#include "power.h"
#include "relational.h"
#include "symbol.h"
+#include "pseries.h"
#include "utils.h"
#ifndef NO_NAMESPACE_GINAC
return power(x, _ex_1());
}
+/*static ex log_series(const ex &x, const relational &rel, int order)
+{
+ const ex x_pt = x.subs(rel);
+ if (!x_pt.info(info_flags::negative) && !x_pt.is_zero())
+ throw do_taylor(); // caught by function::series()
+ // now we either have to care for the branch cut or the branch point:
+ if (x_pt.is_zero()) { // branch point: return a plain log(x).
+ epvector seq;
+ seq.push_back(expair(log(x), _ex0()));
+ return pseries(rel, seq);
+ } // the branch cut:
+ const ex point = rel.rhs();
+ const symbol *s = static_cast<symbol *>(rel.lhs().bp);
+ const symbol foo;
+ // compute the formal series:
+ ex replx = series(log(x),*s==foo,order).subs(foo==point);
+ epvector seq;
+ // FIXME: this is probably off by 2 or so:
+ seq.push_back(expair(-I*csgn(x*I)*Pi,_ex0()));
+ seq.push_back(expair(Order(_ex1()),order));
+ return series(replx + pseries(rel, seq),rel,order);
+}*/
+
+static ex log_series(const ex &x, const relational &r, int order)
+{
+ if (x.subs(r).is_zero()) {
+ epvector seq;
+ seq.push_back(expair(log(x), _ex0()));
+ return pseries(r, seq);
+ } else
+ throw do_taylor();
+}
+
REGISTER_FUNCTION(log, eval_func(log_eval).
evalf_func(log_evalf).
- derivative_func(log_deriv));
+ derivative_func(log_deriv).
+ series_func(log_series));
//////////
// sine (trigonometric function)
if (z.is_equal(_num25())) // tan(5/12*Pi) -> 2+sqrt(3)
return sign*(power(_ex3(),_ex1_2())+_ex2());
if (z.is_equal(_num30())) // tan(Pi/2) -> infinity
- throw (std::domain_error("tan_eval(): infinity"));
+ throw (std::domain_error("tan_eval(): simple pole"));
}
if (is_ex_exactly_of_type(x, function)) {
return (_ex1()+power(tan(x),_ex2()));
}
-static ex tan_series(const ex & x, const symbol & s, const ex & pt, int order)
+static ex tan_series(const ex &x, const relational &rel, int order)
{
// method:
// Taylor series where there is no pole falls back to tan_deriv.
// On a pole simply expand sin(x)/cos(x).
- const ex x_pt = x.subs(s==pt);
+ const ex x_pt = x.subs(rel);
if (!(2*x_pt/Pi).info(info_flags::odd))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole
- return (sin(x)/cos(x)).series(s, pt, order+2);
+ return (sin(x)/cos(x)).series(rel, order+2);
}
REGISTER_FUNCTION(tan, eval_func(tan_eval).
return _ex1()-power(tanh(x),_ex2());
}
-static ex tanh_series(const ex & x, const symbol & s, const ex & pt, int order)
+static ex tanh_series(const ex &x, const relational &rel, int order)
{
// method:
// Taylor series where there is no pole falls back to tanh_deriv.
// On a pole simply expand sinh(x)/cosh(x).
- const ex x_pt = x.subs(s==pt);
+ const ex x_pt = x.subs(rel);
if (!(2*I*x_pt/Pi).info(info_flags::odd))
throw do_taylor(); // caught by function::series()
// if we got here we have to care for a simple pole
- return (sinh(x)/cosh(x)).series(s, pt, order+2);
+ return (sinh(x)/cosh(x)).series(rel, order+2);
}
REGISTER_FUNCTION(tanh, eval_func(tanh_eval).
if (x.is_zero())
return _ex0();
// atanh({+|-}1) -> throw
- if (x.is_equal(_ex1()) || x.is_equal(_ex1()))
- throw (std::domain_error("atanh_eval(): infinity"));
+ if (x.is_equal(_ex1()) || x.is_equal(_ex_1()))
+ throw (std::domain_error("atanh_eval(): logarithmic pole"));
// atanh(float) -> float
if (!x.info(info_flags::crational))
return atanh_evalf(x);