return arg;
}
+static ex conjugate_real_part(const ex & arg)
+{
+ return arg.real_part();
+}
+
+static ex conjugate_imag_part(const ex & arg)
+{
+ return -arg.imag_part();
+}
+
REGISTER_FUNCTION(conjugate_function, eval_func(conjugate_eval).
evalf_func(conjugate_evalf).
print_func<print_latex>(conjugate_print_latex).
conjugate_func(conjugate_conjugate).
+ real_part_func(conjugate_real_part).
+ imag_part_func(conjugate_imag_part).
set_name("conjugate","conjugate"));
+//////////
+// real part
+//////////
+
+static ex real_part_evalf(const ex & arg)
+{
+ if (is_exactly_a<numeric>(arg)) {
+ return ex_to<numeric>(arg).real();
+ }
+ return real_part_function(arg).hold();
+}
+
+static ex real_part_eval(const ex & arg)
+{
+ return arg.real_part();
+}
+
+static void real_part_print_latex(const ex & arg, const print_context & c)
+{
+ c.s << "\\Re"; arg.print(c); c.s << "";
+}
+
+static ex real_part_conjugate(const ex & arg)
+{
+ return real_part_function(arg).hold();
+}
+
+static ex real_part_real_part(const ex & arg)
+{
+ return real_part_function(arg).hold();
+}
+
+static ex real_part_imag_part(const ex & arg)
+{
+ return 0;
+}
+
+REGISTER_FUNCTION(real_part_function, eval_func(real_part_eval).
+ evalf_func(real_part_evalf).
+ print_func<print_latex>(real_part_print_latex).
+ conjugate_func(real_part_conjugate).
+ real_part_func(real_part_real_part).
+ imag_part_func(real_part_imag_part).
+ set_name("real_part","real_part"));
+
+//////////
+// imag part
+//////////
+
+static ex imag_part_evalf(const ex & arg)
+{
+ if (is_exactly_a<numeric>(arg)) {
+ return ex_to<numeric>(arg).imag();
+ }
+ return imag_part_function(arg).hold();
+}
+
+static ex imag_part_eval(const ex & arg)
+{
+ return arg.imag_part();
+}
+
+static void imag_part_print_latex(const ex & arg, const print_context & c)
+{
+ c.s << "\\Im"; arg.print(c); c.s << "";
+}
+
+static ex imag_part_conjugate(const ex & arg)
+{
+ return imag_part_function(arg).hold();
+}
+
+static ex imag_part_real_part(const ex & arg)
+{
+ return imag_part_function(arg).hold();
+}
+
+static ex imag_part_imag_part(const ex & arg)
+{
+ return 0;
+}
+
+REGISTER_FUNCTION(imag_part_function, eval_func(imag_part_eval).
+ evalf_func(imag_part_evalf).
+ print_func<print_latex>(imag_part_print_latex).
+ conjugate_func(imag_part_conjugate).
+ real_part_func(imag_part_real_part).
+ imag_part_func(imag_part_imag_part).
+ set_name("imag_part","imag_part"));
+
//////////
// absolute value
//////////
{
if (is_exactly_a<numeric>(arg))
return abs(ex_to<numeric>(arg));
- else
- return abs(arg).hold();
+
+ if (arg.info(info_flags::nonnegative))
+ return arg;
+
+ if (is_ex_the_function(arg, abs))
+ return arg;
+
+ return abs(arg).hold();
}
static void abs_print_latex(const ex & arg, const print_context & c)
return abs(arg);
}
+static ex abs_real_part(const ex & arg)
+{
+ return abs(arg).hold();
+}
+
+static ex abs_imag_part(const ex& arg)
+{
+ return 0;
+}
+
static ex abs_power(const ex & arg, const ex & exp)
{
if (arg.is_equal(arg.conjugate()) && is_a<numeric>(exp) && ex_to<numeric>(exp).is_even())
print_func<print_csrc_float>(abs_print_csrc_float).
print_func<print_csrc_double>(abs_print_csrc_float).
conjugate_func(abs_conjugate).
+ real_part_func(abs_real_part).
+ imag_part_func(abs_imag_part).
power_func(abs_power));
+//////////
+// Step function
+//////////
+
+static ex step_evalf(const ex & arg)
+{
+ if (is_exactly_a<numeric>(arg))
+ return step(ex_to<numeric>(arg));
+
+ return step(arg).hold();
+}
+
+static ex step_eval(const ex & arg)
+{
+ if (is_exactly_a<numeric>(arg))
+ return step(ex_to<numeric>(arg));
+
+ else if (is_exactly_a<mul>(arg) &&
+ is_exactly_a<numeric>(arg.op(arg.nops()-1))) {
+ numeric oc = ex_to<numeric>(arg.op(arg.nops()-1));
+ if (oc.is_real()) {
+ if (oc > 0)
+ // step(42*x) -> step(x)
+ return step(arg/oc).hold();
+ else
+ // step(-42*x) -> step(-x)
+ return step(-arg/oc).hold();
+ }
+ if (oc.real().is_zero()) {
+ if (oc.imag() > 0)
+ // step(42*I*x) -> step(I*x)
+ return step(I*arg/oc).hold();
+ else
+ // step(-42*I*x) -> step(-I*x)
+ return step(-I*arg/oc).hold();
+ }
+ }
+
+ return step(arg).hold();
+}
+
+static ex step_series(const ex & arg,
+ const relational & rel,
+ int order,
+ unsigned options)
+{
+ const ex arg_pt = arg.subs(rel, subs_options::no_pattern);
+ if (arg_pt.info(info_flags::numeric)
+ && ex_to<numeric>(arg_pt).real().is_zero()
+ && !(options & series_options::suppress_branchcut))
+ throw (std::domain_error("step_series(): on imaginary axis"));
+
+ epvector seq;
+ seq.push_back(expair(step(arg_pt), _ex0));
+ return pseries(rel,seq);
+}
+
+static ex step_conjugate(const ex& arg)
+{
+ return step(arg).hold();
+}
+
+static ex step_real_part(const ex& arg)
+{
+ return step(arg).hold();
+}
+
+static ex step_imag_part(const ex& arg)
+{
+ return 0;
+}
+
+REGISTER_FUNCTION(step, eval_func(step_eval).
