#include "relational.h"
#include "pseries.h"
#include "symbol.h"
+#include "symmetry.h"
#include "utils.h"
namespace GiNaC {
//////////
-// Eta function: log(x*y) == log(x) + log(y) + eta(x,y).
+// Eta function: eta(x,y) == log(x*y) - log(x) - log(y).
//////////
-static ex eta_evalf(const ex & x, const ex & 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));
+ // It seems like we basically have to replicate the eval function here,
+ // since the expression might not be fully evaluated yet.
+ if (x.info(info_flags::positive) || y.info(info_flags::positive))
+ return _ex0();
+
+ if (x.info(info_flags::numeric) && y.info(info_flags::numeric)) {
+ const numeric nx = ex_to<numeric>(x);
+ const numeric ny = ex_to<numeric>(y);
+ const numeric nxy = ex_to<numeric>(x*y);
+ int cut = 0;
+ if (nx.is_real() && nx.is_negative())
+ cut -= 4;
+ if (ny.is_real() && ny.is_negative())
+ cut -= 4;
+ if (nxy.is_real() && nxy.is_negative())
+ cut += 4;
+ return evalf(I/4*Pi)*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
+ (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
+ }
+
+ return eta(x,y).hold();
}
-static ex eta_eval(const ex & x, const ex & y)
+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)) {
+ // trivial: eta(x,c) -> 0 if c is real and positive
+ if (x.info(info_flags::positive) || y.info(info_flags::positive))
+ return _ex0();
+
+ if (x.info(info_flags::numeric) && y.info(info_flags::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));
+ const numeric nx = ex_to<numeric>(x);
+ const numeric ny = ex_to<numeric>(y);
+ const numeric nxy = ex_to<numeric>(x*y);
+ int cut = 0;
+ if (nx.is_real() && nx.is_negative())
+ cut -= 4;
+ if (ny.is_real() && ny.is_negative())
+ cut -= 4;
+ if (nxy.is_real() && nxy.is_negative())
+ cut += 4;
+ return (I/4)*Pi*((csgn(-imag(nx))+1)*(csgn(-imag(ny))+1)*(csgn(imag(nxy))+1)-
+ (csgn(imag(nx))+1)*(csgn(imag(ny))+1)*(csgn(-imag(nxy))+1)+cut);
}
return eta(x,y).hold();
}
-static ex eta_series(const ex & arg1,
- const ex & arg2,
+static ex eta_series(const ex & x, const ex & y,
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"));
- }
+ const ex x_pt = x.subs(rel);
+ const ex y_pt = y.subs(rel);
+ if ((x_pt.info(info_flags::numeric) && x_pt.info(info_flags::negative)) ||
+ (y_pt.info(info_flags::numeric) && y_pt.info(info_flags::negative)) ||
+ ((x_pt*y_pt).info(info_flags::numeric) && (x_pt*y_pt).info(info_flags::negative)))
+ throw (std::domain_error("eta_series(): on discontinuity"));
epvector seq;
- seq.push_back(expair(eta(arg1_pt,arg2_pt), _ex0()));
+ seq.push_back(expair(eta(x_pt,y_pt), _ex0()));
return pseries(rel,seq);
}
REGISTER_FUNCTION(eta, eval_func(eta_eval).
evalf_func(eta_evalf).
- series_func(eta_series).
- latex_name("\\eta"));
+ series_func(eta_series).
+ latex_name("\\eta").
+ set_symmetry(sy_symm(0, 1)));
//////////
// method:
// construct series manually in a dummy symbol s
const symbol s;
- ex ser = zeta(2);
+ ex ser = zeta(_ex2());
// manually construct the primitive expansion
for (int i=1; i<order; ++i)
ser += pow(1-s,i) * (numeric(1,i)*(I*Pi+log(s-1)) - numeric(1,i*i));
series_func(Order_series).
latex_name("\\mathcal{O}"));
-//////////
-// Inert partial differentiation operator
-//////////
-
-ex Derivative_eval(const ex & f, const ex & l)
-{
- if (!is_ex_of_type(f, function))
- throw(std::invalid_argument("Derivative(): 1st argument must be a function"));
- if (!is_ex_of_type(l, lst))
- throw(std::invalid_argument("Derivative(): 2nd argument must be a list"));
-
-#if 0
- // Perform differentiations if possible
- const function &fcn = ex_to<function>(f);
- if (fcn.registered_functions()[fcn.get_serial()].has_derivative() && l.nops() > 0) {
-
- // The function actually seems to have a derivative, let's calculate it
- ex d = fcn.pderivative(ex_to_numeric(l.op(0)).to_int());
-
- // If this was the last differentiation, return the result
- if (l.nops() == 1)
- return d;
-
- // Otherwise recursively continue as long as the derivative is still
- // a function
- if (is_ex_of_type(d, function)) {
- lst l_copy = ex_to<lst>(l);
- l_copy.remove_first();
- return Derivative(d, l_copy);
- }
- }
-#endif
- return Derivative(f, l).hold();
-}
-
-REGISTER_FUNCTION(Derivative, eval_func(Derivative_eval).
- latex_name("\\mathrm{D}"));
-
//////////
// Solve linear system
//////////
if (eqns.info(info_flags::relation_equal)) {
if (!symbols.info(info_flags::symbol))
throw(std::invalid_argument("lsolve(): 2nd argument must be a symbol"));
- ex sol=lsolve(lst(eqns),lst(symbols));
+ const ex sol = lsolve(lst(eqns),lst(symbols));
GINAC_ASSERT(sol.nops()==1);
GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
matrix vars(symbols.nops(),1);
for (unsigned r=0; r<eqns.nops(); r++) {
- ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
+ const ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
ex linpart = eq;
for (unsigned c=0; c<symbols.nops(); c++) {
- ex co = eq.coeff(ex_to<symbol>(symbols.op(c)),1);
+ const ex co = eq.coeff(ex_to<symbol>(symbols.op(c)),1);
linpart -= co*symbols.op(c);
sys(r,c) = co;
}
git://www.ginac.de / ginac.git / blobdiff