#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 "symbol.h"
+#include "print.h"
#include "archive.h"
#include "utils.h"
#include "debugmsg.h"
DEFAULT_UNARCHIVE(pseries)
//////////
-// functions overriding virtual functions from bases classes
+// functions overriding virtual functions from base classes
//////////
-void pseries::print(std::ostream &os, unsigned upper_precedence) const
+void pseries::print(const print_context & c, unsigned level) const
{
debugmsg("pseries print", LOGLEVEL_PRINT);
- if (precedence<=upper_precedence) os << "(";
- // objects of type pseries must not have any zero entries, so the
- // trivial (zero) pseries needs a special treatment here:
- if (seq.size()==0)
- os << '0';
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
- // 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));
- }
- }
- if (precedence<=upper_precedence) os << ")";
-}
+ if (is_a<print_tree>(c)) {
+
+ 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);
-void pseries::printraw(std::ostream &os) const
-{
- debugmsg("pseries printraw", LOGLEVEL_PRINT);
- os << class_name() << "(" << var << ";" << point << ";";
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i)
- os << "(" << (*i).rest << "," << (*i).coeff << "),";
- os << ")";
-}
+ } else {
+ 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;
+ } 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);
+ }
+ }
+ }
+ } else
+ Order(power(var-point,i->coeff)).print(c);
+ ++i;
+ }
-void pseries::printtree(std::ostream & os, unsigned indent) const
-{
- debugmsg("pseries printtree",LOGLEVEL_PRINT);
- os << std::string(indent,' ') << class_name()
- << ", 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;
+ if (precedence() <= level)
+ c.s << ")";
}
- var.printtree(os, indent+delta_indent);
- point.printtree(os, indent+delta_indent);
}
int pseries::compare_same_type(const basic & other) const
return seq.size();
}
-
/** Return the ith term in the series when represented as a sum. */
ex pseries::op(int i) const
{
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 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. */
if (var.is_equal(s)) {
// Return last exponent
if (seq.size())
- return ex_to_numeric((*(seq.end() - 1)).coeff).to_int();
+ return ex_to<numeric>((*(seq.end() - 1)).coeff).to_int();
else
return 0;
} else {
if (var.is_equal(s)) {
// Return first exponent
if (seq.size())
- return ex_to_numeric((*(seq.begin())).coeff).to_int();
+ return ex_to<numeric>((*(seq.begin())).coeff).to_int();
else
return 0;
} else {
ex pseries::coeff(const ex &s, int n) const
{
if (var.is_equal(s)) {
- if (seq.size() == 0)
+ if (seq.empty())
return _ex0();
// Binary search in sequence for given power
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);
+ int cmp = ex_to<numeric>(seq[mid].coeff).compare(looking_for);
switch (cmp) {
case -1:
lo = mid + 1;
}
/** Does nothing. */
-ex pseries::collect(const ex &s) const
+ex pseries::collect(const ex &s, bool distributed) const
{
return *this;
}
-
/** Evaluate coefficients. */
ex pseries::eval(int level) const
{
return (new pseries(relational(var,point), new_seq))->setflag(status_flags::dynallocated | status_flags::evaluated);
}
-
/** Evaluate coefficients numerically. */
ex pseries::evalf(int level) const
{
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
+ex pseries::subs(const lst & ls, const lst & lr, bool no_pattern) 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);
+ return convert_to_poly(true).subs(ls, lr, no_pattern);
// 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), it->coeff));
+ newseq.push_back(expair(it->rest.subs(ls, lr, no_pattern), it->coeff));
++it;
}
- return (new pseries(relational(var,point.subs(ls, lr)), newseq))->setflag(status_flags::dynallocated);
+ return (new pseries(relational(var,point.subs(ls, lr, no_pattern)), 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. */
ex pseries::expand(unsigned options) const
{
epvector newseq;
- for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ 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 | status_flags::expanded);
+ ->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.
* @see ex::diff */
}
}
-
-/** 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;
return e;
}
-
-/** Returns true if there is no order term, i.e. the series terminates and
- * false otherwise. */
bool pseries::is_terminating(void) const
{
- return seq.size() == 0 || !is_order_function((seq.end()-1)->rest);
+ return seq.empty() || !is_order_function((seq.end()-1)->rest);
}
const symbol &s = static_cast<symbol &>(*r.lhs().bp);
if (!coeff.is_zero())
- seq.push_back(expair(coeff, numeric(0)));
+ seq.push_back(expair(coeff, _ex0()));
int n;
for (n=1; n<order; ++n) {
}
break;
} else
- pow_a = ex_to_numeric((*a).coeff).to_int();
+ 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) {
}
break;
} else
- pow_b = ex_to_numeric((*b).coeff).to_int();
+ pow_b = ex_to<numeric>((*b).coeff).to_int();
// a and b are non-empty, compare powers
if (pow_a < pow_b) {
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));
+ 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));
+ acc = ex_to<pseries>(acc).add_series(ex_to<pseries>(op));
}
return acc;
}
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));
+ 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);
+ 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));
+ acc = ex_to<pseries>(acc).mul_series(ex_to<pseries>(op));
}
return acc;
}
ex pseries::power_const(const numeric &p, int deg) const
{
// 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 + ...
// 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.size()==0) {
+ if (seq.empty()) {
// as a spacial case, handle the empty (zero) series honoring the
// usual power laws such as implemented in power::eval()
if (p.real().is_zero())
/** 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;
+ epvector newseq = seq;
+ epvector::iterator i = newseq.begin(), end = newseq.end();
+ while (i != end) {
+ i->coeff += deg;
+ ++i;
+ }
return pseries(relational(var, point), newseq);
}
}
// Power e
- return ex_to_pseries(e).power_const(ex_to_numeric(exponent), order);
+ return ex_to<pseries>(e).power_const(ex_to<numeric>(exponent), order);
}
epvector new_seq;
epvector::const_iterator it = seq.begin(), itend = seq.end();
while (it != itend) {
- int o = ex_to_numeric(it->coeff).to_int();
+ int o = ex_to<numeric>(it->coeff).to_int();
if (o >= order) {
new_seq.push_back(expair(Order(_ex1()), o));
break;
relational rel_;
if (is_ex_exactly_of_type(r,relational))
- rel_ = ex_to_relational(r);
+ rel_ = ex_to<relational>(r);
else if (is_ex_exactly_of_type(r,symbol))
rel_ = relational(r,_ex0());
else
return e;
}
-//////////
-// static member variables
-//////////
-
-// protected
-
-unsigned pseries::precedence = 38; // for clarity just below add::precedence
-
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff