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"
45 static ex Li2_eval(ex const & x)
49 if (x.is_equal(exONE()))
50 return power(Pi, 2) / 6;
51 if (x.is_equal(exMINUSONE()))
52 return -power(Pi, 2) / 12;
56 REGISTER_FUNCTION(Li2, Li2_eval, NULL, NULL, NULL);
62 static ex Li3_eval(ex const & x)
69 REGISTER_FUNCTION(Li3, Li3_eval, NULL, NULL, NULL);
75 static ex factorial_evalf(ex const & x)
77 return factorial(x).hold();
80 static ex factorial_eval(ex const & x)
82 if (is_ex_exactly_of_type(x, numeric))
83 return factorial(ex_to_numeric(x));
85 return factorial(x).hold();
88 REGISTER_FUNCTION(factorial, factorial_eval, factorial_evalf, NULL, NULL);
94 static ex binomial_evalf(ex const & x, ex const & y)
96 return binomial(x, y).hold();
99 static ex binomial_eval(ex const & x, ex const &y)
101 if (is_ex_exactly_of_type(x, numeric) && is_ex_exactly_of_type(y, numeric))
102 return binomial(ex_to_numeric(x), ex_to_numeric(y));
104 return binomial(x, y).hold();
107 REGISTER_FUNCTION(binomial, binomial_eval, binomial_evalf, NULL, NULL);
110 // Order term function (for truncated power series)
113 static ex Order_eval(ex const & x)
115 if (is_ex_exactly_of_type(x, numeric)) {
118 return Order(exONE()).hold();
120 } else if (is_ex_exactly_of_type(x, mul)) {
122 mul *m = static_cast<mul *>(x.bp);
123 if (is_ex_exactly_of_type(m->op(m->nops() - 1), numeric)) {
126 return Order(x / m->op(m->nops() - 1)).hold();
129 return Order(x).hold();
132 static ex Order_series(ex const & x, symbol const & s, ex const & point, int order)
134 // Just wrap the function into a series object
136 new_seq.push_back(expair(Order(exONE()), numeric(min(x.ldegree(s), order))));
137 return series(s, point, new_seq);
140 REGISTER_FUNCTION(Order, Order_eval, NULL, NULL, Order_series);
143 ex lsolve(ex const &eqns, ex const &symbols)
145 // solve a system of linear equations
146 if (eqns.info(info_flags::relation_equal)) {
147 if (!symbols.info(info_flags::symbol)) {
148 throw(std::invalid_argument("lsolve: 2nd argument must be a symbol"));
150 ex sol=lsolve(lst(eqns),lst(symbols));
152 ASSERT(sol.nops()==1);
153 ASSERT(is_ex_exactly_of_type(sol.op(0),relational));
155 return sol.op(0).op(1); // return rhs of first solution
159 if (!eqns.info(info_flags::list)) {
160 throw(std::invalid_argument("lsolve: 1st argument must be a list"));
162 for (int i=0; i<eqns.nops(); i++) {
163 if (!eqns.op(i).info(info_flags::relation_equal)) {
164 throw(std::invalid_argument("lsolve: 1st argument must be a list of equations"));
167 if (!symbols.info(info_flags::list)) {
168 throw(std::invalid_argument("lsolve: 2nd argument must be a list"));
170 for (int i=0; i<symbols.nops(); i++) {
171 if (!symbols.op(i).info(info_flags::symbol)) {
172 throw(std::invalid_argument("lsolve: 2nd argument must be a list of symbols"));
176 // build matrix from equation system
177 matrix sys(eqns.nops(),symbols.nops());
178 matrix rhs(eqns.nops(),1);
179 matrix vars(symbols.nops(),1);
181 for (int r=0; r<eqns.nops(); r++) {
182 ex eq=eqns.op(r).op(0)-eqns.op(r).op(1); // lhs-rhs==0
184 for (int c=0; c<symbols.nops(); c++) {
185 ex co=eq.coeff(ex_to_symbol(symbols.op(c)),1);
186 linpart -= co*symbols.op(c);
189 linpart=linpart.expand();
190 rhs.set(r,0,-linpart);
193 // test if system is linear and fill vars matrix
194 for (int i=0; i<symbols.nops(); i++) {
195 vars.set(i,0,symbols.op(i));
196 if (sys.has(symbols.op(i))) {
197 throw(std::logic_error("lsolve: system is not linear"));
199 if (rhs.has(symbols.op(i))) {
200 throw(std::logic_error("lsolve: system is not linear"));
204 //matrix solution=sys.solve(rhs);
207 solution=sys.fraction_free_elim(vars,rhs);
208 } catch (runtime_error const & e) {
209 // probably singular matrix (or other error)
210 // return empty solution list
211 // cerr << e.what() << endl;
215 // return a list of equations
216 if (solution.cols()!=1) {
217 throw(std::runtime_error("lsolve: strange number of columns returned from matrix::solve"));
219 if (solution.rows()!=symbols.nops()) {
220 cout << "symbols.nops()=" << symbols.nops() << endl;
221 cout << "solution.rows()=" << solution.rows() << endl;
222 throw(std::runtime_error("lsolve: strange number of rows returned from matrix::solve"));
225 // return list of the form lst(var1==sol1,var2==sol2,...)
227 for (int i=0; i<symbols.nops(); i++) {
228 sollist.append(symbols.op(i)==solution(i,0));
234 /** non-commutative power. */
235 ex ncpower(ex const &basis, unsigned exponent)
243 for (unsigned i=0; i<exponent; ++i) {