* methods for series expansion. */
/*
- * GiNaC Copyright (C) 1999-2002 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2007 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
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
-#include <iostream>
+#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 "integral.h"
#include "archive.h"
#include "utils.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() : inherited(TINFO_pseries) { }
-
-void pseries::copy(const pseries &other)
-{
- inherited::copy(other);
- seq = other.seq;
- var = other.var;
- point = other.point;
-}
-
-DEFAULT_DESTROY(pseries)
+pseries::pseries() : inherited(&pseries::tinfo_static) { }
/*
* @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(&pseries::tinfo_static), seq(ops_)
{
GINAC_ASSERT(is_a<relational>(rel_));
GINAC_ASSERT(is_a<symbol>(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)
{
- for (unsigned int i=0; true; ++i) {
+ archive_node::archive_node_cit first = n.find_first("coeff");
+ archive_node::archive_node_cit last = n.find_last("power");
+ ++last;
+ seq.reserve((last-first)/2);
+
+ for (archive_node::archive_node_cit loc = first; loc < last;) {
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_by_loc(loc++, rest, sym_lst);
+ n.find_ex_by_loc(loc++, coeff, sym_lst);
+ seq.push_back(expair(rest, coeff));
}
+
n.find_ex("var", var, sym_lst);
n.find_ex("point", point, sym_lst);
}
// 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
{
- if (is_a<print_tree>(c)) {
+ 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';
- 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);
+ epvector::const_iterator i = seq.begin(), end = seq.end();
+ while (i != end) {
- } 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 {
+ // print a sign, if needed
+ if (i != seq.begin())
+ c.s << '+';
- 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;
+ 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
- var.print(c);
- 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);
- 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);
+}
+
+void pseries::do_print_latex(const print_latex & c, unsigned level) const
+{
+ print_series(c, "{", "}", " ", "^", level);
+}
- if (precedence() <= level)
- c.s << ")";
+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
}
/** 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"));
+ if (is_order_function(seq[i].rest))
+ return Order(power(var-point, seq[i].coeff));
+ return seq[i].rest * power(var - point, seq[i].coeff);
}
/** Return degree of highest power of the series. This is usually the exponent
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
+{
+ if(!var.info(info_flags::real))
+ return conjugate_function(*this).hold();
+
+ epvector * newseq = conjugateepvector(seq);
+ ex newpoint = point.conjugate();
+
+ if (!newseq && are_ex_trivially_equal(point, newpoint)) {
+ return *this;
+ }
+
+ ex result = (new pseries(var==newpoint, newseq ? *newseq : seq))->setflag(status_flags::dynallocated);
+ if (newseq) {
+ delete newseq;
+ }
+ return result;
+}
+
+ex pseries::real_part() const
+{
+ if(!var.info(info_flags::real))
+ return real_part_function(*this).hold();
+ ex newpoint = point.real_part();
+ if(newpoint != point)
+ return real_part_function(*this).hold();
+
+ epvector v;
+ v.reserve(seq.size());
+ for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+ v.push_back(expair((i->rest).real_part(), i->coeff));
+ return (new pseries(var==point, v))->setflag(status_flags::dynallocated);
+}
+
+ex pseries::imag_part() const
+{
+ if(!var.info(info_flags::real))
+ return imag_part_function(*this).hold();
+ ex newpoint = point.real_part();
+ if(newpoint != point)
+ return imag_part_function(*this).hold();
+
+ epvector v;
+ v.reserve(seq.size());
+ for(epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
+ v.push_back(expair((i->rest).imag_part(), i->coeff));
+ return (new pseries(var==point, v))->setflag(status_flags::dynallocated);
+}
+
+ex pseries::eval_integ() const
+{
+ epvector *newseq = NULL;
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ if (newseq) {
+ newseq->push_back(expair(i->rest.eval_integ(), i->coeff));
+ continue;
+ }
+ ex newterm = i->rest.eval_integ();
+ if (!are_ex_trivially_equal(newterm, i->rest)) {
+ newseq = new epvector;
+ newseq->reserve(seq.size());
+ for (epvector::const_iterator j=seq.begin(); j!=i; ++j)
+ newseq->push_back(*j);
+ newseq->push_back(expair(newterm, i->coeff));
+ }
+ }
+
+ ex newpoint = point.eval_integ();
+ if (newseq || !are_ex_trivially_equal(newpoint, point))
+ return (new pseries(var==newpoint, *newseq))
+ ->setflag(status_flags::dynallocated);
+ return *this;
+}
+
+ex pseries::evalm() const
+{
+ // evalm each coefficient
+ epvector newseq;
+ bool something_changed = false;
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ if (something_changed) {
+ ex newcoeff = i->rest.evalm();
+ if (!newcoeff.is_zero())
+ newseq.push_back(expair(newcoeff, i->coeff));
+ }
+ else {
+ ex newcoeff = i->rest.evalm();
+ if (!are_ex_trivially_equal(newcoeff, i->rest)) {
+ something_changed = true;
+ newseq.reserve(seq.size());
+ std::copy(seq.begin(), i, std::back_inserter<epvector>(newseq));
+ if (!newcoeff.is_zero())
+ newseq.push_back(expair(newcoeff, i->coeff));
