[PATCH 1/3] Automatic evaluation of (e^t)^s = e^(ts).

[ginac.git] / ginac / inifcns_trans.cpp

diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp
index 98e0caff36aaae386448293c36c4371837513f2e..f6550f6d734ba7e4dfa1798d6de3cee6595e05fb 100644 (file)
--- a/ginac/inifcns_trans.cpp
+++ b/ginac/inifcns_trans.cpp
@@ -4,7 +4,7 @@
  *  functions. */
 
 /*
- *  GiNaC Copyright (C) 1999-2016 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
@@ -128,6 +128,24 @@ static ex exp_conjugate(const ex & x)
        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).
@@ -135,6 +153,7 @@ REGISTER_FUNCTION(exp, eval_func(exp_eval).
                        real_part_func(exp_real_part).
                        imag_part_func(exp_imag_part).
                        conjugate_func(exp_conjugate).
+                       power_func(exp_power).
                        latex_name("\\exp"));
 
 //////////
@@ -197,7 +216,7 @@ static ex log_series(const ex &arg,
        // 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