>From 9a652134fbaae7888f62888809caf5a10c07e8c6 Mon Sep 17 00:00:00 2001 From: "Vladimir V. Kisil" Date: Mon, 6 Apr 2020 13:34:04 +0100 Subject: [PATCH 1/3] Automatic evaluation of (e^t)^s = e^(ts). If it safe to evaluate (e^t)^s = e^(ts) at least in two cases: a) t and s are reals, the respective formula can be found in any analysis textbook. b) if s is an integer, then the ambiguity of t up to the term 2*Pi*k does not cause a different value. Signed-off-by: Vladimir V. Kisil --- ginac/inifcns_trans.cpp | 19 +++++++++++++++++++ 1 file changed, 19 insertions(+) diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp index d4ec2d67..868e0389 100644 --- a/ginac/inifcns_trans.cpp +++ b/ginac/inifcns_trans.cpp @@ -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")); ////////// -- 2.26.2