
- return 0;
- int max_pow = INT_MIN;
- while (it != itend) {
- int pow = it->rest.degree(s);
- if (pow > max_pow)
- max_pow = pow;
- ++it;
- }
- return max_pow;
- }
+int pseries::degree(const ex &s) const
+{
+ if (var.is_equal(s)) {
+ // Return last exponent
+ if (seq.size())
+ return ex_to<numeric>((seq.end()-1)->coeff).to_int();
+ else
+ return 0;
+ } else {
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ if (it == itend)
+ return 0;
+ int max_pow = INT_MIN;
+ while (it != itend) {
+ int pow = it->rest.degree(s);
+ if (pow > max_pow)
+ max_pow = pow;
+ ++it;
+ }
+ return max_pow;
+ }
}
/** Return degree of lowest power of the series. This is usually the exponent
* series is examined termwise. If s is the expansion variable but the
* expansion point is not zero the series is not expanded to find the degree.
* I.e.: (1-x) + (1-x)^2 + Order((1-x)^3) has ldegree(x) 1, not 0. */
-int pseries::ldegree(const symbol &s) const
-{
- if (var.is_equal(s)) {
- // Return first exponent
- if (seq.size())
- return ex_to_numeric((*(seq.begin())).coeff).to_int();
- else
- return 0;
- } else {
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- if (it == itend)
- return 0;
- int min_pow = INT_MAX;
- while (it != itend) {
- int pow = it->rest.ldegree(s);
- if (pow < min_pow)
- min_pow = pow;
- ++it;
- }
- return min_pow;
- }
-}
-
-ex pseries::coeff(const symbol &s, int n) const
-{
- if (var.is_equal(s)) {
- if (seq.size() == 0)
- return _ex0();
-
- // Binary search in sequence for given power
- numeric looking_for = numeric(n);
- int lo = 0, hi = seq.size() - 1;
- while (lo <= hi) {
- int mid = (lo + hi) / 2;
- GINAC_ASSERT(is_ex_exactly_of_type(seq[mid].coeff, numeric));
- int cmp = ex_to_numeric(seq[mid].coeff).compare(looking_for);
- switch (cmp) {
- case -1:
- lo = mid + 1;
- break;
- case 0:
- return seq[mid].rest;
- case 1:
- hi = mid - 1;
- break;
- default:
- throw(std::logic_error("pseries::coeff: compare() didn't return -1, 0 or 1"));
- }
- }
- return _ex0();
- } else
- return convert_to_poly().coeff(s, n);
-}
-
-
-ex pseries::collect(const symbol &s) const
-{
- return *this;
-}
-
-
-/** Evaluate coefficients. */
+int pseries::ldegree(const ex &s) const
+{
+ if (var.is_equal(s)) {
+ // Return first exponent
+ if (seq.size())
+ return ex_to<numeric>((seq.begin())->coeff).to_int();
+ else
+ return 0;
+ } else {
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ if (it == itend)
+ return 0;
+ int min_pow = INT_MAX;
+ while (it != itend) {
+ int pow = it->rest.ldegree(s);
+ if (pow < min_pow)
+ min_pow = pow;
+ ++it;
+ }
+ return min_pow;
+ }
+}
+
+/** Return coefficient of degree n in power series if s is the expansion
+ * variable. If the expansion point is nonzero, by definition the n=1
+ * coefficient in s of a+b*(s-z)+c*(s-z)^2+Order((s-z)^3) is b (assuming
+ * the expansion took place in the s in the first place).
