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 REGISTER_FUNCTION(csgn, eval_func(csgn_eval).
111 evalf_func(csgn_evalf));
117 static ex Li2_eval(const ex & x)
121 if (x.is_equal(_ex1()))
122 return power(Pi, _ex2()) / _ex6();
123 if (x.is_equal(_ex_1()))
124 return -power(Pi, _ex2()) / _ex12();
125 return Li2(x).hold();
128 REGISTER_FUNCTION(Li2, eval_func(Li2_eval));
134 static ex Li3_eval(const ex & x)
138 return Li3(x).hold();
141 REGISTER_FUNCTION(Li3, eval_func(Li3_eval));
147 static ex factorial_evalf(const ex & x)
149 return factorial(x).hold();
152 static ex factorial_eval(const ex & x)
154 if (is_ex_exactly_of_type(x, numeric))
155 return factorial(ex_to_numeric(x));
157 return factorial(x).hold();
160 REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
161 evalf_func(factorial_evalf));
167 static ex binomial_evalf(const ex & x, const ex & y)
169 return binomial(x, y).hold();
172 static ex binomial_eval(const ex & x, const ex &y)
174 if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
175 return binomial(ex_to_numeric(x), ex_to_numeric(y));
177 return binomial(x, y).hold();
180 REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
181 evalf_func(binomial_evalf));
184 // Order term function (for truncated power series)
187 static ex Order_eval(const ex & x)
189 if (is_ex_exactly_of_type(x, numeric)) {
192 return Order(_ex1()).hold();
194 } else if (is_ex_exactly_of_type(x, mul)) {
196 mul *m = static_cast<mul *>(x.bp);
197 if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric)) {
200 return Order(x / m->op(m->nops() - 1)).hold();
203 return Order(x).hold();
206 static ex Order_series(const ex & x, const relational & r, int order)
208 // Just wrap the function into a pseries object
210 GINAC_ASSERT(is_ex_exactly_of_type(r.lhs(),symbol));
211 const symbol *s = static_cast<symbol *>(r.lhs().bp);
212 new_seq.push_back(expair(Order(_ex1()), numeric(min(x.ldegree(*s), order))));
213 return pseries(r, new_seq);
216 // Differentiation is handled in function::derivative because of its special requirements
218 REGISTER_FUNCTION(Order, eval_func(Order_eval).
219 series_func(Order_series));
222 // Inert partial differentiation operator
225 static ex Derivative_eval(const ex & f, const ex & l)
227 if (!is_ex_exactly_of_type(f, function)) {
228 throw(std::invalid_argument("Derivative(): 1st argument must be a function"));
230 if (!is_ex_exactly_of_type(l, lst)) {
231 throw(std::invalid_argument("Derivative(): 2nd argument must be a list"));
233 return Derivative(f, l).hold();
236 REGISTER_FUNCTION(Derivative, eval_func(Derivative_eval));
239 // Solve linear system
242 ex lsolve(const ex &eqns, const ex &symbols)
244 // solve a system of linear equations
245 if (eqns.info(info_flags::relation_equal)) {
246 if (!symbols.info(info_flags::symbol)) {
247 throw(std::invalid_argument("lsolve: 2nd argument must be a symbol"));
249 ex sol=lsolve(lst(eqns),lst(symbols));
251 GINAC_ASSERT(sol.nops()==1);
252 GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
254 return sol.op(0).op(1); // return rhs of first solution
258 if (!eqns.info(info_flags::list)) {
259 throw(std::invalid_argument("lsolve: 1st argument must be a list"));
261 for (unsigned i=0; i<eqns.nops(); i++) {
262 if (!eqns.op(i).info(info_flags::relation_equal)) {
263 throw(std::invalid_argument("lsolve: 1st argument must be a list of equations"));
266 if (!symbols.info(info_flags::list)) {
267 throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
269 for (unsigned i=0; i<symbols.nops(); i++) {
270 if (!symbols.op(i).info(info_flags::symbol)) {
271 throw(std::invalid_argument("lsolve: 2nd argument must be a list of symbols"));
275 // build matrix from equation system
276 matrix sys(eqns.nops(),symbols.nops());
277 matrix rhs(eqns.nops(),1);
278 matrix vars(symbols.nops(),1);
280 for (unsigned r=0; r<eqns.nops(); r++) {
281 ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
283 for (unsigned c=0; c<symbols.nops(); c++) {
284 ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
285 linpart -= co*symbols.op(c);
288 linpart=linpart.expand();
289 rhs.set(r,0,-linpart);
292 // test if system is linear and fill vars matrix
293 for (unsigned i=0; i<symbols.nops(); i++) {
294 vars.set(i,0,symbols.op(i));
295 if (sys.has(symbols.op(i)))
296 throw(std::logic_error("lsolve: system is not linear"));
297 if (rhs.has(symbols.op(i)))
298 throw(std::logic_error("lsolve: system is not linear"));
301 //matrix solution=sys.solve(rhs);
304 solution = sys.fraction_free_elim(vars,rhs);
305 } catch (const runtime_error & e) {
306 // probably singular matrix (or other error)
307 // return empty solution list
308 // cerr << e.what() << endl;
312 // return a list of equations
313 if (solution.cols()!=1) {
314 throw(std::runtime_error("lsolve: strange number of columns returned from matrix::solve"));
316 if (solution.rows()!=symbols.nops()) {
317 cout << "symbols.nops()=" << symbols.nops() << endl;
318 cout << "solution.rows()=" << solution.rows() << endl;
319 throw(std::runtime_error("lsolve: strange number of rows returned from matrix::solve"));
322 // return list of the form lst(var1==sol1,var2==sol2,...)
324 for (unsigned i=0; i<symbols.nops(); i++) {
325 sollist.append(symbols.op(i)==solution(i,0));
331 /** non-commutative power. */
332 ex ncpower(const ex &basis, unsigned exponent)
340 for (unsigned i=0; i<exponent; ++i) {
347 /** Force inclusion of functions from initcns_gamma and inifcns_zeta
348 * for static lib (so ginsh will see them). */
349 unsigned force_include_tgamma = function_index_tgamma;
350 unsigned force_include_zeta1 = function_index_zeta1;
352 #ifndef NO_NAMESPACE_GINAC
354 #endif // ndef NO_NAMESPACE_GINAC