3 * Collection of all flags used through the GiNaC framework. */
6 * GiNaC Copyright (C) 1999-2005 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., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
23 #ifndef __GINAC_FLAGS_H__
24 #define __GINAC_FLAGS_H__
28 /** Flags to control the behavior of expand(). */
29 class expand_options {
32 expand_indexed = 0x0001, ///< expands (a+b).i to a.i+b.i
33 expand_function_args = 0x0002 ///< expands the arguments of functions
37 /** Flags to control the behavior of has(). */
41 algebraic = 0x0001, ///< enable algebraic matching
45 /** Flags to control the behavior of subs(). */
49 no_pattern = 0x0001, ///< disable pattern matching
50 subs_no_pattern = 0x0001, // for backwards compatibility
51 algebraic = 0x0002, ///< enable algebraic substitutions
52 subs_algebraic = 0x0002, // for backwards compatibility
53 pattern_is_product = 0x0004, ///< used internally by expairseq::subschildren()
54 pattern_is_not_product = 0x0008, ///< used internally by expairseq::subschildren()
55 no_index_renaming = 0x0010
59 /** Domain of an object */
68 /** Flags to control series expansion. */
69 class series_options {
72 /** Suppress branch cuts in series expansion. Branch cuts manifest
73 * themselves as step functions, if this option is not passed. If
74 * it is passed and expansion at a point on a cut is performed, then
75 * the analytic continuation of the function is expanded. */
76 suppress_branchcut = 0x0001
80 /** Switch to control algorithm for determinant computation. */
81 class determinant_algo {
84 /** Let the system choose. A heuristics is applied for automatic
85 * determination of a suitable algorithm. */
87 /** Gauss elimination. If \f$m_{i,j}^{(0)}\f$ are the entries of the
88 * original matrix, then the matrix is transformed into triangular
89 * form by applying the rules
91 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}
93 * The determinant is then just the product of diagonal elements.
94 * Choose this algorithm only for purely numerical matrices. */
96 /** Division-free elimination. This is a modification of Gauss
97 * elimination where the division by the pivot element is not
98 * carried out. If \f$m_{i,j}^{(0)}\f$ are the entries of the
99 * original matrix, then the matrix is transformed into triangular
100 * form by applying the rules
102 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}
104 * The determinant can later be computed by inspecting the diagonal
105 * elements only. This algorithm is only there for the purpose of
106 * cross-checks. It is never fast. */
108 /** Laplace elimination. This is plain recursive elimination along
109 * minors although multiple minors are avoided by the algorithm.
110 * Although the algorithm is exponential in complexity it is
111 * frequently the fastest one when the matrix is populated by
112 * complicated symbolic expressions. */
114 /** Bareiss fraction-free elimination. This is a modification of
115 * Gauss elimination where the division by the pivot element is
116 * <EM>delayed</EM> until it can be carried out without computing
117 * GCDs. If \f$m_{i,j}^{(0)}\f$ are the entries of the original
118 * matrix, then the matrix is transformed into triangular form by
121 * m_{i,j}^{(k+1)} = (m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}) / m_{k-1,k-1}^{(k-1)}
123 * (We have set \f$m_{-1,-1}^{(-1)}=1\f$ in order to avoid a case
124 * distinction in above formula.) It can be shown that nothing more
125 * than polynomial long division is needed for carrying out the
126 * division. The determinant can then be read of from the lower
127 * right entry. This algorithm is rarely fast for computing
133 /** Switch to control algorithm for linear system solving. */
137 /** Let the system choose. A heuristics is applied for automatic
138 * determination of a suitable algorithm. */
140 /** Gauss elimination. If \f$m_{i,j}^{(0)}\f$ are the entries of the
141 * original matrix, then the matrix is transformed into triangular
142 * form by applying the rules
144 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}
146 * This algorithm is well-suited for numerical matrices but generally
147 * suffers from the expensive division (and computation of GCDs) at
150 /** Division-free elimination. This is a modification of Gauss
151 * elimination where the division by the pivot element is not
152 * carried out. If \f$m_{i,j}^{(0)}\f$ are the entries of the
153 * original matrix, then the matrix is transformed into triangular
154 * form by applying the rules
156 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}
158 * This algorithm is only there for the purpose of cross-checks.
159 * It suffers from exponential intermediate expression swell. Use it
160 * only for small systems. */
162 /** Bareiss fraction-free elimination. This is a modification of
163 * Gauss elimination where the division by the pivot element is
164 * <EM>delayed</EM> until it can be carried out without computing
165 * GCDs. If \f$m_{i,j}^{(0)}\f$ are the entries of the original
166 * matrix, then the matrix is transformed into triangular form by
169 * m_{i,j}^{(k+1)} = (m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}) / m_{k-1,k-1}^{(k-1)}
171 * (We have set \f$m_{-1,-1}^{(-1)}=1\f$ in order to avoid a case
172 * distinction in above formula.) It can be shown that nothing more
173 * than polynomial long division is needed for carrying out the
174 * division. This is generally the fastest algorithm for solving
175 * linear systems. In contrast to division-free elimination it only
176 * has a linear expression swell. For two-dimensional systems, the
177 * two algorithms are equivalent, however. */
182 /** Flags to store information about the state of an object.
183 * @see basic::flags */
187 dynallocated = 0x0001, ///< heap-allocated (i.e. created by new if we want to be clever and bypass the stack, @see ex::construct_from_basic() )
188 evaluated = 0x0002, ///< .eval() has already done its job
189 expanded = 0x0004, ///< .expand(0) has already done its job (other expand() options ignore this flag)
190 hash_calculated = 0x0008, ///< .calchash() has already done its job
191 not_shareable = 0x0010 ///< don't share instances of this object between different expressions unless explicitly asked to (used by ex::compare())
195 /** Possible attributes an object can have. */
199 // answered by class numeric
216 // answered by class relation
221 relation_less_or_equal,
223 relation_greater_or_equal,
225 // answered by class symbol
228 // answered by class lst
231 // answered by class exprseq
234 // answered by classes numeric, symbol, add, mul, power
239 crational_polynomial,
243 // answered by class indexed
244 indexed, // class can carry indices
245 has_indices, // object has at least one index
247 // answered by class idx
257 noncommutative_composite
261 /** Strategies how to clean up the function remember cache.
262 * @see remember_table */
263 class remember_strategies {
266 delete_never, ///< Let table grow undefinitely
267 delete_lru, ///< Least recently used
268 delete_lfu, ///< Least frequently used
269 delete_cyclic ///< First (oldest) one in list
275 #endif // ndef __GINAC_FLAGS_H__