+ * If s is not the expansion variable, an attempt is made to convert the
+ * series to a polynomial and return the corresponding coefficient from
+ * there. */
+ex pseries::coeff(const ex &s, int n) const
+{
+ if (var.is_equal(s)) {
+ if (seq.empty())
+ return _ex0;
+
+ // Binary search in sequence for given power
+ numeric looking_for = numeric(n);
+ int lo = 0, hi = seq.size() - 1;
+ while (lo <= hi) {
+ int mid = (lo + hi) / 2;
+ GINAC_ASSERT(is_exactly_a<numeric>(seq[mid].coeff));
+ int cmp = ex_to<numeric>(seq[mid].coeff).compare(looking_for);
+ switch (cmp) {
+ case -1:
+ lo = mid + 1;
+ break;
+ case 0:
+ return seq[mid].rest;
+ case 1:
+ hi = mid - 1;
+ break;
+ default:
+ throw(std::logic_error("pseries::coeff: compare() didn't return -1, 0 or 1"));
+ }
+ }
+ return _ex0;
+ } else
+ return convert_to_poly().coeff(s, n);
+}
+
+/** Does nothing. */
+ex pseries::collect(const ex &s, bool distributed) const
+{
+ return *this;
+}
+
+/** Perform coefficient-wise automatic term rewriting rules in this class. */
ex pseries::eval(int level) const
{
- if (level == 1)
- return this->hold();
-
- if (level == -max_recursion_level)
- throw (std::runtime_error("pseries::eval(): recursion limit exceeded"));
-
- // Construct a new series with evaluated coefficients
- epvector new_seq;
- new_seq.reserve(seq.size());
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- new_seq.push_back(expair(it->rest.eval(level-1), it->coeff));
- ++it;
- }
- return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
+ if (level == 1)
+ return this->hold();
+
+ if (level == -max_recursion_level)
+ throw (std::runtime_error("pseries::eval(): recursion limit exceeded"));
+
+ // Construct a new series with evaluated coefficients
+ epvector new_seq;
+ new_seq.reserve(seq.size());
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ new_seq.push_back(expair(it->rest.eval(level-1), it->coeff));
+ ++it;
+ }
+ return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
-
/** Evaluate coefficients numerically. */
ex pseries::evalf(int level) const
{
- if (level == 1)
- return *this;
-
- if (level == -max_recursion_level)
- throw (std::runtime_error("pseries::evalf(): recursion limit exceeded"));
-
- // Construct a new series with evaluated coefficients
- epvector new_seq;
- new_seq.reserve(seq.size());
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- new_seq.push_back(expair(it->rest.evalf(level-1), it->coeff));
- ++it;
- }
- return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
-}
-
-
-ex pseries::subs(const lst & ls, const lst & lr) 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);
-
- // Otherwise construct a new series with substituted coefficients and
- // expansion point
- epvector newseq;
- 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), it->coeff));
- ++it;
- }
- return (new pseries(relational(var,point.subs(ls, lr)), newseq))->setflag(status_flags::dynallocated);
+ if (level == 1)
+ return *this;
+
+ if (level == -max_recursion_level)
+ throw (std::runtime_error("pseries::evalf(): recursion limit exceeded"));
+
+ // Construct a new series with evaluated coefficients
+ epvector new_seq;
+ new_seq.reserve(seq.size());
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ new_seq.push_back(expair(it->rest.evalf(level-1), it->coeff));
+ ++it;
+ }
+ return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
+}
+
+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 (m.find(var) != m.end())
+ return convert_to_poly(true).subs(m, options);
+
+ // Otherwise construct a new series with substituted coefficients and
+ // expansion point
+ epvector newseq;
+ newseq.reserve(seq.size());
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ newseq.push_back(expair(it->rest.subs(m, options), it->coeff));
+ ++it;
+ }
+ 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
- * terms individually and returns the resulting series as a new pseries.
