* Implementation of GiNaC's initially known functions. */
/*
- * GiNaC Copyright (C) 1999-2011 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2014 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
return -arg.imag_part();
}
+static bool func_arg_info(const ex & arg, unsigned inf)
+{
+ // for some functions we can return the info() of its argument
+ // (think of conjugate())
+ switch (inf) {
+ case info_flags::polynomial:
+ case info_flags::integer_polynomial:
+ case info_flags::cinteger_polynomial:
+ case info_flags::rational_polynomial:
+ case info_flags::real:
+ case info_flags::rational:
+ case info_flags::integer:
+ case info_flags::crational:
+ case info_flags::cinteger:
+ case info_flags::even:
+ case info_flags::odd:
+ case info_flags::prime:
+ case info_flags::crational_polynomial:
+ case info_flags::rational_function:
+ case info_flags::algebraic:
+ case info_flags::positive:
+ case info_flags::negative:
+ case info_flags::nonnegative:
+ case info_flags::posint:
+ case info_flags::negint:
+ case info_flags::nonnegint:
+ case info_flags::has_indices:
+ return arg.info(inf);
+ }
+ return false;
+}
+
+static bool conjugate_info(const ex & arg, unsigned inf)
+{
+ return func_arg_info(arg, inf);
+}
+
REGISTER_FUNCTION(conjugate_function, eval_func(conjugate_eval).
evalf_func(conjugate_evalf).
+ info_func(conjugate_info).
print_func<print_latex>(conjugate_print_latex).
conjugate_func(conjugate_conjugate).
real_part_func(conjugate_real_part).
if (is_ex_the_function(arg, abs))
return arg;
+ if (is_ex_the_function(arg, exp))
+ return exp(arg.op(0).real_part());
+
+ if (is_exactly_a<power>(arg)) {
+ const ex& base = arg.op(0);
+ const ex& exponent = arg.op(1);
+ if (base.info(info_flags::positive) || exponent.info(info_flags::real))
+ return pow(abs(base), exponent.real_part());
+ }
+
+ if (is_ex_the_function(arg, conjugate_function))
+ return abs(arg.op(0));
+
+ if (is_ex_the_function(arg, step))
+ return arg;
+
return abs(arg).hold();
}
+static ex abs_expand(const ex & arg, unsigned options)
+{
+ if ((options & expand_options::expand_transcendental)
+ && is_exactly_a<mul>(arg)) {
+ exvector prodseq;
+ prodseq.reserve(arg.nops());
+ for (const_iterator i = arg.begin(); i != arg.end(); ++i) {
+ if (options & expand_options::expand_function_args)
+ prodseq.push_back(abs(i->expand(options)));
+ else
+ prodseq.push_back(abs(*i));
+ }
+ return (new mul(prodseq))->setflag(status_flags::dynallocated | status_flags::expanded);
+ }
+
+ if (options & expand_options::expand_function_args)
+ return abs(arg.expand(options)).hold();
+ else
+ return abs(arg).hold();
+}
+
static void abs_print_latex(const ex & arg, const print_context & c)
{
c.s << "{|"; arg.print(c); c.s << "|}";
static ex abs_conjugate(const ex & arg)
{
- return abs(arg);
+ return abs(arg).hold();
}
static ex abs_real_part(const ex & arg)
static ex abs_power(const ex & arg, const ex & exp)
{
- if (arg.is_equal(arg.conjugate()) && is_a<numeric>(exp) && ex_to<numeric>(exp).is_even())
+ if (arg.is_equal(arg.conjugate()) && ((is_a<numeric>(exp) && ex_to<numeric>(exp).is_even())
+ || exp.info(info_flags::even)))
return power(arg, exp);
else
return power(abs(arg), exp).hold();
}
+bool abs_info(const ex & arg, unsigned inf)
+{
+ switch (inf) {
+ case info_flags::integer:
+ case info_flags::even:
+ case info_flags::odd:
+ case info_flags::prime:
+ return arg.info(inf);
+ case info_flags::nonnegint:
+ return arg.info(info_flags::integer);
+ case info_flags::nonnegative:
+ case info_flags::real:
+ return true;
+ case info_flags::negative:
+ return false;
+ case info_flags::positive:
+ return arg.info(info_flags::positive) || arg.info(info_flags::negative);
+ case info_flags::has_indices: {
+ if (arg.info(info_flags::has_indices))
+ return true;
+ else
+ return false;
+ }
+ }
+ return false;
+}
+
REGISTER_FUNCTION(abs, eval_func(abs_eval).
evalf_func(abs_evalf).
+ expand_func(abs_expand).
+ info_func(abs_info).
print_func<print_latex>(abs_print_latex).
print_func<print_csrc_float>(abs_print_csrc_float).
print_func<print_csrc_double>(abs_print_csrc_float).
{
if (is_a<numeric>(exp) && exp.info(info_flags::positive) && ex_to<numeric>(exp).is_integer()) {
if (ex_to<numeric>(exp).is_odd())
- return csgn(arg);
+ return csgn(arg).hold();
else
return power(csgn(arg), _ex2).hold();
} else
static ex eta_conjugate(const ex & x, const ex & y)
{
- return -eta(x, y);
+ return -eta(x, y).hold();
}
static ex eta_real_part(const ex & x, const ex & y)
// conjugate(Li2(x))==Li2(conjugate(x)) unless on the branch cuts which
// run along the positive real axis beginning at 1.
if (x.info(info_flags::negative)) {
- return Li2(x);
+ return Li2(x).hold();
}
if (is_exactly_a<numeric>(x) &&
(!x.imag_part().is_zero() || x < *_num1_p)) {
if (n.info(info_flags::numeric)) {
// zetaderiv(0,x) -> zeta(x)
if (n.is_zero())
- return zeta(x);
+ return zeta(x).hold();
}
return zetaderiv(n, x).hold();