Expansion rules for exp(), log(), and abs().
[ginac.git] / ginac / inifcns_trans.cpp
index 10a36758f43001f6c02774531522c7fd2667c7c2..6ee0a23b0c388d1146123cb2c4654536f0442b3e 100644 (file)
@@ -24,6 +24,8 @@
 #include "inifcns.h"
 #include "ex.h"
 #include "constant.h"
+#include "add.h"
+#include "mul.h"
 #include "numeric.h"
 #include "power.h"
 #include "operators.h"
@@ -81,6 +83,27 @@ static ex exp_eval(const ex & x)
        return exp(x).hold();
 }
 
+static ex exp_expand(const ex & arg, unsigned options)
+{
+       ex exp_arg;
+       if (options & expand_options::expand_function_args)
+               exp_arg = arg.expand(options);
+       else
+               exp_arg=arg;
+
+       if ((options & expand_options::expand_transcendental)
+               && is_exactly_a<add>(exp_arg)) {
+               exvector prodseq;
+               prodseq.reserve(exp_arg.nops());
+               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 exp(exp_arg).hold();
+}
+
 static ex exp_deriv(const ex & x, unsigned deriv_param)
 {
        GINAC_ASSERT(deriv_param==0);
@@ -107,6 +130,7 @@ static ex exp_conjugate(const ex & x)
 
 REGISTER_FUNCTION(exp, eval_func(exp_eval).
                        evalf_func(exp_evalf).
+                       expand_func(exp_expand).
                        derivative_func(exp_deriv).
                        real_part_func(exp_real_part).
                        imag_part_func(exp_imag_part).
@@ -265,6 +289,53 @@ static ex log_imag_part(const ex & x)
        return atan2(GiNaC::imag_part(x), GiNaC::real_part(x));
 }
 
+static ex log_expand(const ex & arg, unsigned options)
+{
+       if ((options & expand_options::expand_transcendental)
+               && is_exactly_a<mul>(arg) && !arg.info(info_flags::indefinite)) {
+               exvector sumseq;
+               exvector prodseq;
+               sumseq.reserve(arg.nops());
+               prodseq.reserve(arg.nops());
+               bool possign=true;
+
+               // searching for positive/negative factors
+               for (const_iterator i = arg.begin(); i != arg.end(); ++i) {
+                       ex e;
+                       if (options & expand_options::expand_function_args)
+                               e=i->expand(options);
+                       else
+                               e=*i;
+                       if (e.info(info_flags::positive))
+                               sumseq.push_back(log(e));
+                       else if (e.info(info_flags::negative)) {
+                               sumseq.push_back(log(-e));
+                               possign = !possign;
+                       } else
+                               prodseq.push_back(e);
+               }
+
+               if (sumseq.size() > 0) {
+                       ex newarg;
+                       if (options & expand_options::expand_function_args)
+                               newarg=((possign?_ex1:_ex_1)*mul(prodseq)).expand(options);
+                       else {
+                               newarg=(possign?_ex1:_ex_1)*mul(prodseq);
+                               ex_to<basic>(newarg).setflag(status_flags::purely_indefinite);
+                       }
+                       return add(sumseq)+log(newarg);
+               } else {
+                       if (!(options & expand_options::expand_function_args))
+                               ex_to<basic>(arg).setflag(status_flags::purely_indefinite);
+               }
+       }
+
+       if (options & expand_options::expand_function_args)
+               return log(arg.expand(options)).hold();
+       else
+               return log(arg).hold();
+}
+
 static ex log_conjugate(const ex & x)
 {
        // conjugate(log(x))==log(conjugate(x)) unless on the branch cut which
@@ -281,6 +352,7 @@ static ex log_conjugate(const ex & x)
 
 REGISTER_FUNCTION(log, eval_func(log_eval).
                        evalf_func(log_evalf).
+                       expand_func(log_expand).
                        derivative_func(log_deriv).
                        series_func(log_series).
                        real_part_func(log_real_part).