- * @see ex::diff */
+ * terms individually and returns the resulting series as a new pseries. */
ex pseries::expand(unsigned options) const
{
- epvector newseq;
- newseq.reserve(seq.size());
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
- newseq.push_back(expair(i->rest.expand(), i->coeff));
- return (new pseries(relational(var,point), newseq))
- ->setflag(status_flags::dynallocated |
- status_flags::expanded);
+ epvector newseq;
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
+ ex restexp = i->rest.expand();
+ if (!restexp.is_zero())
+ newseq.push_back(expair(restexp, i->coeff));
+ ++i;
+ }
+ return (new pseries(relational(var,point), newseq))
+ ->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
{
- if (s == var) {
- epvector new_seq;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
-
- // FIXME: coeff might depend on var
- while (it != itend) {
- if (is_order_function(it->rest)) {
- new_seq.push_back(expair(it->rest, it->coeff - 1));
- } else {
- ex c = it->rest * it->coeff;
- if (!c.is_zero())
- new_seq.push_back(expair(c, it->coeff - 1));
- }
- ++it;
- }
- return pseries(relational(var,point), new_seq);
- } else {
- return *this;
- }
+ epvector new_seq;
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+
+ if (s == var) {
+
+ // FIXME: coeff might depend on var
+ while (it != itend) {
+ if (is_order_function(it->rest)) {
+ new_seq.push_back(expair(it->rest, it->coeff - 1));
+ } else {
+ ex c = it->rest * it->coeff;
+ if (!c.is_zero())
+ new_seq.push_back(expair(c, it->coeff - 1));
+ }
+ ++it;
+ }
+
+ } else {
+
+ 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);
}
-
-/*
- * Construct ordinary polynomial out of series
- */
-
-/** Convert a pseries object to an ordinary polynomial.
- *
- * @param no_order flag: discard higher order terms */
ex pseries::convert_to_poly(bool no_order) const
{
- ex e;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
-
- while (it != itend) {
- if (is_order_function(it->rest)) {
- if (!no_order)
- e += Order(power(var - point, it->coeff));
- } else
- e += it->rest * power(var - point, it->coeff);
- ++it;
- }
- return e;
+ ex e;
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+
+ while (it != itend) {
+ if (is_order_function(it->rest)) {
+ if (!no_order)
+ e += Order(power(var - point, it->coeff));
+ } else
+ e += it->rest * power(var - point, it->coeff);
+ ++it;
+ }
+ return e;
}
-/** Returns true if there is no order term, i.e. the series terminates and
- * false otherwise. */
-bool pseries::is_terminating(void) const
+bool pseries::is_terminating() const
{
- return !is_order_function((seq.end()-1)->rest);
+ return seq.empty() || !is_order_function((seq.end()-1)->rest);
}
/*
- * Implementation of series expansion
+ * Implementations of series expansion
*/
/** Default implementation of ex::series(). This performs Taylor expansion.
* @see ex::series */
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 = static_cast<symbol *>(r.lhs().bp);
-
- if (!coeff.is_zero())
- seq.push_back(expair(coeff, numeric(0)));
-
- int n;
- for (n=1; n<order; ++n) {
- fac = fac.mul(numeric(n));
- deriv = deriv.diff(*s).expand();
- if (deriv.is_zero()) {
- // Series terminates
- return pseries(r, seq);
- }
- coeff = deriv.subs(r);
- if (!coeff.is_zero())
- seq.push_back(expair(fac.inverse() * coeff, numeric(n)));
- }
-
- // Higher-order terms, if present
- deriv = deriv.diff(*s);
- if (!deriv.expand().is_zero())
- seq.push_back(expair(Order(_ex1()), numeric(n)));
- return pseries(r, seq);
+ epvector seq;
+ numeric fac = 1;
+ ex deriv = *this;
+ ex coeff = deriv.subs(r, subs_options::no_pattern);
+ const symbol &s = ex_to<symbol>(r.lhs());
+
+ if (!coeff.is_zero())
+ seq.push_back(expair(coeff, _ex0));
+
+ int n;
+ for (n=1; n<order; ++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
+ return pseries(r, seq);
+
+ coeff = deriv.subs(r, subs_options::no_pattern);
+ if (!coeff.is_zero())
+ 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), n));
+ return pseries(r, seq);
}
* @see ex::series */
ex symbol::series(const relational & r, int order, unsigned options) const
{
- epvector seq;
- const ex point = r.rhs();
- GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
-
- if (this->is_equal(*s)) {
- if (order > 0 && !point.is_zero())
- seq.push_back(expair(point, _ex0()));
- if (order > 1)
- seq.push_back(expair(_ex1(), _ex1()));
- else
- seq.push_back(expair(Order(_ex1()), numeric(order)));
- } else
- seq.push_back(expair(*this, _ex0()));
- return pseries(r, seq);
+ epvector seq;
+ const ex point = r.rhs();
+ 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));
+ if (order > 1)
+ seq.push_back(expair(_ex1, _ex1));
+ else
+ seq.push_back(expair(Order(_ex1), numeric(order)));
+ } else
+ seq.push_back(expair(*this, _ex0));
+ return pseries(r, seq);
}
* @return the sum as a pseries */
ex pseries::add_series(const pseries &other) const
{
- // Adding two series with different variables or expansion points
- // results in an empty (constant) series
- if (!is_compatible_to(other)) {
- epvector nul;
- nul.push_back(expair(Order(_ex1()), _ex0()));
- return pseries(relational(var,point), nul);
- }
-
- // Series addition
- epvector new_seq;
- epvector::const_iterator a = seq.begin();
- epvector::const_iterator b = other.seq.begin();
- epvector::const_iterator a_end = seq.end();
- epvector::const_iterator b_end = other.seq.end();
- int pow_a = INT_MAX, pow_b = INT_MAX;
- for (;;) {
- // If a is empty, fill up with elements from b and stop
- if (a == a_end) {
- while (b != b_end) {
- new_seq.push_back(*b);
- ++b;
- }
- 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) {
- new_seq.push_back(*a);
- ++a;
- }
- 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
- new_seq.push_back(*a);
- if (is_order_function((*a).rest))
- break;
- ++a;
- } else if (pow_b < pow_a) {
- // b has lesser power, get coefficient from b
- new_seq.push_back(*b);
- if (is_order_function((*b).rest))
- break;
- ++b;
- } 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));
- break; // Order term ends the sequence
- } else {
- ex sum = (*a).rest + (*b).rest;
- if (!(sum.is_zero()))
- new_seq.push_back(expair(sum, numeric(pow_a)));
- ++a;
- ++b;
- }
- }
- }
- return pseries(relational(var,point), new_seq);
+ // Adding two series with different variables or expansion points
+ // results in an empty (constant) series
+ if (!is_compatible_to(other)) {
+ epvector nul;
+ nul.push_back(expair(Order(_ex1), _ex0));
+ return pseries(relational(var,point), nul);
+ }
+
+ // Series addition
+ epvector new_seq;
+ epvector::const_iterator a = seq.begin();
+ epvector::const_iterator b = other.seq.begin();
+ epvector::const_iterator a_end = seq.end();
+ epvector::const_iterator b_end = other.seq.end();
+ int pow_a = INT_MAX, pow_b = INT_MAX;
+ for (;;) {
+ // If a is empty, fill up with elements from b and stop
+ if (a == a_end) {
+ while (b != b_end) {
+ new_seq.push_back(*b);
+ ++b;
+ }
+ 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) {
+ new_seq.push_back(*a);
+ ++a;
+ }
+ 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
+ new_seq.push_back(*a);
+ if (is_order_function((*a).rest))
+ break;
+ ++a;
+ } else if (pow_b < pow_a) {
+ // b has lesser power, get coefficient from b
+ new_seq.push_back(*b);
+ if (is_order_function((*b).rest))
+ break;
+ ++b;
+ } 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));
+ break; // Order term ends the sequence
+ } else {
+ ex sum = (*a).rest + (*b).rest;
+ if (!(sum.is_zero()))
+ new_seq.push_back(expair(sum, numeric(pow_a)));
+ ++a;
+ ++b;
+ }
+ }
+ }
+ return pseries(relational(var,point), new_seq);
}
* @see ex::series */
ex add::series(const relational & r, int order, unsigned options) const
{
- ex acc; // Series accumulator
-
- // Get first term from overall_coeff
- acc = overall_coeff.series(r, order, options);
-
- // Add remaining terms
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- for (; it!=itend; ++it) {
- ex op;
- if (is_ex_exactly_of_type(it->rest, pseries))
- op = it->rest;
- else
- op = it->rest.series(r, order, options);
- if (!it->coeff.is_equal(_ex1()))
- op = ex_to_pseries(op).mul_const(ex_to_numeric(it->coeff));
-
- // Series addition
- acc = ex_to_pseries(acc).add_series(ex_to_pseries(op));
