#include "power.h"
#include "relational.h"
#include "symbol.h"
+#include "print.h"
#include "archive.h"
#include "utils.h"
#include "debugmsg.h"
// functions overriding virtual functions from bases 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_of_type(c, print_tree)) {
-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 << ")";
-}
+ 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;
+ for (unsigned i=0; i<seq.size(); ++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 {
-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 << "(";
+
+ std::string par_open = is_of_type(c, print_latex) ? "{(" : "(";
+ std::string par_close = is_of_type(c, print_latex) ? ")}" : ")";
+
+ // objects of type pseries must not have any zero entries, so the
+ // trivial (zero) pseries needs a special treatment here:
+ if (seq.size() == 0)
+ c.s << '0';
+ for (epvector::const_iterator i=seq.begin(); i!=seq.end(); ++i) {
+ // 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_of_type(c, print_latex))
+ 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_of_type(c, print_latex)) {
+ c.s << '{';
+ i->coeff.print(c);
+ c.s << '}';
+ } else
+ i->coeff.print(c);
+ }
+ }
+ }
+ } else
+ Order(power(var-point,i->coeff)).print(c);
+ }
+
+ 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. */
-int pseries::degree(const symbol &s) const
+int pseries::degree(const ex &s) const
{
if (var.is_equal(s)) {
// Return last 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
+int pseries::ldegree(const ex &s) const
{
if (var.is_equal(s)) {
// Return first exponent
* 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 symbol &s, int n) const
+ex pseries::coeff(const ex &s, int n) const
{
if (var.is_equal(s)) {
if (seq.size() == 0)
}
/** Does nothing. */
-ex pseries::collect(const symbol &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
{
// If expansion variable is being substituted, convert the series to a
return (new pseries(relational(var,point.subs(ls, lr)), 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
->setflag(status_flags::dynallocated | status_flags::expanded);
}
-
/** 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);
numeric fac(1);
ex deriv = *this;
ex coeff = deriv.subs(r);
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
+ 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();
+ deriv = deriv.diff(s).expand();
if (deriv.is_zero()) {
// Series terminates
return pseries(r, seq);
}
// Higher-order terms, if present
- deriv = deriv.diff(*s);
+ deriv = deriv.diff(s);
if (!deriv.expand().is_zero())
seq.push_back(expair(Order(_ex1()), numeric(n)));
return pseries(r, seq);
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);
+ ex s = r.lhs();
- if (this->is_equal(*s)) {
+ if (this->is_equal(*s.bp)) {
if (order > 0 && !point.is_zero())
seq.push_back(expair(point, _ex0()));
if (order > 1)
// 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 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(*s, a_max)))
+ if (is_order_function(coeff(var, a_max)))
higher_order_a = a_max + b_min;
- if (is_order_function(other.coeff(*s, b_max)))
+ 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)
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);
+ 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 (higher_order_c < INT_MAX)
new_seq.push_back(expair(Order(_ex1()), numeric(higher_order_c)));
- return pseries(relational(var,point), new_seq);
+ return pseries(relational(var, point), new_seq);
}
return *this;
}
- const symbol *s = static_cast<symbol *>(var.bp);
- int ldeg = ldegree(*s);
+ int ldeg = ldegree(var);
// Compute coefficients of the powered series
exvector co;
co.reserve(deg);
- co.push_back(power(coeff(*s, ldeg), p));
+ 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(*s, j + ldeg);
+ ex c = coeff(var, j + ldeg);
if (is_order_function(c)) {
co.push_back(Order(_ex1()));
break;
}
if (!sum.is_zero())
all_sums_zero = false;
- co.push_back(sum / coeff(*s, ldeg) / numeric(i));
+ co.push_back(sum / coeff(var, ldeg) / numeric(i));
}
// Construct new series (of non-zero coefficients)
{
const ex p = r.rhs();
GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
+ const symbol &s = static_cast<symbol &>(*r.lhs().bp);
- if (var.is_equal(*s) && point.is_equal(p)) {
- if (order > degree(*s))
+ if (var.is_equal(s) && point.is_equal(p)) {
+ if (order > degree(s))
return *this;
else {
epvector new_seq;
git://www.ginac.de / ginac.git / blobdiff