* Implementation of GiNaC's initially known functions. */
/*
- * GiNaC Copyright (C) 1999 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
#include "numeric.h"
#include "power.h"
#include "relational.h"
-#include "series.h"
+#include "pseries.h"
#include "symbol.h"
+#include "utils.h"
+
+#ifndef NO_NAMESPACE_GINAC
+namespace GiNaC {
+#endif // ndef NO_NAMESPACE_GINAC
+
+//////////
+// absolute value
+//////////
+
+static ex abs_evalf(const ex & x)
+{
+ BEGIN_TYPECHECK
+ TYPECHECK(x,numeric)
+ END_TYPECHECK(abs(x))
+
+ return abs(ex_to_numeric(x));
+}
+
+static ex abs_eval(const ex & x)
+{
+ if (is_ex_exactly_of_type(x, numeric))
+ return abs(ex_to_numeric(x));
+ else
+ return abs(x).hold();
+}
+
+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));
+
+ else 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
//////////
-ex Li2_eval(ex const & x)
+static ex Li2_eval(const ex & x)
{
if (x.is_zero())
return x;
- if (x.is_equal(exONE()))
- return power(Pi, 2) / 6;
- if (x.is_equal(exMINUSONE()))
- return -power(Pi, 2) / 12;
+ if (x.is_equal(_ex1()))
+ return power(Pi, _ex2()) / _ex6();
+ if (x.is_equal(_ex_1()))
+ return -power(Pi, _ex2()) / _ex12();
return Li2(x).hold();
}
-REGISTER_FUNCTION(Li2, Li2_eval, NULL, NULL, NULL);
+REGISTER_FUNCTION(Li2, eval_func(Li2_eval));
//////////
// trilogarithm
//////////
-ex Li3_eval(ex const & x)
+static ex Li3_eval(const ex & x)
{
if (x.is_zero())
return x;
return Li3(x).hold();
}
-REGISTER_FUNCTION(Li3, Li3_eval, NULL, NULL, NULL);
+REGISTER_FUNCTION(Li3, eval_func(Li3_eval));
//////////
// factorial
//////////
-ex factorial_evalf(ex const & x)
+static ex factorial_evalf(const ex & x)
{
return factorial(x).hold();
}
-ex factorial_eval(ex const & x)
+static ex factorial_eval(const ex & x)
{
if (is_ex_exactly_of_type(x, numeric))
return factorial(ex_to_numeric(x));
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
//////////
-ex binomial_evalf(ex const & x, ex const & y)
+static ex binomial_evalf(const ex & x, const ex & y)
{
return binomial(x, y).hold();
}
-ex binomial_eval(ex const & x, ex const &y)
+static ex binomial_eval(const ex & x, const ex &y)
{
if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
return binomial(ex_to_numeric(x), ex_to_numeric(y));
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)
//////////
-ex Order_eval(ex const & x)
+static ex Order_eval(const ex & x)
{
if (is_ex_exactly_of_type(x, numeric)) {
// O(c)=O(1)
- return Order(exONE()).hold();
+ return Order(_ex1()).hold();
} else if (is_ex_exactly_of_type(x, mul)) {
return Order(x).hold();
}
-ex Order_series(ex const & x, symbol const & s, ex const & point, int order)
+static ex Order_series(const ex & x, const relational & r, int order)
{
- // Just wrap the function into a series object
+ // Just wrap the function into a pseries object
epvector new_seq;
- new_seq.push_back(expair(Order(exONE()), numeric(min(x.ldegree(s), order))));
- return series(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);
}
-REGISTER_FUNCTION(Order, Order_eval, NULL, NULL, Order_series);
+// Differentiation is handled in function::derivative because of its special requirements
+
+REGISTER_FUNCTION(Order, eval_func(Order_eval).
+ series_func(Order_series));
-/** linear solve. */
-ex lsolve(ex const &eqns, ex const &symbols)
+//////////
+// 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(Derivative, eval_func(Derivative_eval));
+
+//////////
+// Solve linear system
+//////////
+
+ex lsolve(const ex &eqns, const ex &symbols)
{
// solve a system of linear equations
if (eqns.info(info_flags::relation_equal)) {
}
ex sol=lsolve(lst(eqns),lst(symbols));
- ASSERT(sol.nops()==1);
- ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
+ GINAC_ASSERT(sol.nops()==1);
+ GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
return sol.op(0).op(1); // return rhs of first solution
}
if (!eqns.info(info_flags::list)) {
throw(std::invalid_argument("lsolve: 1st argument must be a list"));
}
- for (int i=0; i<eqns.nops(); i++) {
+ 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"));
}
if (!symbols.info(info_flags::list)) {
throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
}
- for (int i=0; i<symbols.nops(); i++) {
+ 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"));
}
matrix sys(eqns.nops(),symbols.nops());
matrix rhs(eqns.nops(),1);
matrix vars(symbols.nops(),1);
-
- for (int r=0; r<eqns.nops(); r++) {
- ex eq=eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
- ex linpart=eq;
- for (int c=0; c<symbols.nops(); c++) {
- ex co=eq.coeff(ex_to_symbol(symbols.op(c)),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;
+ for (unsigned c=0; c<symbols.nops(); c++) {
+ 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 (int i=0; i<symbols.nops(); i++) {
+ 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);
- } catch (runtime_error const & e) {
+ solution = sys.fraction_free_elim(vars,rhs);
+ } catch (const runtime_error & e) {
// probably singular matrix (or other error)
// return empty solution list
- cerr << e.what() << endl;
+ // cerr << e.what() << endl;
return lst();
}
// return list of the form lst(var1==sol1,var2==sol2,...)
lst sollist;
- for (int i=0; i<symbols.nops(); i++) {
+ for (unsigned i=0; i<symbols.nops(); i++) {
sollist.append(symbols.op(i)==solution(i,0));
}
}
/** non-commutative power. */
-ex ncpower(ex const &basis, unsigned exponent)
+ex ncpower(const ex &basis, unsigned exponent)
{
if (exponent==0) {
- return exONE();
+ return _ex1();
}
exvector v;
return ncmul(v,1);
}
+
+/** Force inclusion of functions from initcns_gamma and inifcns_zeta
+ * for static lib (so ginsh will see them). */
+unsigned force_include_tgamma = function_index_tgamma;
+unsigned force_include_zeta1 = function_index_zeta1;
+
+#ifndef NO_NAMESPACE_GINAC
+} // namespace GiNaC
+#endif // ndef NO_NAMESPACE_GINAC
git://www.ginac.de / ginac.git / blobdiff