[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 <kisilv@maths.leeds.ac.uk>

diff --git a/check/exam_misc.cpp b/check/exam_misc.cpp
index 93b6f8e7d2de414eefb707babcb54b1ef6960c0f..8c28fb5344edcde971182e42616bb75b5f721381 100644 (file)
--- a/check/exam_misc.cpp
+++ b/check/exam_misc.cpp
@@ -255,6 +255,29 @@ static unsigned exam_subs_algebraic()
        return result;
 }
 
        return result;
 }
 

+/* Test suitable cases of the exponent power law: (e^t)^s=e^(ts). */
+static unsigned exam_exponent_power_law()
+{
+       unsigned result = 0;
+       symbol x("x");
+       realsymbol s("s");
+       possymbol t("t");
+
+       exmap pwr_exp =
+               { {pow(exp(x), 2), exp(2*x)},
+                 {pow(exp(s), t), exp(s*t)},
+                 {exp(x)*pow(exp(x),-1), 1} };
+
+       for (auto e : pwr_exp) {
+               if (! (e.first.is_equal(e.second)) ) {
+                       clog << "power of exponent  " << e.first << " produces error.\n";
+                       ++result;
+               }
+       }
+
+       return result;
+}
+

 unsigned exam_misc()
 {
        unsigned result = 0;
 unsigned exam_misc()
 {
        unsigned result = 0;


@@ -268,6 +291,7 @@ unsigned exam_misc()
        result += exam_subs(); cout << '.' << flush;
        result += exam_joris(); cout << '.' << flush;
        result += exam_subs_algebraic(); cout << '.' << flush;
        result += exam_subs(); cout << '.' << flush;
        result += exam_joris(); cout << '.' << flush;
        result += exam_subs_algebraic(); cout << '.' << flush;

+       result += exam_exponent_power_law(); cout << '.' << flush;

        
        return result;
 }
        
        return result;
 }

diff --git a/ginac/inifcns_trans.cpp b/ginac/inifcns_trans.cpp
index 49e30047f9f78485e84ff4d3650dfd737bc59ef9..f6550f6d734ba7e4dfa1798d6de3cee6595e05fb 100644 (file)
--- 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());
 }
 
        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).
 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).
                        real_part_func(exp_real_part).
                        imag_part_func(exp_imag_part).
                        conjugate_func(exp_conjugate).

+                       power_func(exp_power).

                        latex_name("\\exp"));
 
 //////////
                        latex_name("\\exp"));
 
 //////////