+ }
+ }
+ }
+ if (something_changed)
+ return (new pseries(var==point, newseq))->setflag(status_flags::dynallocated);
+ else
+ return *this;
+}
+
+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
return e;
}
-bool pseries::is_terminating(void) const
+bool pseries::is_terminating() const
{
return seq.empty() || !is_order_function((seq.end()-1)->rest);
}
+ex pseries::coeffop(size_t i) const
+{
+ if (i >=nops())
+ throw (std::out_of_range("coeffop() out of range"));
+ return seq[i].rest;
+}
+
+ex pseries::exponop(size_t i) const
+{
+ if (i >= nops())
+ throw (std::out_of_range("exponop() out of range"));
+ return seq[i].coeff;
+}
+
/*
* Implementations of series expansion
ex basic::series(const relational & r, int order, unsigned options) const
{
epvector seq;
+ const symbol &s = ex_to<symbol>(r.lhs());
+
+ // 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);
- const symbol &s = ex_to<symbol>(r.lhs());
-
- if (!coeff.is_zero())
+ 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(n);
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, n));
}
nul.push_back(expair(Order(_ex1), _ex0));
return pseries(relational(var,point), nul);
}
+
+ if (seq.empty() || other.seq.empty()) {
+ return (new pseries(var==point, epvector()))
+ ->setflag(status_flags::dynallocated);
+ }
// Series multiplication
epvector 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
+ int numcoeff = deg - (p*ldeg).to_int();
+ if (numcoeff <= 0) {
+ epvector epv;
+ epv.reserve(1);
+ epv.push_back(expair(Order(_ex1), deg));
+ return (new pseries(relational(var,point), epv))
+ ->setflag(status_flags::dynallocated);
+ }
+
// 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.reserve(numcoeff);
co.push_back(power(coeff(var, ldeg), p));
- bool all_sums_zero = true;
- for (int i=1; i<deg; ++i) {
+ for (int i=1; i<numcoeff; ++i) {
ex sum = _ex0;
for (int j=1; j<=i; ++j) {
ex c = coeff(var, j + ldeg);
} 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) {
+ for (int i=0; i<numcoeff; ++i) {
if (!co[i].is_zero())
new_seq.push_back(expair(co[i], p * ldeg + i));
if (is_order_function(co[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 + numcoeff));
+
return pseries(relational(var,point), new_seq);
}
// 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) || !is_a<numeric>(exponent)))
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) || !is_a<numeric>(exponent)))
return basic::series(r, order, options);
// Singularity encountered, is the basis equal to (var - point)?
}
// 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;
}
return convert_to_poly().series(r, order, options);
}
+ex integral::series(const relational & r, int order, unsigned options) const
+{
+ if (x.subs(r) != x)
+ throw std::logic_error("Cannot series expand wrt dummy variable");
+
+ // Expanding integrant with r substituted taken in boundaries.
+ ex fseries = f.series(r, order, options);
+ epvector fexpansion;
+ fexpansion.reserve(fseries.nops());
+ for (size_t i=0; i<fseries.nops(); ++i) {
+ ex currcoeff = ex_to<pseries>(fseries).coeffop(i);
+ currcoeff = (currcoeff == Order(_ex1))
+ ? currcoeff
+ : integral(x, a.subs(r), b.subs(r), currcoeff);
+ if (currcoeff != 0)
+ fexpansion.push_back(
+ expair(currcoeff, ex_to<pseries>(fseries).exponop(i)));
+ }
+
+ // Expanding lower boundary
+ ex result = (new pseries(r, fexpansion))->setflag(status_flags::dynallocated);
+ ex aseries = (a-a.subs(r)).series(r, order, options);
+ fseries = f.series(x == (a.subs(r)), order, options);
+ for (size_t i=0; i<fseries.nops(); ++i) {
+ ex currcoeff = ex_to<pseries>(fseries).coeffop(i);
+ if (is_order_function(currcoeff))
+ break;
+ ex currexpon = ex_to<pseries>(fseries).exponop(i);
+ int orderforf = order-ex_to<numeric>(currexpon).to_int()-1;
+ currcoeff = currcoeff.series(r, orderforf);
+ ex term = ex_to<pseries>(aseries).power_const(ex_to<numeric>(currexpon+1),order);
+ term = ex_to<pseries>(term).mul_const(ex_to<numeric>(-1/(currexpon+1)));
+ term = ex_to<pseries>(term).mul_series(ex_to<pseries>(currcoeff));
+ result = ex_to<pseries>(result).add_series(ex_to<pseries>(term));
+ }
+
+ // Expanding upper boundary
+ ex bseries = (b-b.subs(r)).series(r, order, options);
+ fseries = f.series(x == (b.subs(r)), order, options);
+ for (size_t i=0; i<fseries.nops(); ++i) {
+ ex currcoeff = ex_to<pseries>(fseries).coeffop(i);
+ if (is_order_function(currcoeff))
+ break;
+ ex currexpon = ex_to<pseries>(fseries).exponop(i);
+ int orderforf = order-ex_to<numeric>(currexpon).to_int()-1;
+ currcoeff = currcoeff.series(r, orderforf);
+ ex term = ex_to<pseries>(bseries).power_const(ex_to<numeric>(currexpon+1),order);
+ term = ex_to<pseries>(term).mul_const(ex_to<numeric>(1/(currexpon+1)));
+ term = ex_to<pseries>(term).mul_series(ex_to<pseries>(currcoeff));
+ result = ex_to<pseries>(result).add_series(ex_to<pseries>(term));
+ }
+
+ return result;
+}
+
/** Compute the truncated series expansion of an expression.
* This function returns an expression containing an object of class pseries
* @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_exactly_a<relational>(r))
+ if (is_a<relational>(r))
rel_ = ex_to<relational>(r);
else if (is_a<symbol>(r))
rel_ = relational(r,_ex0);
git://www.ginac.de / ginac.git / blobdiff