* functions. */
/*
- * GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2016 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 "inifcns.h"
#include "ex.h"
#include "constant.h"
+#include "add.h"
+#include "mul.h"
#include "numeric.h"
#include "power.h"
#include "operators.h"
return exp(x).hold();
}
+static ex exp_expand(const ex & arg, unsigned options)
+{
+ ex exp_arg;
+ if (options & expand_options::expand_function_args)
+ exp_arg = arg.expand(options);
+ else
+ exp_arg=arg;
+
+ if ((options & expand_options::expand_transcendental)
+ && is_exactly_a<add>(exp_arg)) {
+ exvector prodseq;
+ prodseq.reserve(exp_arg.nops());
+ for (const_iterator i = exp_arg.begin(); i != exp_arg.end(); ++i)
+ prodseq.push_back(exp(*i));
+
+ return dynallocate<mul>(prodseq).setflag(status_flags::expanded);
+ }
+
+ return exp(exp_arg).hold();
+}
+
static ex exp_deriv(const ex & x, unsigned deriv_param)
{
GINAC_ASSERT(deriv_param==0);
REGISTER_FUNCTION(exp, eval_func(exp_eval).
evalf_func(exp_evalf).
+ expand_func(exp_expand).
derivative_func(exp_deriv).
real_part_func(exp_real_part).
imag_part_func(exp_imag_part).
if (t.info(info_flags::real))
return t;
}
-
+
return log(x).hold();
}
if (arg_pt.is_zero())
must_expand_arg = true;
+ if (arg.diff(ex_to<symbol>(rel.lhs())).is_zero()) {
+ throw do_taylor();
+ }
+
if (must_expand_arg) {
// method:
// This is the branch point: Series expand the argument first, then
// in this case n more (or less) terms are needed
// (sadly, to generate them, we have to start from the beginning)
if (n == 0 && coeff == 1) {
- epvector epv;
- ex acc = (new pseries(rel, epv))->setflag(status_flags::dynallocated);
- epv.reserve(2);
- epv.push_back(expair(-1, _ex0));
- epv.push_back(expair(Order(_ex1), order));
- ex rest = pseries(rel, epv).add_series(argser);
+ ex rest = pseries(rel, epvector{expair(-1, _ex0), expair(Order(_ex1), order)}).add_series(argser);
+ ex acc = dynallocate<pseries>(rel, epvector());
for (int i = order-1; i>0; --i) {
- epvector cterm;
- cterm.reserve(1);
- cterm.push_back(expair(i%2 ? _ex1/i : _ex_1/i, _ex0));
- acc = pseries(rel, cterm).add_series(ex_to<pseries>(acc));
+ epvector cterm { expair(i%2 ? _ex1/i : _ex_1/i, _ex0) };
+ acc = pseries(rel, std::move(cterm)).add_series(ex_to<pseries>(acc));
acc = (ex_to<pseries>(rest)).mul_series(ex_to<pseries>(acc));
}
return acc;
}
const ex newarg = ex_to<pseries>((arg/coeff).series(rel, order+n, options)).shift_exponents(-n).convert_to_poly(true);
- return pseries(rel, s
eq).add_series(ex_to<pseries>(log(newarg).series(rel, order, options)));
+ return pseries(rel, s
td::move(seq)).add_series(ex_to<pseries>(log(newarg).series(rel, order, options)));
} else // it was a monomial
- return pseries(rel, seq);
+ return pseries(rel, std::move(seq));
}
if (!(options & series_options::suppress_branchcut) &&
arg_pt.info(info_flags::negative)) {
const symbol foo;
const ex replarg = series(log(arg), s==foo, order).subs(foo==point, subs_options::no_pattern);
epvector seq;
- seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0));
+ if (order > 0) {
+ seq.reserve(2);
+ seq.push_back(expair(-I*csgn(arg*I)*Pi, _ex0));
+ }
seq.push_back(expair(Order(_ex1), order));
- return series(replarg - I*Pi + pseries(rel, seq), rel, order);
+ return series(replarg - I*Pi + pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor(); // caught by function::series()
}
return atan2(GiNaC::imag_part(x), GiNaC::real_part(x));
}
+static ex log_expand(const ex & arg, unsigned options)
+{
+ if ((options & expand_options::expand_transcendental)
+ && is_exactly_a<mul>(arg) && !arg.info(info_flags::indefinite)) {
+ exvector sumseq;
+ exvector prodseq;
+ sumseq.reserve(arg.nops());
+ prodseq.reserve(arg.nops());
+ bool possign=true;
+
+ // searching for positive/negative factors
+ for (const_iterator i = arg.begin(); i != arg.end(); ++i) {
+ ex e;
+ if (options & expand_options::expand_function_args)
+ e=i->expand(options);
+ else
+ e=*i;
+ if (e.info(info_flags::positive))
+ sumseq.push_back(log(e));
+ else if (e.info(info_flags::negative)) {
+ sumseq.push_back(log(-e));
+ possign = !possign;
+ } else
+ prodseq.push_back(e);
+ }
+
+ if (sumseq.size() > 0) {
+ ex newarg;
+ if (options & expand_options::expand_function_args)
+ newarg=((possign?_ex1:_ex_1)*mul(prodseq)).expand(options);
+ else {
+ newarg=(possign?_ex1:_ex_1)*mul(prodseq);
+ ex_to<basic>(newarg).setflag(status_flags::purely_indefinite);
+ }
+ return add(sumseq)+log(newarg);
+ } else {
+ if (!(options & expand_options::expand_function_args))
+ ex_to<basic>(arg).setflag(status_flags::purely_indefinite);
+ }
+ }
+
+ if (options & expand_options::expand_function_args)
+ return log(arg.expand(options)).hold();
+ else
+ return log(arg).hold();
+}
+
static ex log_conjugate(const ex & x)
{
// conjugate(log(x))==log(conjugate(x)) unless on the branch cut which
REGISTER_FUNCTION(log, eval_func(log_eval).