+ evalf_func(step_evalf).
+ series_func(step_series).
+ conjugate_func(step_conjugate).
+ real_part_func(step_real_part).
+ imag_part_func(step_imag_part));
+
//////////
// Complex sign
//////////
static ex csgn_conjugate(const ex& arg)
{
- return csgn(arg);
+ return csgn(arg).hold();
}
+static ex csgn_real_part(const ex& arg)
+{
+ return csgn(arg).hold();
+}
+
+static ex csgn_imag_part(const ex& arg)
+{
+ return 0;
+}
+
+static ex csgn_power(const ex & arg, const ex & exp)
+{
+ if (is_a<numeric>(exp) && exp.info(info_flags::positive) && ex_to<numeric>(exp).is_integer()) {
+ if (ex_to<numeric>(exp).is_odd())
+ return csgn(arg);
+ else
+ return power(csgn(arg), _ex2).hold();
+ } else
+ return power(csgn(arg), exp).hold();
+}
+
+
REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
evalf_func(csgn_evalf).
series_func(csgn_series).
- conjugate_func(csgn_conjugate));
+ conjugate_func(csgn_conjugate).
+ real_part_func(csgn_real_part).
+ imag_part_func(csgn_imag_part).
+ power_func(csgn_power));
//////////
static ex eta_conjugate(const ex & x, const ex & y)
{
- return -eta(x,y);
+ return -eta(x, y);
+}
+
+static ex eta_real_part(const ex & x, const ex & y)
+{
+ return 0;
+}
+
+static ex eta_imag_part(const ex & x, const ex & y)
+{
+ return -I*eta(x, y).hold();
}
REGISTER_FUNCTION(eta, eval_func(eta_eval).
series_func(eta_series).
latex_name("\\eta").
set_symmetry(sy_symm(0, 1)).
- conjugate_func(eta_conjugate));
+ conjugate_func(eta_conjugate).
+ real_part_func(eta_real_part).
+ imag_part_func(eta_imag_part));
//////////
static ex factorial_conjugate(const ex & x)
{
- return factorial(x);
+ return factorial(x).hold();
+}
+
+static ex factorial_real_part(const ex & x)
+{
+ return factorial(x).hold();
+}
+
+static ex factorial_imag_part(const ex & x)
+{
+ return 0;
}
REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
evalf_func(factorial_evalf).
print_func<print_dflt>(factorial_print_dflt_latex).
print_func<print_latex>(factorial_print_dflt_latex).
- conjugate_func(factorial_conjugate));
+ conjugate_func(factorial_conjugate).
+ real_part_func(factorial_real_part).
+ imag_part_func(factorial_imag_part));
//////////
// binomial
// function, also complex conjugation should be changed (or rather, deleted).
static ex binomial_conjugate(const ex & x, const ex & y)
{
- return binomial(x,y);
+ return binomial(x,y).hold();
+}
+
+static ex binomial_real_part(const ex & x, const ex & y)
+{
+ return binomial(x,y).hold();
+}
+
+static ex binomial_imag_part(const ex & x, const ex & y)
+{
+ return 0;
}
REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
evalf_func(binomial_evalf).
- conjugate_func(binomial_conjugate));
+ conjugate_func(binomial_conjugate).
+ real_part_func(binomial_real_part).
+ imag_part_func(binomial_imag_part));
//////////
// Order term function (for truncated power series)
static ex Order_conjugate(const ex & x)
{
- return Order(x);
+ return Order(x).hold();
+}
+
+static ex Order_real_part(const ex & x)
+{
+ return Order(x).hold();
+}
+
+static ex Order_imag_part(const ex & x)
+{
+ if(x.info(info_flags::real))
+ return 0;
+ return Order(x).hold();
}
// Differentiation is handled in function::derivative because of its special requirements
REGISTER_FUNCTION(Order, eval_func(Order_eval).
series_func(Order_series).
latex_name("\\mathcal{O}").
- conjugate_func(Order_conjugate));
+ conjugate_func(Order_conjugate).
+ real_part_func(Order_real_part).
+ imag_part_func(Order_imag_part));
//////////
// Solve linear system
git://www.ginac.de / ginac.git / blobdiff