* Implementation of GiNaC's initially known functions. */
/*
- * GiNaC Copyright (C) 1999-2001 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2002 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
#include "relational.h"
#include "pseries.h"
#include "symbol.h"
+#include "symmetry.h"
#include "utils.h"
namespace GiNaC {
static ex abs_evalf(const ex & arg)
{
- BEGIN_TYPECHECK
- TYPECHECK(arg,numeric)
- END_TYPECHECK(abs(arg))
+ if (is_exactly_a<numeric>(arg))
+ return abs(ex_to<numeric>(arg));
- return abs(ex_to<numeric>(arg));
+ return abs(arg).hold();
}
static ex abs_eval(const ex & arg)
static ex csgn_evalf(const ex & arg)
{
- BEGIN_TYPECHECK
- TYPECHECK(arg,numeric)
- END_TYPECHECK(csgn(arg))
+ if (is_exactly_a<numeric>(arg))
+ return csgn(ex_to<numeric>(arg));
- return csgn(ex_to<numeric>(arg));
+ return csgn(arg).hold();
}
static ex csgn_eval(const ex & arg)
if (is_ex_exactly_of_type(arg, numeric))
return csgn(ex_to<numeric>(arg));
- else if (is_ex_of_type(arg, mul) &&
+ else if (is_ex_exactly_of_type(arg, mul) &&
is_ex_of_type(arg.op(arg.nops()-1),numeric)) {
numeric oc = ex_to<numeric>(arg.op(arg.nops()-1));
if (oc.is_real()) {
throw (std::domain_error("csgn_series(): on imaginary axis"));
epvector seq;
- seq.push_back(expair(csgn(arg_pt), _ex0()));
+ seq.push_back(expair(csgn(arg_pt), _ex0));
return pseries(rel,seq);
}
//////////
// Eta function: eta(x,y) == log(x*y) - log(x) - log(y).
+// This function is closely related to the unwinding number K, sometimes found
+// in modern literature: K(z) == (z-log(exp(z)))/(2*Pi*I).
//////////
static ex eta_evalf(const ex &x, const ex &y)
// It seems like we basically have to replicate the eval function here,
// since the expression might not be fully evaluated yet.
if (x.info(info_flags::positive) || y.info(info_flags::positive))
- return _ex0();
+ return _ex0;
if (x.info(info_flags::numeric) && y.info(info_flags::numeric)) {
const numeric nx = ex_to<numeric>(x);
{
// trivial: eta(x,c) -> 0 if c is real and positive
if (x.info(info_flags::positive) || y.info(info_flags::positive))
- return _ex0();
+ return _ex0;
if (x.info(info_flags::numeric) && y.info(info_flags::numeric)) {
// don't call eta_evalf here because it would call Pi.evalf()!
((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative)))
throw (std::domain_error("eta_series(): on discontinuity"));
epvector seq;
- seq.push_back(expair(eta(x_pt,y_pt), _ex0()));
+ seq.push_back(expair(eta(x_pt,y_pt), _ex0));
return pseries(rel,seq);
}
REGISTER_FUNCTION(eta, eval_func(eta_eval).
evalf_func(eta_evalf).
- series_func(eta_series).
- latex_name("\\eta"));
+ series_func(eta_series).
+ latex_name("\\eta").
+ set_symmetry(sy_symm(0, 1)));
//////////
static ex Li2_evalf(const ex & x)
{
- BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(Li2(x))
+ if (is_exactly_a<numeric>(x))
+ return Li2(ex_to<numeric>(x));
- return Li2(ex_to<numeric>(x)); // -> numeric Li2(numeric)
+ return Li2(x).hold();
}
static ex Li2_eval(const ex & x)
if (x.info(info_flags::numeric)) {
// Li2(0) -> 0
if (x.is_zero())
- return _ex0();
+ return _ex0;
// Li2(1) -> Pi^2/6
- if (x.is_equal(_ex1()))
- return power(Pi,_ex2())/_ex6();
+ if (x.is_equal(_ex1))
+ return power(Pi,_ex2)/_ex6;
// Li2(1/2) -> Pi^2/12 - log(2)^2/2
- if (x.is_equal(_ex1_2()))
- return power(Pi,_ex2())/_ex12() + power(log(_ex2()),_ex2())*_ex_1_2();
+ if (x.is_equal(_ex1_2))
+ return power(Pi,_ex2)/_ex12 + power(log(_ex2),_ex2)*_ex_1_2;
// Li2(-1) -> -Pi^2/12
- if (x.is_equal(_ex_1()))
- return -power(Pi,_ex2())/_ex12();
+ if (x.is_equal(_ex_1))
+ return -power(Pi,_ex2)/_ex12;
// Li2(I) -> -Pi^2/48+Catalan*I
if (x.is_equal(I))
- return power(Pi,_ex2())/_ex_48() + Catalan*I;
+ return power(Pi,_ex2)/_ex_48 + Catalan*I;
// Li2(-I) -> -Pi^2/48-Catalan*I
if (x.is_equal(-I))
- return power(Pi,_ex2())/_ex_48() - Catalan*I;
+ return power(Pi,_ex2)/_ex_48 - Catalan*I;
// Li2(float)
if (!x.info(info_flags::crational))
- return Li2_evalf(x);
+ return Li2(ex_to<numeric>(x));
}
return Li2(x).hold();
GINAC_ASSERT(deriv_param==0);
// d/dx Li2(x) -> -log(1-x)/x
- return -log(1-x)/x;
+ return -log(_ex1-x)/x;
}
static ex Li2_series(const ex &x, const relational &rel, int order, unsigned options)
ex ser;
// manually construct the primitive expansion
for (int i=1; i<order; ++i)
- ser += pow(s,i) / pow(numeric(i), _num2());
+ ser += pow(s,i) / pow(numeric(i), _num2);
// substitute the argument's series expansion
ser = ser.subs(s==x.series(rel, order));
// maybe that was terminating, so add a proper order term
epvector nseq;
- nseq.push_back(expair(Order(_ex1()), order));
+ nseq.push_back(expair(Order(_ex1), order));
ser += pseries(rel, nseq);
// reexpanding it will collapse the series again
return ser.series(rel, order);
// obsolete!
