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));
72 static ex Li2_eval(const ex & x)
76 if (x.is_equal(_ex1()))
77 return power(Pi, _ex2()) / _ex6();
78 if (x.is_equal(_ex_1()))
79 return -power(Pi, _ex2()) / _ex12();
83 REGISTER_FUNCTION(Li2, eval_func(Li2_eval));
89 static ex Li3_eval(const ex & x)
96 REGISTER_FUNCTION(Li3, eval_func(Li3_eval));
102 static ex factorial_evalf(const ex & x)
104 return factorial(x).hold();
107 static ex factorial_eval(const ex & x)
109 if (is_ex_exactly_of_type(x, numeric))
110 return factorial(ex_to_numeric(x));
112 return factorial(x).hold();
115 REGISTER_FUNCTION(factorial, eval_func(factorial_eval).
116 evalf_func(factorial_evalf));
122 static ex binomial_evalf(const ex & x, const ex & y)
124 return binomial(x, y).hold();
127 static ex binomial_eval(const ex & x, const ex &y)
129 if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
130 return binomial(ex_to_numeric(x), ex_to_numeric(y));
132 return binomial(x, y).hold();
135 REGISTER_FUNCTION(binomial, eval_func(binomial_eval).
136 evalf_func(binomial_evalf));
139 // Order term function (for truncated power series)
142 static ex Order_eval(const ex & x)
144 if (is_ex_exactly_of_type(x, numeric)) {
147 return Order(_ex1()).hold();
149 } else if (is_ex_exactly_of_type(x, mul)) {
151 mul *m = static_cast<mul *>(x.bp);
152 if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric)) {
155 return Order(x / m->op(m->nops() - 1)).hold();
158 return Order(x).hold();
161 static ex Order_series(const ex & x, const symbol & s, const ex & point, int order)
163 // Just wrap the function into a pseries object
165 new_seq.push_back(expair(Order(_ex1()), numeric(min(x.ldegree(s), order))));
166 return pseries(s, point, new_seq);
169 // Differentiation is handled in function::derivative because of its special requirements
171 REGISTER_FUNCTION(Order, eval_func(Order_eval).
172 series_func(Order_series));
175 // Inert differentiation
178 static ex Diff_eval(const ex & f, const ex & x)
180 return Diff(f, x).hold();
183 static ex Diff_deriv(const ex & f, const ex & x, unsigned deriv_param)
185 GINAC_ASSERT(deriv_param == 0 || deriv_param == 1);
186 if (deriv_param == 1)
187 return Diff(Diff(f, x), x);
192 REGISTER_FUNCTION(Diff, eval_func(Diff_eval).
193 derivative_func(Diff_deriv));
196 // Inert partial differentiation operator
199 static ex Derivative_eval(const ex & f, const ex & n)
201 if (is_ex_exactly_of_type(n, numeric) && ex_to_numeric(n).is_nonneg_integer()) {
202 unsigned i = ex_to_numeric(n).to_int();
203 if (is_ex_exactly_of_type(f, function)) {
204 if (i < f.nops() && is_ex_exactly_of_type(f.op(i), symbol))
205 return Diff(f, f.op(i));
208 return Derivative(f, n).hold();
211 REGISTER_FUNCTION(Derivative, eval_func(Derivative_eval));
214 // Solve linear system
217 ex lsolve(const ex &eqns, const ex &symbols)
219 // solve a system of linear equations
220 if (eqns.info(info_flags::relation_equal)) {
221 if (!symbols.info(info_flags::symbol)) {
222 throw(std::invalid_argument("lsolve: 2nd argument must be a symbol"));
224 ex sol=lsolve(lst(eqns),lst(symbols));
226 GINAC_ASSERT(sol.nops()==1);
227 GINAC_ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
229 return sol.op(0).op(1); // return rhs of first solution
233 if (!eqns.info(info_flags::list)) {
234 throw(std::invalid_argument("lsolve: 1st argument must be a list"));
236 for (unsigned i=0; i<eqns.nops(); i++) {
237 if (!eqns.op(i).info(info_flags::relation_equal)) {
238 throw(std::invalid_argument("lsolve: 1st argument must be a list of equations"));
241 if (!symbols.info(info_flags::list)) {
242 throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
244 for (unsigned i=0; i<symbols.nops(); i++) {
245 if (!symbols.op(i).info(info_flags::symbol)) {
246 throw(std::invalid_argument("lsolve: 2nd argument must be a list of symbols"));
250 // build matrix from equation system
251 matrix sys(eqns.nops(),symbols.nops());
252 matrix rhs(eqns.nops(),1);
253 matrix vars(symbols.nops(),1);
255 for (unsigned r=0; r<eqns.nops(); r++) {
256 ex eq = eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
258 for (unsigned c=0; c<symbols.nops(); c++) {
259 ex co = eq.coeff(ex_to_symbol(symbols.op(c)),1);
260 linpart -= co*symbols.op(c);
263 linpart=linpart.expand();
264 rhs.set(r,0,-linpart);
267 // test if system is linear and fill vars matrix
268 for (unsigned i=0; i<symbols.nops(); i++) {
269 vars.set(i,0,symbols.op(i));
270 if (sys.has(symbols.op(i)))
271 throw(std::logic_error("lsolve: system is not linear"));
272 if (rhs.has(symbols.op(i)))
273 throw(std::logic_error("lsolve: system is not linear"));
276 //matrix solution=sys.solve(rhs);
279 solution = sys.fraction_free_elim(vars,rhs);
280 } catch (const runtime_error & e) {
281 // probably singular matrix (or other error)
282 // return empty solution list
283 // cerr << e.what() << endl;
287 // return a list of equations
288 if (solution.cols()!=1) {
289 throw(std::runtime_error("lsolve: strange number of columns returned from matrix::solve"));
291 if (solution.rows()!=symbols.nops()) {
292 cout << "symbols.nops()=" << symbols.nops() << endl;
293 cout << "solution.rows()=" << solution.rows() << endl;
294 throw(std::runtime_error("lsolve: strange number of rows returned from matrix::solve"));
297 // return list of the form lst(var1==sol1,var2==sol2,...)
299 for (unsigned i=0; i<symbols.nops(); i++) {
300 sollist.append(symbols.op(i)==solution(i,0));
306 /** non-commutative power. */
307 ex ncpower(const ex &basis, unsigned exponent)
315 for (unsigned i=0; i<exponent; ++i) {
322 /** Force inclusion of functions from initcns_gamma and inifcns_zeta
323 * for static lib (so ginsh will see them). */
324 unsigned force_include_gamma = function_index_gamma;
325 unsigned force_include_zeta1 = function_index_zeta1;
327 #ifndef NO_NAMESPACE_GINAC
329 #endif // ndef NO_NAMESPACE_GINAC