* 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 <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 "archive.h"
* @return newly constructed pseries */
pseries::pseries(const ex &rel_, const epvector &ops_) : basic(TINFO_pseries), seq(ops_)
{
- 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)
{
for (unsigned int i=0; true; ++i) {
ex rest;
<< 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) {
+ size_t num = seq.size();
+ for (size_t 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);
+ } else if (is_a<print_python_repr>(c)) {
+ 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 << "])";
} else {
if (precedence() <= level)
} else
var.print(c);
if (i->coeff.compare(_ex1)) {
- c.s << '^';
+ 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);
}
/** Return the number of operands including a possible order term. */
-unsigned pseries::nops(void) const
+size_t pseries::nops(void) 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
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::subs(const lst & ls, const lst & lr, 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);
+ return convert_to_poly(true).subs(ls, lr, 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(ls, lr, 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(ls, lr, 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
epvector seq;
numeric fac = 1;
ex deriv = *this;
- ex coeff = deriv.subs(r);
+ ex coeff = deriv.subs(r, subs_options::no_pattern);
const symbol &s = ex_to<symbol>(r.lhs());
if (!coeff.is_zero())
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));
}
deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
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())
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);
{
pseries acc; // Series accumulator
+ GINAC_ASSERT(is_a<symbol>(r.lhs()));
+ const ex& sym = r.lhs();
+
+ // holds ldegrees of the series of individual factors
+ std::vector<int> ldegrees;
+ // flag if series have to be re-calculated
+ bool negldegree = false;
+
// 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);
+ int ldeg = op.ldegree(sym);
+ ldegrees.push_back(ldeg);
+ if (ldeg < 0) {
+ negldegree = true;
+ }
+
// 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));
+
+ if (seq.size() > 1) {
+
+ // re-calculation of series
+
+ pseries newacc;
+
+ const int degsum = std::accumulate(ldegrees.begin(), ldegrees.end(), 0);
+
+ // Multiply with remaining terms
+ const epvector::const_reverse_iterator itbeg = seq.rbegin();
+ const epvector::const_reverse_iterator itend = seq.rend();
+ std::vector<int>::const_reverse_iterator itd = ldegrees.rbegin();
+ for (epvector::const_reverse_iterator it=itbeg; it!=itend; ++it, ++itd) {
+
+ ex op = recombine_pair_to_ex(*it).series(r, order-degsum+(*itd), options);
+
+ // Series multiplication
+ if (it==itbeg)
+ newacc = ex_to<pseries>(op);
+ else
+ newacc = ex_to<pseries>(newacc.mul_series(ex_to<pseries>(op)));
+ }
+ return newacc.mul_const(ex_to<numeric>(overall_coeff));
+ } else {
+ 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.to_int()*ldeg;
+
// 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);
}
if (!higher_order && !all_sums_zero)
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))
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())
return basic::series(r, order, options);
// Singularity encountered, is the basis equal to (var - point)?
}
// No, expand basis into series
+ int intexp = ex_to<numeric>(exponent).to_int();
ex e = basis.series(r, order, options);
- return ex_to<pseries>(e).power_const(ex_to<numeric>(exponent), order);
+ int ldeg = ex_to<pseries>(e).ldegree(r.lhs());
+ if (intexp * ldeg < 0) {
+ e = basis.series(r, order + ldeg*(1-intexp), options);
+ }
+ return ex_to<pseries>(e).power_const(intexp, order);
}
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)) {
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))
+ 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