- }
- return acc;
+ ex acc; // Series accumulator
+
+ // Get first term from overall_coeff
+ acc = overall_coeff.series(r, order, options);
+
+ // Add remaining terms
+ epvector::const_iterator it = seq.begin();
+ epvector::const_iterator itend = seq.end();
+ for (; it!=itend; ++it) {
+ ex op;
+ if (is_exactly_a<pseries>(it->rest))
+ op = it->rest;
+ else
+ op = it->rest.series(r, order, options);
+ if (!it->coeff.is_equal(_ex1))
+ op = ex_to<pseries>(op).mul_const(ex_to<numeric>(it->coeff));
+
+ // Series addition
+ acc = ex_to<pseries>(acc).add_series(ex_to<pseries>(op));
+ }
+ return acc;
}
* @return the product as a pseries */
ex pseries::mul_const(const numeric &other) const
{
- 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))
- new_seq.push_back(expair(it->rest * other, it->coeff));
- else
- new_seq.push_back(*it);
- ++it;
- }
- return pseries(relational(var,point), new_seq);
+ 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))
+ new_seq.push_back(expair(it->rest * other, it->coeff));
+ else
+ new_seq.push_back(*it);
+ ++it;
+ }
+ return pseries(relational(var,point), new_seq);
}
* @return the product as a pseries */
ex pseries::mul_series(const pseries &other) const
{
- // Multiplying two series with different variables or expansion points
- // results in an empty (constant) series
- if (!is_compatible_to(other)) {
- epvector nul;
- nul.push_back(expair(Order(_ex1()), _ex0()));
- return pseries(relational(var,point), nul);
- }
-
- // 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 a_min = ldegree(*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)))
- higher_order_a = a_max + b_min;
- if (is_order_function(other.coeff(*s, b_max)))
- higher_order_b = b_max + a_min;
- int higher_order_c = std::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 = _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(*s, i);
- ex b_coeff = other.coeff(*s, cdeg-i);
- if (!is_order_function(a_coeff) && !is_order_function(b_coeff))
- co += a_coeff * b_coeff;
- }
- if (!co.is_zero())
- 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)));
- return pseries(relational(var,point), new_seq);
+ // Multiplying two series with different variables or expansion points
+ // results in an empty (constant) series
+ if (!is_compatible_to(other)) {
+ epvector nul;
+ nul.push_back(expair(Order(_ex1), _ex0));
+ return pseries(relational(var,point), nul);
+ }
+
+ // Series multiplication
+ epvector new_seq;
+ int a_max = degree(var);
+ int b_max = other.degree(var);
+ int a_min = ldegree(var);
+ int b_min = other.ldegree(var);
+ 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(var, a_max)))
+ higher_order_a = a_max + b_min;
+ if (is_order_function(other.coeff(var, b_max)))
+ higher_order_b = b_max + a_min;
+ int higher_order_c = std::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 = _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);
+ ex b_coeff = other.coeff(var, cdeg-i);
+ if (!is_order_function(a_coeff) && !is_order_function(b_coeff))
+ co += a_coeff * b_coeff;
+ }
+ if (!co.is_zero())
+ 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)));
+ return pseries(relational(var, point), new_seq);
}
* @see ex::series */
ex mul::series(const relational & r, int order, unsigned options) const
{
- ex acc; // Series accumulator
-
- // Get first term from overall_coeff
- acc = overall_coeff.series(r, order, options);
-
- // Multiply with remaining terms
- epvector::const_iterator it = seq.begin();
- epvector::const_iterator itend = seq.end();
- for (; it!=itend; ++it) {
- ex op = it->rest;
- if (op.info(info_flags::numeric)) {
- // series * const (special case, faster)
- ex f = power(op, it->coeff);
- acc = ex_to_pseries(acc).mul_const(ex_to_numeric(f));
- continue;
- } else if (!is_ex_exactly_of_type(op, pseries))
- op = op.series(r, order, options);
- if (!it->coeff.is_equal(_ex1()))
- op = ex_to_pseries(op).power_const(ex_to_numeric(it->coeff), order);
-
- // Series multiplication
- acc = ex_to_pseries(acc).mul_series(ex_to_pseries(op));
- }
- return acc;
+ pseries acc; // Series accumulator
+
+ // Multiply with remaining terms
