3 * Implementation of GiNaC's initially known functions. */
6 * GiNaC Copyright (C) 1999-2000 Johannes Gutenberg University Mainz, Germany
8 * This program is free software; you can redistribute it and/or modify
9 * it under the terms of the GNU General Public License as published by
10 * the Free Software Foundation; either version 2 of the License, or
11 * (at your option) any later version.
13 * This program is distributed in the hope that it will be useful,
14 * but WITHOUT ANY WARRANTY; without even the implied warranty of
15 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
16 * GNU General Public License for more details.
18 * You should have received a copy of the GNU General Public License
19 * along with this program; if not, write to the Free Software
20 * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
35 #include "relational.h"
40 #ifndef NO_NAMESPACE_GINAC
42 #endif // ndef NO_NAMESPACE_GINAC
48 static ex abs_evalf(const ex & x)
54 return abs(ex_to_numeric(x));
57 static ex abs_eval(const ex & x)
59 if (is_ex_exactly_of_type(x, numeric))
60 return abs(ex_to_numeric(x));
65 REGISTER_FUNCTION(abs, eval_func(abs_eval).
66 evalf_func(abs_evalf));
73 static ex csgn_evalf(const ex & x)
77 END_TYPECHECK(csgn(x))
79 return csgn(ex_to_numeric(x));
82 static ex csgn_eval(const ex & x)
84 if (is_ex_exactly_of_type(x, numeric))
85 return csgn(ex_to_numeric(x));
87 if (is_ex_exactly_of_type(x, mul)) {
88 numeric oc = ex_to_numeric(x.op(x.nops()-1));
91 // csgn(42*x) -> csgn(x)
92 return csgn(x/oc).hold();
94 // csgn(-42*x) -> -csgn(x)
95 return -csgn(x/oc).hold();
97 if (oc.real().is_zero()) {
99 // csgn(42*I*x) -> csgn(I*x)
100 return csgn(I*x/oc).hold();
102 // csgn(-42*I*x) -> -csgn(I*x)
103 return -csgn(I*x/oc).hold();
107 return csgn(x).hold();
110 static ex csgn_series(const ex & x, const relational & rel, int order)
112 const ex x_pt = x.subs(rel);
113 if (x_pt.info(info_flags::numeric)) {
114 if (ex_to_numeric(x_pt).real().is_zero())
115 throw (std::domain_error("csgn_series(): on imaginary axis"));
117 seq.push_back(expair(csgn(x_pt), _ex0()));
118 return pseries(rel,seq);
121 seq.push_back(expair(csgn(x_pt), _ex0()));
122 return pseries(rel,seq);
125 REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
126 evalf_func(csgn_evalf).
127 series_func(csgn_series));
133 static ex Li2_eval(const ex & x)
137 if (x.is_equal(_ex1()))
138 return power(Pi, _ex2()) / _ex6();
139 if (x.is_equal(_ex_1()))
140 return -power(Pi, _ex2()) / _ex12();
141 return Li2(x).hold();
144 REGISTER_FUNCTION(Li2, eval_func(Li2_eval));
150 static ex Li3_eval(const ex & x)
154 return Li3(x).hold();
157 REGISTER_FUNCTION(Li3, eval_func(Li3_eval));
163 static ex factorial_evalf(const ex & x)
165 return factorial(x).hold();
168 static ex factorial_eval(const ex & x)
170 if (is_ex_exactly_of_type(x, numeric))
171 return factorial(ex_to_numeric(x));
173 return factorial(x).hold();
176 REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
177 evalf_func(factorial_evalf));
183 static ex binomial_evalf(const ex & x, const ex & y)
185 return binomial(x, y).hold();
188 static ex binomial_eval(const ex & x, const ex &y)
190 if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
191 return binomial(ex_to_numeric(x), ex_to_numeric(y));
193 return binomial(x, y).hold();
196 REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
197 evalf_func(binomial_evalf));
200 // Order term function (for truncated power series)
203 static ex Order_eval(const ex & x)
205 if (is_ex_exactly_of_type(x, numeric)) {
208 return Order(_ex1()).hold();
210 } else if (is_ex_exactly_of_type(x, mul)) {
212 mul *m = static_cast<mul *>(x.bp);
213 if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric)) {
216 return Order(x / m->op(m->nops() - 1)).hold();
219 return Order(x).hold();
222 static ex Order_series(const ex & x, const relational & r, int order)
224 // Just wrap the function into a pseries object
226 GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
227 const symbol *s = static_cast<symbol *>(r.lhs().bp);
228 new_seq.push_back(expair(Order(_ex1()), numeric(min(x.ldegree(*s), order))));
229 return pseries(r, new_seq);
232 // Differentiation is handled in function::derivative because of its special requirements
