* functions. */
/*
- * GiNaC Copyright (C) 1999-2015 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2020 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
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 dynallocate<mul>(prodseq).setflag(status_flags::expanded);
}
return exp(exp_arg).hold();
return exp(x.conjugate());
}
+static ex exp_power(const ex & x, const ex & a)
+{
+ /*
+ * The power law (e^x)^a=e^(x*a) is used in two cases:
+ * a) a is an integer and x may be complex;
+ * b) both x and a are reals.
+ * Negative a is excluded to keep automatic simplifications like exp(x)/exp(x)=1.
+ */
+ if (a.info(info_flags::nonnegative)
+ && (a.info(info_flags::integer) || (x.info(info_flags::real) && a.info(info_flags::real))))
+ return exp(x*a);
+ else if (a.info(info_flags::negative)
+ && (a.info(info_flags::integer) || (x.info(info_flags::real) && a.info(info_flags::real))))
+ return power(exp(-x*a), _ex_1).hold();
+
+ return power(exp(x), a).hold();
+}
+
REGISTER_FUNCTION(exp, eval_func(exp_eval).
evalf_func(exp_evalf).
expand_func(exp_expand).
real_part_func(exp_real_part).
imag_part_func(exp_imag_part).
conjugate_func(exp_conjugate).
+ power_func(exp_power).
latex_name("\\exp"));
//////////
// maybe substitution of rel into arg fails because of a pole
try {
arg_pt = arg.subs(rel, subs_options::no_pattern);
- } catch (pole_error) {
+ } catch (pole_error &) {
must_expand_arg = true;
}
// or we are at the branch point anyways
// 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()
}
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 ((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