evalf_func(log_evalf).
+ expand_func(log_expand).
derivative_func(log_deriv).
series_func(log_series).
real_part_func(log_real_part).
else
Order0correction += log((I*arg_pt+_ex1)/(I*arg_pt+_ex_1))*I*_ex1_2;
epvector seq;
- seq.push_back(expair(Order0correction, _ex0));
+ if (order > 0) {
+ seq.reserve(2);
+ seq.push_back(expair(Order0correction, _ex0));
+ }
seq.push_back(expair(Order(_ex1), order));
- return series(replarg - pseries(rel, seq), rel, order);
+ return series(replarg - pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();
}
return cosh(GiNaC::real_part(x))*sin(GiNaC::imag_part(x));
}
+static ex sinh_conjugate(const ex & x)
+{
+ // conjugate(sinh(x))==sinh(conjugate(x))
+ return sinh(x.conjugate());
+}
+
REGISTER_FUNCTION(sinh, eval_func(sinh_eval).
evalf_func(sinh_evalf).
derivative_func(sinh_deriv).
real_part_func(sinh_real_part).
imag_part_func(sinh_imag_part).
+ conjugate_func(sinh_conjugate).
latex_name("\\sinh"));
//////////
return sinh(GiNaC::real_part(x))*sin(GiNaC::imag_part(x));
}
+static ex cosh_conjugate(const ex & x)
+{
+ // conjugate(cosh(x))==cosh(conjugate(x))
+ return cosh(x.conjugate());
+}
+
REGISTER_FUNCTION(cosh, eval_func(cosh_eval).
evalf_func(cosh_evalf).
derivative_func(cosh_deriv).
real_part_func(cosh_real_part).
imag_part_func(cosh_imag_part).
+ conjugate_func(cosh_conjugate).
latex_name("\\cosh"));
//////////
return tan(b)/(1+power(tanh(a),2)*power(tan(b),2));
}
+static ex tanh_conjugate(const ex & x)
+{
+ // conjugate(tanh(x))==tanh(conjugate(x))
+ return tanh(x.conjugate());
+}
+
REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
evalf_func(tanh_evalf).
derivative_func(tanh_deriv).
series_func(tanh_series).
real_part_func(tanh_real_part).
imag_part_func(tanh_imag_part).
+ conjugate_func(tanh_conjugate).
latex_name("\\tanh"));
//////////
return ((log(_ex1+arg)-log(_ex1-arg))*_ex1_2).series(rel, order, options);
// ...and the branch cuts (the discontinuity at the cut being just I*Pi)
if (!(options & series_options::suppress_branchcut)) {
- // method:
- // This is the branch cut: assemble the primitive series manually and
- // then add the corresponding complex step function.
- const symbol &s = ex_to<symbol>(rel.lhs());
- const ex &point = rel.rhs();
- const symbol foo;
- const ex replarg = series(atanh(arg), s==foo, order).subs(foo==point, subs_options::no_pattern);
+ // method:
+ // This is the branch cut: assemble the primitive series manually and
+ // then add the corresponding complex step function.
+ const symbol &s = ex_to<symbol>(rel.lhs());
+ const ex &point = rel.rhs();
+ const symbol foo;
+ const ex replarg = series(atanh(arg), s==foo, order).subs(foo==point, subs_options::no_pattern);
ex Order0correction = replarg.op(0)+csgn(I*arg)*Pi*I*_ex1_2;
if (arg_pt<_ex0)
Order0correction += log((arg_pt+_ex_1)/(arg_pt+_ex1))*_ex1_2;
else
Order0correction += log((arg_pt+_ex1)/(arg_pt+_ex_1))*_ex_1_2;
- epvector seq;
- seq.push_back(expair(Order0correction, _ex0));
- seq.push_back(expair(Order(_ex1), order));
- return series(replarg - pseries(rel, seq), rel, order);
+ epvector seq;
+ if (order > 0) {
+ seq.reserve(2);
+ seq.push_back(expair(Order0correction, _ex0));
+ }
+ seq.push_back(expair(Order(_ex1), order));
+ return series(replarg - pseries(rel, std::move(seq)), rel, order);
}
throw do_taylor();
}
git://www.ginac.de / ginac.git / blobdiff