}
// second special case: x==1 (branch point)
- if (x_pt == _ex1()) {
+ if (x_pt.is_equal(_ex1)) {
// method:
// construct series manually in a dummy symbol s
const symbol s;
- ex ser = zeta(_ex2());
+ ex ser = zeta(_ex2);
// manually construct the primitive expansion
for (int i=1; i<order; ++i)
ser += pow(1-s,i) * (numeric(1,i)*(I*Pi+log(s-1)) - numeric(1,i*i));
ser = ser.subs(s==x.series(rel, order));
// maybe that was terminating, so add a proper order term
epvector nseq;
- nseq.push_back(expair(Order(_ex1()), order));
+ nseq.push_back(expair(Order(_ex1), order));
ser += pseries(rel, nseq);
// reexpanding it will collapse the series again
return ser.series(rel, order);
// method:
// This is the branch cut: assemble the primitive series manually
// and then add the corresponding complex step function.
- const symbol *s = static_cast<symbol *>(rel.lhs().bp);
+ const symbol &s = ex_to<symbol>(rel.lhs());
const ex point = rel.rhs();
const symbol foo;
epvector seq;
// zeroth order term:
- seq.push_back(expair(Li2(x_pt), _ex0()));
+ seq.push_back(expair(Li2(x_pt), _ex0));
// compute the intermediate terms:
- ex replarg = series(Li2(x), *s==foo, order);
+ ex replarg = series(Li2(x), s==foo, order);
for (unsigned i=1; i<replarg.nops()-1; ++i)
- seq.push_back(expair((replarg.op(i)/power(*s-foo,i)).series(foo==point,1,options).op(0).subs(foo==*s),i));
+ seq.push_back(expair((replarg.op(i)/power(s-foo,i)).series(foo==point,1,options).op(0).subs(foo==s),i));
// append an order term:
- seq.push_back(expair(Order(_ex1()), replarg.nops()-1));
+ seq.push_back(expair(Order(_ex1), replarg.nops()-1));
return pseries(rel, seq);
}
}
if (is_ex_exactly_of_type(x, numeric)) {
// O(c) -> O(1) or 0
if (!x.is_zero())
- return Order(_ex1()).hold();
+ return Order(_ex1).hold();
else
- return _ex0();
+ return _ex0;
} else if (is_ex_exactly_of_type(x, mul)) {
- mul *m = static_cast<mul *>(x.bp);
+ const mul &m = ex_to<mul>(x);
// O(c*expr) -> O(expr)
- if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric))
- return Order(x / m->op(m->nops() - 1)).hold();
+ if (is_ex_exactly_of_type(m.op(m.nops() - 1), numeric))
+ return Order(x / m.op(m.nops() - 1)).hold();
}
return Order(x).hold();
}
{
// Just wrap the function into a pseries object
epvector new_seq;
- GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
- const symbol *s = static_cast<symbol *>(r.lhs().bp);
- new_seq.push_back(expair(Order(_ex1()), numeric(std::min(x.ldegree(*s), order))));
+ GINAC_ASSERT(is_a<symbol>(r.lhs()));
+ const symbol &s = ex_to<symbol>(r.lhs());
+ new_seq.push_back(expair(Order(_ex1), numeric(std::min(x.ldegree(s), order))));
return pseries(r, new_seq);
}
// Solve linear system
//////////
-ex lsolve(const ex &eqns, const ex &symbols)
+ex lsolve(const ex &eqns, const ex &symbols, unsigned options)
{
// solve a system of linear equations
if (eqns.info(info_flags::relation_equal)) {
const ex sol = lsolve(lst(eqns),lst(symbols));
GINAC_ASSERT(sol.nops()==1);
- GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
+ GINAC_ASSERT(is_exactly_a<relational>(sol.op(0)));
return sol.op(0).op(1); // return rhs of first solution
}
matrix solution;
try {
- solution = sys.solve(vars,rhs);
+ solution = sys.solve(vars,rhs,options);
} catch (const std::runtime_error & e) {
// Probably singular matrix or otherwise overdetermined system:
// It is consistent to return an empty list
return lst();
- }
+ }
GINAC_ASSERT(solution.cols()==1);
GINAC_ASSERT(solution.rows()==symbols.nops());
git://www.ginac.de / ginac.git / blobdiff