* functions. */
/*
- * GiNaC Copyright (C) 1999-2010 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2011 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 (new mul(prodseq))->setflag(status_flags::dynallocated | 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;
}
-
+
+ // log(p^a) -> a*log(p), if p>0 and a is real
+ if (is_exactly_a<power>(x) && x.op(0).info(info_flags::positive) && x.op(1).info(info_flags::real)) {
+ return x.op(1)*log(x.op(0));
+ }
+
return log(x).hold();
}
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).
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"));
//////////