234 REGISTER_FUNCTION(Order, eval_func(Order_eval).
235 series_func(Order_series));
238 // Inert partial differentiation operator
241 static ex Derivative_eval(const ex & f, const ex & l)
243 if (!is_ex_exactly_of_type(f, function)) {
244 throw(std::invalid_argument("Derivative(): 1st argument must be a function"));
246 if (!is_ex_exactly_of_type(l, lst)) {
247 throw(std::invalid_argument("Derivative(): 2nd argument must be a list"));
249 return Derivative(f, l).hold();
252 REGISTER_FUNCTION(Derivative, eval_func(Derivative_eval));
255 // Solve linear system
258 ex lsolve(const ex &eqns, const ex &symbols)
260 // solve a system of linear equations
261 if (eqns.info(info_flags::relation_equal)) {
262 if (!symbols.info(info_flags::symbol)) {
263 throw(std::invalid_argument("lsolve: 2nd argument must be a symbol"));
265 ex sol=lsolve(lst(eqns),lst(symbols));
267 GINAC_ASSERT(sol.nops()==1);
268 GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
270 return sol.op(0).op(1); // return rhs of first solution
274 if (!eqns.info(info_flags::list)) {
275 throw(std::invalid_argument("lsolve: 1st argument must be a list"));
277 for (unsigned i=0; i<eqns.nops(); i++) {
278 if (!eqns.op(i).info(info_flags::relation_equal)) {
279 throw(std::invalid_argument("lsolve: 1st argument must be a list of equations"));
282 if (!symbols.info(info_flags::list)) {
283 throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
285 for (unsigned i=0; i<symbols.nops(); i++) {
286 if (!symbols.op(i).info(info_flags::symbol)) {
287 throw(std::invalid_argument("lsolve: 2nd argument must be a list of symbols"));
291 // build matrix from equation system
292 matrix sys(eqns.nops(),symbols.nops());
293 matrix rhs(eqns.nops(),1);
294 matrix vars(symbols.nops(),1);
296 for (unsigned r=0; r<eqns.nops(); r++) {
297 ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
299 for (unsigned c=0; c<symbols.nops(); c++) {
300 ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
301 linpart -= co*symbols.op(c);
304 linpart=linpart.expand();
305 rhs.set(r,0,-linpart);
308 // test if system is linear and fill vars matrix
309 for (unsigned i=0; i<symbols.nops(); i++) {
310 vars.set(i,0,symbols.op(i));
311 if (sys.has(symbols.op(i)))
312 throw(std::logic_error("lsolve: system is not linear"));
313 if (rhs.has(symbols.op(i)))
314 throw(std::logic_error("lsolve: system is not linear"));
317 //matrix solution=sys.solve(rhs);
320 solution = sys.fraction_free_elim(vars,rhs);
321 } catch (const runtime_error & e) {
322 // probably singular matrix (or other error)
323 // return empty solution list
324 // cerr << e.what() << endl;
328 // return a list of equations
329 if (solution.cols()!=1) {
330 throw(std::runtime_error("lsolve: strange number of columns returned from matrix::solve"));
332 if (solution.rows()!=symbols.nops()) {
333 cout << "symbols.nops()=" << symbols.nops() << endl;
334 cout << "solution.rows()=" << solution.rows() << endl;
335 throw(std::runtime_error("lsolve: strange number of rows returned from matrix::solve"));
338 // return list of the form lst(var1==sol1,var2==sol2,...)
340 for (unsigned i=0; i<symbols.nops(); i++) {
341 sollist.append(symbols.op(i)==solution(i,0));
347 /** non-commutative power. */
348 ex ncpower(const ex &basis, unsigned exponent)
356 for (unsigned i=0; i<exponent; ++i) {
363 /** Force inclusion of functions from initcns_gamma and inifcns_zeta
364 * for static lib (so ginsh will see them). */
365 unsigned force_include_tgamma = function_index_tgamma;
366 unsigned force_include_zeta1 = function_index_zeta1;
368 #ifndef NO_NAMESPACE_GINAC
370 #endif // ndef NO_NAMESPACE_GINAC