+ 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);
+
+ // Series multiplication
+ 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));
}
* @param deg truncation order of series calculation */
ex pseries::power_const(const numeric &p, int deg) const
{
- int i;
- const symbol *s = static_cast<symbol *>(var.bp);
- int ldeg = ldegree(*s);
-
- // Calculate coefficients of powered series
- exvector co;
- co.reserve(deg);
- ex co0;
- co.push_back(co0 = power(coeff(*s, ldeg), p));
- bool all_sums_zero = true;
- for (i=1; i<deg; ++i) {
- ex sum = _ex0();
- for (int j=1; j<=i; ++j) {
- ex c = coeff(*s, j + ldeg);
- if (is_order_function(c)) {
- 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(co0 * sum / numeric(i));
- }
-
- // Construct new series (of non-zero coefficients)
- epvector new_seq;
- bool higher_order = false;
- for (i=0; i<deg; ++i) {
- if (!co[i].is_zero())
- new_seq.push_back(expair(co[i], numeric(i) + p * ldeg));
- if (is_order_function(co[i])) {
- higher_order = true;
- break;
- }
- }
- if (!higher_order && !all_sums_zero)
- new_seq.push_back(expair(Order(_ex1()), numeric(deg) + p * ldeg));
- return pseries(relational(var,point), new_seq);
+ // method:
+ // (due to Leonhard Euler)
+ // let A(x) be this series and for the time being let it start with a
+ // constant (later we'll generalize):
+ // A(x) = a_0 + a_1*x + a_2*x^2 + ...
+ // We want to compute
+ // C(x) = A(x)^p
+ // C(x) = c_0 + c_1*x + c_2*x^2 + ...
+ // Taking the derivative on both sides and multiplying with A(x) one
+ // immediately arrives at
+ // C'(x)*A(x) = p*C(x)*A'(x)
+ // Multiplying this out and comparing coefficients we get the recurrence
+ // formula
+ // c_i = (i*p*a_i*c_0 + ((i-1)*p-1)*a_{i-1}*c_1 + ...
+ // ... + (p-(i-1))*a_1*c_{i-1})/(a_0*i)
+ // which can easily be solved given the starting value c_0 = (a_0)^p.
+ // For the more general case where the leading coefficient of A(x) is not
+ // a constant, just consider A2(x) = A(x)*x^m, with some integer m and
+ // repeat the above derivation. The leading power of C2(x) = A2(x)^2 is
+ // then of course x^(p*m) but the recurrence formula still holds.
+
+ if (seq.empty()) {
+ // as a special case, handle the empty (zero) series honoring the
+ // usual power laws such as implemented in power::eval()
+ if (p.real().is_zero())
+ throw std::domain_error("pseries::power_const(): pow(0,I) is undefined");
+ else if (p.real().is_negative())
+ throw pole_error("pseries::power_const(): division by zero",1);
+ else
+ return *this;
+ }
+
+ const int ldeg = ldegree(var);
+ if (!(p*ldeg).is_integer())
+ throw std::runtime_error("pseries::power_const(): trying to assemble a Puiseux series");
+
+ // 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);
+
+ // Compute coefficients of the powered series
+ 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;
+ for (int j=1; j<=i; ++j) {
+ ex c = coeff(var, j + ldeg);
+ if (is_order_function(c)) {
+ 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);
+ }
+
+ // Construct new series (of non-zero coefficients)
+ epvector new_seq;
+ bool higher_order = false;
+ for (int i=0; i<deg; ++i) {
+ if (!co[i].is_zero())
+ new_seq.push_back(expair(co[i], p * ldeg + i));
+ if (is_order_function(co[i])) {
+ higher_order = true;
+ break;
+ }
+ }
+ if (!higher_order && !all_sums_zero)
+ new_seq.push_back(expair(Order(_ex1), p * ldeg + deg));
+ return pseries(relational(var,point), new_seq);
}
/** Return a new pseries object with the powers shifted by deg. */
pseries pseries::shift_exponents(int deg) const
{
- epvector newseq(seq);
- for (epvector::iterator i=newseq.begin(); i!=newseq.end(); ++i)
- i->coeff = i->coeff + deg;
- return pseries(relational(var, point), newseq);
+ epvector newseq = seq;
+ epvector::iterator i = newseq.begin(), end = newseq.end();
+ while (i != end) {
+ i->coeff += deg;
+ ++i;
+ }
+ return pseries(relational(var, point), newseq);
}
* @see ex::series */
ex power::series(const relational & r, int order, unsigned options) const
{
- ex e;
- if (!is_ex_exactly_of_type(basis, pseries)) {
- // Basis is not a series, may there be a singulary?
