return abs(x).hold();
}
-REGISTER_FUNCTION(abs, abs_eval, abs_evalf, NULL, NULL);
+REGISTER_FUNCTION(abs, eval_func(abs_eval).
+ evalf_func(abs_evalf));
+
+
+//////////
+// Complex sign
+//////////
+
+static ex csgn_evalf(const ex & x)
+{
+ BEGIN_TYPECHECK
+ TYPECHECK(x,numeric)
+ END_TYPECHECK(csgn(x))
+
+ return csgn(ex_to_numeric(x));
+}
+
+static ex csgn_eval(const ex & x)
+{
+ if (is_ex_exactly_of_type(x, numeric))
+ return csgn(ex_to_numeric(x));
+
+ if (is_ex_exactly_of_type(x, mul)) {
+ numeric oc = ex_to_numeric(x.op(x.nops()-1));
+ if (oc.is_real()) {
+ if (oc > 0)
+ // csgn(42*x) -> csgn(x)
+ return csgn(x/oc).hold();
+ else
+ // csgn(-42*x) -> -csgn(x)
+ return -csgn(x/oc).hold();
+ }
+ if (oc.real().is_zero()) {
+ if (oc.imag() > 0)
+ // csgn(42*I*x) -> csgn(I*x)
+ return csgn(I*x/oc).hold();
+ else
+ // csgn(-42*I*x) -> -csgn(I*x)
+ return -csgn(I*x/oc).hold();
+ }
+ }
+
+ return csgn(x).hold();
+}
+
+static ex csgn_series(const ex & x, const relational & rel, int order)
+{
+ const ex x_pt = x.subs(rel);
+ if (x_pt.info(info_flags::numeric)) {
+ if (ex_to_numeric(x_pt).real().is_zero())
+ throw (std::domain_error("csgn_series(): on imaginary axis"));
+ epvector seq;
+ seq.push_back(expair(csgn(x_pt), _ex0()));
+ return pseries(rel,seq);
+ }
+ epvector seq;
+ seq.push_back(expair(csgn(x_pt), _ex0()));
+ return pseries(rel,seq);
+}
+
+REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
+ evalf_func(csgn_evalf).
+ series_func(csgn_series));
//////////
// dilogarithm
return Li2(x).hold();
}
-REGISTER_FUNCTION(Li2, Li2_eval, NULL, NULL, NULL);
+REGISTER_FUNCTION(Li2, eval_func(Li2_eval));
//////////
// trilogarithm
return Li3(x).hold();
}
-REGISTER_FUNCTION(Li3, Li3_eval, NULL, NULL, NULL);
+REGISTER_FUNCTION(Li3, eval_func(Li3_eval));
//////////
// factorial
return factorial(x).hold();
}
-REGISTER_FUNCTION(factorial, factorial_eval, factorial_evalf, NULL, NULL);
+REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
+ evalf_func(factorial_evalf));
//////////
// binomial
return binomial(x, y).hold();
}
-REGISTER_FUNCTION(binomial, binomial_eval, binomial_evalf, NULL, NULL);
+REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
+ evalf_func(binomial_evalf));
//////////
// Order term function (for truncated power series)
return Order(x).hold();
}
-static ex Order_series(const ex & x, const symbol & s, const ex & point, int order)
+static ex Order_series(const ex & x, const relational & r, int order)
{
// Just wrap the function into a pseries object
epvector new_seq;
- new_seq.push_back(expair(Order(_ex1()), numeric(min(x.ldegree(s), order))));
- return pseries(s, point, new_seq);
+ GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
+ const symbol *s = static_cast<symbol *>(r.lhs().bp);
+ new_seq.push_back(expair(Order(_ex1()), numeric(min(x.ldegree(*s), order))));
+ return pseries(r, new_seq);
+}
+
+// Differentiation is handled in function::derivative because of its special requirements
+
+REGISTER_FUNCTION(Order, eval_func(Order_eval).
+ series_func(Order_series));
+
+//////////
+// Inert partial differentiation operator
+//////////
+
+static ex Derivative_eval(const ex & f, const ex & l)
+{
+ if (!is_ex_exactly_of_type(f, function)) {
+ throw(std::invalid_argument("Derivative(): 1st argument must be a function"));
+ }
+ if (!is_ex_exactly_of_type(l, lst)) {
+ throw(std::invalid_argument("Derivative(): 2nd argument must be a list"));
+ }
+ return Derivative(f, l).hold();
}
-REGISTER_FUNCTION(Order, Order_eval, NULL, NULL, Order_series);
+REGISTER_FUNCTION(Derivative, eval_func(Derivative_eval));
//////////
// Solve linear system
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
- ex linpart=eq;
+ 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);
+ ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
linpart -= co*symbols.op(c);
sys.set(r,c,co);
}
// test if system is linear and fill vars matrix
for (unsigned i=0; i<symbols.nops(); i++) {
vars.set(i,0,symbols.op(i));
- if (sys.has(symbols.op(i))) {
+ if (sys.has(symbols.op(i)))
throw(std::logic_error("lsolve: system is not linear"));
- }
- if (rhs.has(symbols.op(i))) {
+ if (rhs.has(symbols.op(i)))
throw(std::logic_error("lsolve: system is not linear"));
- }
}
//matrix solution=sys.solve(rhs);
matrix solution;
try {
- solution=sys.fraction_free_elim(vars,rhs);
+ solution = sys.fraction_free_elim(vars,rhs);
} catch (const runtime_error & e) {
// probably singular matrix (or other error)
// return empty solution list
/** Force inclusion of functions from initcns_gamma and inifcns_zeta
* for static lib (so ginsh will see them). */
-unsigned force_include_gamma = function_index_gamma;
+unsigned force_include_tgamma = function_index_tgamma;
unsigned force_include_zeta1 = function_index_zeta1;
#ifndef NO_NAMESPACE_GINAC