[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 12a082a4b2d2b0ae15440a2474a64ffb30dc1002..f6550f6d734ba7e4dfa1798d6de3cee6595e05fb 100644 (file)
--- a/ginac/inifcns_trans.cpp
+++ b/ginac/inifcns_trans.cpp
@@ -4,7 +4,7 @@
  *  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
@@ -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
@@ -265,8 +284,12 @@ static ex log_series(const ex &arg,
                const ex &point = rel.rhs();
                const symbol foo;
                const ex replarg = series(log(arg), s==foo, order).subs(foo==point, subs_options::no_pattern);
-               epvector seq { expair(-I*csgn(arg*I)*Pi, _ex0),
-                              expair(Order(_ex1), order) };
+               epvector seq;
+               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, std::move(seq)), rel, order);
        }
        throw do_taylor();  // caught by function::series()
@@ -928,8 +951,12 @@ static ex atan_series(const ex &arg,
                        Order0correction += log((I*arg_pt+_ex_1)/(I*arg_pt+_ex1))*I*_ex_1_2;
                else
                        Order0correction += log((I*arg_pt+_ex1)/(I*arg_pt+_ex_1))*I*_ex1_2;
-               epvector seq { expair(Order0correction, _ex0),
-                              expair(Order(_ex1), 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();
@@ -1534,8 +1561,12 @@ static ex atanh_series(const ex &arg,
                        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 { expair(Order0correction, _ex0),
-                              expair(Order(_ex1), 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();