// absolute value
//////////
-static ex abs_evalf(const ex & x)
+static ex abs_evalf(const ex & arg)
{
BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(abs(x))
+ TYPECHECK(arg,numeric)
+ END_TYPECHECK(abs(arg))
- return abs(ex_to_numeric(x));
+ return abs(ex_to_numeric(arg));
}
-static ex abs_eval(const ex & x)
+static ex abs_eval(const ex & arg)
{
- if (is_ex_exactly_of_type(x, numeric))
- return abs(ex_to_numeric(x));
+ if (is_ex_exactly_of_type(arg, numeric))
+ return abs(ex_to_numeric(arg));
else
- return abs(x).hold();
+ return abs(arg).hold();
}
REGISTER_FUNCTION(abs, eval_func(abs_eval).
// Complex sign
//////////
-static ex csgn_evalf(const ex & x)
+static ex csgn_evalf(const ex & arg)
{
BEGIN_TYPECHECK
- TYPECHECK(x,numeric)
- END_TYPECHECK(csgn(x))
+ TYPECHECK(arg,numeric)
+ END_TYPECHECK(csgn(arg))
- return csgn(ex_to_numeric(x));
+ return csgn(ex_to_numeric(arg));
}
-static ex csgn_eval(const ex & x)
+static ex csgn_eval(const ex & arg)
{
- if (is_ex_exactly_of_type(x, numeric))
- return csgn(ex_to_numeric(x));
+ if (is_ex_exactly_of_type(arg, numeric))
+ return csgn(ex_to_numeric(arg));
- else if (is_ex_exactly_of_type(x, mul)) {
- numeric oc = ex_to_numeric(x.op(x.nops()-1));
+ else if (is_ex_exactly_of_type(arg, mul)) {
+ numeric oc = ex_to_numeric(arg.op(arg.nops()-1));
if (oc.is_real()) {
if (oc > 0)
// csgn(42*x) -> csgn(x)
- return csgn(x/oc).hold();
+ return csgn(arg/oc).hold();
else
// csgn(-42*x) -> -csgn(x)
- return -csgn(x/oc).hold();
+ return -csgn(arg/oc).hold();
}
if (oc.real().is_zero()) {
if (oc.imag() > 0)
// csgn(42*I*x) -> csgn(I*x)
- return csgn(I*x/oc).hold();
+ return csgn(I*arg/oc).hold();
else
// csgn(-42*I*x) -> -csgn(I*x)
- return -csgn(I*x/oc).hold();
+ return -csgn(I*arg/oc).hold();
}
}
- return csgn(x).hold();
+ return csgn(arg).hold();
}
static ex csgn_series(const ex & arg,
const relational & rel,
int order,
- bool branchcut)
+ unsigned options)
{
const ex arg_pt = arg.subs(rel);
- if (arg_pt.info(info_flags::numeric)) {
- if (ex_to_numeric(arg_pt).real().is_zero())
- throw (std::domain_error("csgn_series(): on imaginary axis"));
- epvector seq;
- seq.push_back(expair(csgn(arg_pt), _ex0()));
- return pseries(rel,seq);
- }
+ if (arg_pt.info(info_flags::numeric) &&
+ ex_to_numeric(arg_pt).real().is_zero())
+ throw (std::domain_error("csgn_series(): on imaginary axis"));
+
epvector seq;
seq.push_back(expair(csgn(arg_pt), _ex0()));
return pseries(rel,seq);
evalf_func(csgn_evalf).
series_func(csgn_series));
+
+//////////
+// Eta function: log(x*y) == log(x) + log(y) + eta(x,y).
+//////////
+
+static ex eta_evalf(const ex & x, const ex & y)
+{
+ BEGIN_TYPECHECK
+ TYPECHECK(x,numeric)
+ TYPECHECK(y,numeric)
+ END_TYPECHECK(eta(x,y))
+
+ numeric xim = imag(ex_to_numeric(x));
+ numeric yim = imag(ex_to_numeric(y));
+ numeric xyim = imag(ex_to_numeric(x*y));
+ return evalf(I/4*Pi)*((csgn(-xim)+1)*(csgn(-yim)+1)*(csgn(xyim)+1)-(csgn(xim)+1)*(csgn(yim)+1)*(csgn(-xyim)+1));
+}
+
+static ex eta_eval(const ex & x, const ex & y)
+{
+ if (is_ex_exactly_of_type(x, numeric) &&
+ is_ex_exactly_of_type(y, numeric)) {
+ // don't call eta_evalf here because it would call Pi.evalf()!
+ numeric xim = imag(ex_to_numeric(x));
+ numeric yim = imag(ex_to_numeric(y));
+ numeric xyim = imag(ex_to_numeric(x*y));
+ return (I/4)*Pi*((csgn(-xim)+1)*(csgn(-yim)+1)*(csgn(xyim)+1)-(csgn(xim)+1)*(csgn(yim)+1)*(csgn(-xyim)+1));
+ }
+
+ return eta(x,y).hold();
+}
+
+static ex eta_series(const ex & arg1,
+ const ex & arg2,
+ const relational & rel,
+ int order,
+ unsigned options)
+{
+ const ex arg1_pt = arg1.subs(rel);
+ const ex arg2_pt = arg2.subs(rel);
+ if (ex_to_numeric(arg1_pt).imag().is_zero() ||
+ ex_to_numeric(arg2_pt).imag().is_zero() ||
+ ex_to_numeric(arg1_pt*arg2_pt).imag().is_zero()) {
+ throw (std::domain_error("eta_series(): on discontinuity"));
+ }
+ epvector seq;
+ seq.push_back(expair(eta(arg1_pt,arg2_pt), _ex0()));
+ return pseries(rel,seq);
+}
+
+REGISTER_FUNCTION(eta, eval_func(eta_eval).
+ evalf_func(eta_evalf).
+ series_func(eta_series));
+
+
//////////
// dilogarithm
//////////
return -log(1-x)/x;
}
-static ex Li2_series(const ex &x, const relational &rel, int order, bool branchcut)
+static ex Li2_series(const ex &x, const relational &rel, int order, unsigned options)
{
const ex x_pt = x.subs(rel);
if (x_pt.info(info_flags::numeric)) {
return ser.series(rel, order);
}
// third special case: x real, >=1 (branch cut)
- if (ex_to_numeric(x_pt).is_real() && ex_to_numeric(x_pt)>1) {
+ if (!(options & series_options::suppress_branchcut) &&
+ ex_to_numeric(x_pt).is_real() && ex_to_numeric(x_pt)>1) {
// method:
// This is the branch cut: assemble the primitive series manually
// and then add the corresponding complex step function.
// compute the intermediate terms:
ex replarg = series(Li2(x), *s==foo, order);
for (unsigned i=1; i<replarg.nops()-1; ++i)
- seq.push_back(expair((replarg.op(i)/power(*s-foo,i)).series(foo==point,1,branchcut).op(0).subs(foo==*s),i));
+ seq.push_back(expair((replarg.op(i)/power(*s-foo,i)).series(foo==point,1,options).op(0).subs(foo==*s),i));
// append an order term:
seq.push_back(expair(Order(_ex1()), replarg.nops()-1));
return pseries(rel, seq);
return Order(x).hold();
}
-static ex Order_series(const ex & x, const relational & r, int order, bool branchcut)
+static ex Order_series(const ex & x, const relational & r, int order, unsigned options)
{
// Just wrap the function into a pseries object
epvector new_seq;
git://www.ginac.de / ginac.git / blobdiff