// 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,
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
//////////
static ex Order_eval(const ex & x)
{
- if (is_ex_exactly_of_type(x, numeric)) {
-
- // O(c)=O(1)
- return Order(_ex1()).hold();
-
- } else if (is_ex_exactly_of_type(x, mul)) {
-
- mul *m = static_cast<mul *>(x.bp);
- if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric)) {
-
- // O(c*expr)=O(expr)
- return Order(x / m->op(m->nops() - 1)).hold();
- }
- }
- return Order(x).hold();
+ if (is_ex_exactly_of_type(x, numeric)) {
+ // O(c) -> O(1) or 0
+ if (!x.is_zero())
+ return Order(_ex1()).hold();
+ else
+ return _ex0();
+ } else if (is_ex_exactly_of_type(x, mul)) {
+ mul *m = static_cast<mul *>(x.bp);
+ // O(c*expr) -> O(expr)
+ if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric))
+ return Order(x / m->op(m->nops() - 1)).hold();
+ }
+ return Order(x).hold();
}
static ex Order_series(const ex & x, const relational & r, int order, unsigned options)
// solve a system of linear equations
if (eqns.info(info_flags::relation_equal)) {
if (!symbols.info(info_flags::symbol))
- throw(std::invalid_argument("lsolve: 2nd argument must be a symbol"));
+ throw(std::invalid_argument("lsolve(): 2nd argument must be a symbol"));
ex sol=lsolve(lst(eqns),lst(symbols));
GINAC_ASSERT(sol.nops()==1);
// syntax checks
if (!eqns.info(info_flags::list)) {
- throw(std::invalid_argument("lsolve: 1st argument must be a list"));
+ throw(std::invalid_argument("lsolve(): 1st argument must be a list"));
}
for (unsigned i=0; i<eqns.nops(); i++) {
if (!eqns.op(i).info(info_flags::relation_equal)) {
- throw(std::invalid_argument("lsolve: 1st argument must be a list of equations"));
+ throw(std::invalid_argument("lsolve(): 1st argument must be a list of equations"));
}
}
if (!symbols.info(info_flags::list)) {
- throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
+ throw(std::invalid_argument("lsolve(): 2nd argument must be a list"));
}
for (unsigned i=0; i<symbols.nops(); i++) {
if (!symbols.op(i).info(info_flags::symbol)) {
- throw(std::invalid_argument("lsolve: 2nd argument must be a list of symbols"));
+ throw(std::invalid_argument("lsolve(): 2nd argument must be a list of symbols"));
}
}
linpart -= co*symbols.op(c);
sys.set(r,c,co);
}
- linpart=linpart.expand();
+ linpart = linpart.expand();
rhs.set(r,0,-linpart);
}
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.solve(vars,rhs);
} catch (const runtime_error & e) {
- // probably singular matrix (or other error)
- // return empty solution list
- // cerr << e.what() << endl;
+ // Probably singular matrix or otherwise overdetermined system:
+ // It is consistent to return an empty list
return lst();
- }
+ }
+ GINAC_ASSERT(solution.cols()==1);
+ GINAC_ASSERT(solution.rows()==symbols.nops());
- // return a list of equations
- if (solution.cols()!=1) {
- throw(std::runtime_error("lsolve: strange number of columns returned from matrix::solve"));
- }
- if (solution.rows()!=symbols.nops()) {
- cout << "symbols.nops()=" << symbols.nops() << endl;
- cout << "solution.rows()=" << solution.rows() << endl;
- throw(std::runtime_error("lsolve: strange number of rows returned from matrix::solve"));
- }
-
- // return list of the form lst(var1==sol1,var2==sol2,...)
+ // return list of equations of the form lst(var1==sol1,var2==sol2,...)
lst sollist;
- for (unsigned i=0; i<symbols.nops(); i++) {
+ for (unsigned i=0; i<symbols.nops(); i++)
sollist.append(symbols.op(i)==solution(i,0));
- }
return sollist;
}
git://www.ginac.de / ginac.git / blobdiff