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_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();
{
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();