3 * Implementation of symbolic differentiation in all of GiNaC's classes. */
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
29 #include "expairseq.h"
36 #include "relational.h"
40 #ifndef NO_GINAC_NAMESPACE
42 #endif // ndef NO_GINAC_NAMESPACE
44 /** Default implementation of ex::diff(). It prints and error message and returns a fail object.
46 ex basic::diff(symbol const & s) const
48 throw(std::logic_error("differentiation not supported by this type"));
52 /** Implementation of ex::diff() for a numeric. It always returns 0.
55 ex numeric::diff(symbol const & s) const
61 /** Implementation of ex::diff() for single differentiation of a symbol.
65 ex symbol::diff(symbol const & s) const
67 if (compare_same_type(s)) {
74 /** Implementation of ex::diff() for a constant. It always returns 0.
77 ex constant::diff(symbol const & s) const
82 /** Implementation of ex::diff() for multiple differentiation of a symbol.
83 * It returns the symbol, 1 or 0.
85 * @param nth order of differentiation
87 ex symbol::diff(symbol const & s, unsigned nth) const
89 if (compare_same_type(s)) {
106 /** Implementation of ex::diff() for an indexed object. It always returns 0.
108 ex indexed::diff(symbol const & s) const
114 /** Implementation of ex::diff() for an expairseq. It differentiates all elements of the sequence.
116 ex expairseq::diff(symbol const & s) const
118 return thisexpairseq(diffchildren(s),overall_coeff);
122 /** Implementation of ex::diff() for a sum. It differentiates each term.
124 ex add::diff(symbol const & s) const
126 // D(a+b+c)=D(a)+D(b)+D(c)
127 return (new add(diffchildren(s)))->setflag(status_flags::dynallocated);
131 /** Implementation of ex::diff() for a product. It applies the product rule.
133 ex mul::diff(symbol const & s) const
136 new_seq.reserve(seq.size());
138 // D(a*b*c)=D(a)*b*c+a*D(b)*c+a*b*D(c)
139 for (unsigned i=0; i!=seq.size(); i++) {
140 epvector sub_seq=seq;
141 sub_seq[i] = split_ex_to_pair(sub_seq[i].coeff*
142 power(sub_seq[i].rest,sub_seq[i].coeff-1)*
143 sub_seq[i].rest.diff(s));
144 new_seq.push_back((new mul(sub_seq,overall_coeff))->setflag(status_flags::dynallocated));
146 return (new add(new_seq))->setflag(status_flags::dynallocated);
150 /** Implementation of ex::diff() for a non-commutative product. It always returns 0.
152 ex ncmul::diff(symbol const & s) const
158 /** Implementation of ex::diff() for a power.
160 ex power::diff(symbol const & s) const
162 if (exponent.info(info_flags::real)) {
163 // D(b^r) = r * b^(r-1) * D(b) (faster than the formula below)
164 return mul(mul(exponent, power(basis, exponent - exONE())), basis.diff(s));
166 // D(b^e) = b^e * (D(e)*ln(b) + e*D(b)/b)
167 return mul(power(basis, exponent),
168 add(mul(exponent.diff(s), log(basis)),
169 mul(mul(exponent, basis.diff(s)), power(basis, -1))));
174 /** Implementation of ex::diff() for functions. It applies the chain rule,
175 * except for the Order term function.
177 ex function::diff(symbol const & s) const
181 if (serial==function_index_Order) {
182 // Order Term function only differentiates the argument
183 return Order(seq[0].diff(s));
187 for (unsigned i=0; i!=seq.size(); i++) {
188 arg_diff = seq[i].diff(s);
189 // We apply the chain rule only when it makes sense. This is not
190 // just for performance reasons but also to allow functions to
191 // throw when differentiated with respect to one of its arguments
192 // without running into trouble with our automatic full
194 if (!arg_diff.is_zero())
195 new_seq.push_back(mul(pdiff(i), arg_diff));
202 /** Implementation of ex::diff() for a power-series. It treats the series as a polynomial.
204 ex series::diff(symbol const & s) const
208 epvector::const_iterator it = seq.begin(), itend = seq.end();
210 // FIXME: coeff might depend on var
211 while (it != itend) {
212 if (is_order_function(it->rest)) {
213 new_seq.push_back(expair(it->rest, it->coeff - 1));
215 ex c = it->rest * it->coeff;
217 new_seq.push_back(expair(c, it->coeff - 1));
221 return series(var, point, new_seq);
228 /** Compute partial derivative of an expression.
230 * @param s symbol by which the expression is derived
231 * @param nth order of derivative (default 1)
232 * @return partial derivative as a new expression */
234 ex ex::diff(symbol const & s, unsigned nth) const
242 ex ndiff = bp->diff(s);
244 ndiff = ndiff.diff(s);
250 #ifndef NO_GINAC_NAMESPACE
252 #endif // ndef NO_GINAC_NAMESPACE