- if (!exponent.info(info_flags::negint))
- return basic::series(r, order, options);
-
- // Expression is of type something^(-int), check for singularity
- if (!basis.subs(r).is_zero())
- return basic::series(r, order, options);
-
- // Singularity encountered, expand basis into series
- e = basis.series(r, order, options);
- } else {
- // Basis is a series
- e = basis;
- }
-
- // Power e
- return ex_to_pseries(e).power_const(ex_to_numeric(exponent), order);
+ // If basis is already a series, just power it
+ 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, 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))
+ return basic::series(r, order, options);
+
+ // Is the expression of type 0^something?
+ if (!must_expand_basis && !basis.subs(r, subs_options::no_pattern).is_zero())
+ 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));
+ else
+ 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);
}
/** Re-expansion of a pseries object. */
ex pseries::series(const relational & r, int order, unsigned options) const
{
- const ex p = r.rhs();
- GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
-
- if (var.is_equal(*s) && point.is_equal(p)) {
- if (order > degree(*s))
- return *this;
- else {
- epvector new_seq;
- epvector::const_iterator it = seq.begin(), itend = seq.end();
- while (it != itend) {
- int o = ex_to_numeric(it->coeff).to_int();
- if (o >= order) {
- new_seq.push_back(expair(Order(_ex1()), o));
- break;
- }
- new_seq.push_back(*it);
- ++it;
- }
- return pseries(r, new_seq);
- }
- } else
- return convert_to_poly().series(r, order, options);
+ const ex p = r.rhs();
+ GINAC_ASSERT(is_a<symbol>(r.lhs()));
+ const symbol &s = ex_to<symbol>(r.lhs());
+
+ if (var.is_equal(s) && point.is_equal(p)) {
+ if (order > degree(s))
+ return *this;
+ else {
+ epvector new_seq;
+ epvector::const_iterator it = seq.begin(), itend = seq.end();
+ while (it != itend) {
+ int o = ex_to<numeric>(it->coeff).to_int();
+ if (o >= order) {
+ new_seq.push_back(expair(Order(_ex1), o));
+ break;
+ }
+ new_seq.push_back(*it);
+ ++it;
+ }
+ return pseries(r, new_seq);
+ }
+ } else
+ return convert_to_poly().series(r, order, options);
}
* @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))
- rel_ = ex_to_relational(r);
- else if (is_ex_exactly_of_type(r,symbol))
- rel_ = relational(r,_ex0());
- else
- throw (std::logic_error("ex::series(): expansion point has unknown type"));
-
- try {
- e = bp->series(rel_, order, options);
- } catch (std::exception &x) {
- throw (std::logic_error(std::string("unable to compute series (") + x.what() + ")"));
- }
- return e;
-}
-
-
-// Global constants
-const pseries some_pseries;
-const type_info & typeid_pseries = typeid(some_pseries);
-
-#ifndef NO_NAMESPACE_GINAC
+ ex e;
+ relational rel_;
+
+ if (is_a<relational>(r))
+ rel_ = ex_to<relational>(r);
+ else if (is_a<symbol>(r))
+ rel_ = relational(r,_ex0);
+ else
+ throw (std::logic_error("ex::series(): expansion point has unknown type"));
+
+ try {
+ e = bp->series(rel_, order, options);
+ } catch (std::exception &x) {
+ throw (std::logic_error(std::string("unable to compute series (") + x.what() + ")"));
+ }
+ return e;
+}
+
} // namespace GiNaC
-#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff