3 * Implementation of GiNaC's initially known functions. */
6 * GiNaC Copyright (C) 1999 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"
43 ex Li2_eval(ex const & x)
47 if (x.is_equal(exONE()))
48 return power(Pi, 2) / 6;
49 if (x.is_equal(exMINUSONE()))
50 return -power(Pi, 2) / 12;
54 REGISTER_FUNCTION(Li2, Li2_eval, NULL, NULL, NULL);
60 ex Li3_eval(ex const & x)
67 REGISTER_FUNCTION(Li3, Li3_eval, NULL, NULL, NULL);
73 ex factorial_evalf(ex const & x)
75 return factorial(x).hold();
78 ex factorial_eval(ex const & x)
80 if (is_ex_exactly_of_type(x, numeric))
81 return factorial(ex_to_numeric(x));
83 return factorial(x).hold();
86 REGISTER_FUNCTION(factorial, factorial_eval, factorial_evalf, NULL, NULL);
92 ex binomial_evalf(ex const & x, ex const & y)
94 return binomial(x, y).hold();
97 ex binomial_eval(ex const & x, ex const &y)
99 if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
100 return binomial(ex_to_numeric(x), ex_to_numeric(y));
102 return binomial(x, y).hold();
105 REGISTER_FUNCTION(binomial, binomial_eval, binomial_evalf, NULL, NULL);
108 // Order term function (for truncated power series)
111 ex Order_eval(ex const & x)
113 if (is_ex_exactly_of_type(x, numeric)) {
116 return Order(exONE()).hold();
118 } else if (is_ex_exactly_of_type(x, mul)) {
120 mul *m = static_cast<mul *>(x.bp);
121 if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric)) {
124 return Order(x / m->op(m->nops() - 1)).hold();
127 return Order(x).hold();
130 ex Order_series(ex const & x, symbol const & s, ex const & point, int order)
132 // Just wrap the function into a series object
134 new_seq.push_back(expair(Order(exONE()), numeric(min(x.ldegree(s), order))));
135 return series(s, point, new_seq);
138 REGISTER_FUNCTION(Order, Order_eval, NULL, NULL, Order_series);
141 ex lsolve(ex const &eqns, ex const &symbols)
143 // solve a system of linear equations
144 if (eqns.info(info_flags::relation_equal)) {
145 if (!symbols.info(info_flags::symbol)) {
146 throw(std::invalid_argument("lsolve: 2nd argument must be a symbol"));
148 ex sol=lsolve(lst(eqns),lst(symbols));
150 ASSERT(sol.nops()==1);
151 ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
153 return sol.op(0).op(1); // return rhs of first solution
157 if (!eqns.info(info_flags::list)) {
158 throw(std::invalid_argument("lsolve: 1st argument must be a list"));
160 for (int i=0; i<eqns.nops(); i++) {
161 if (!eqns.op(i).info(info_flags::relation_equal)) {
162 throw(std::invalid_argument("lsolve: 1st argument must be a list of equations"));
165 if (!symbols.info(info_flags::list)) {
166 throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
168 for (int i=0; i<symbols.nops(); i++) {
169 if (!symbols.op(i).info(info_flags::symbol)) {
170 throw(std::invalid_argument("lsolve: 2nd argument must be a list of symbols"));
174 // build matrix from equation system
175 matrix sys(eqns.nops(),symbols.nops());
176 matrix rhs(eqns.nops(),1);
177 matrix vars(symbols.nops(),1);
179 for (int r=0; r<eqns.nops(); r++) {
180 ex eq=eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
182 for (int c=0; c<symbols.nops(); c++) {
183 ex co=eq.coeff(ex_to_symbol(symbols.op(c)),1);
184 linpart -= co*symbols.op(c);
187 linpart=linpart.expand();
188 rhs.set(r,0,-linpart);
191 // test if system is linear and fill vars matrix
192 for (int i=0; i<symbols.nops(); i++) {
193 vars.set(i,0,symbols.op(i));
194 if (sys.has(symbols.op(i))) {
195 throw(std::logic_error("lsolve: system is not linear"));
197 if (rhs.has(symbols.op(i))) {
198 throw(std::logic_error("lsolve: system is not linear"));
202 //matrix solution=sys.solve(rhs);
205 solution=sys.fraction_free_elim(vars,rhs);
206 } catch (runtime_error const & e) {
207 // probably singular matrix (or other error)
208 // return empty solution list
209 cerr << e.what() << endl;
213 // return a list of equations
214 if (solution.cols()!=1) {
215 throw(std::runtime_error("lsolve: strange number of columns returned from matrix::solve"));
217 if (solution.rows()!=symbols.nops()) {
218 cout << "symbols.nops()=" << symbols.nops() << endl;
219 cout << "solution.rows()=" << solution.rows() << endl;
220 throw(std::runtime_error("lsolve: strange number of rows returned from matrix::solve"));
223 // return list of the form lst(var1==sol1,var2==sol2,...)
225 for (int i=0; i<symbols.nops(); i++) {
226 sollist.append(symbols.op(i)==solution(i,0));
232 /** non-commutative power. */
233 ex ncpower(ex const &basis, unsigned exponent)
241 for (unsigned i=0; i<exponent; ++i) {