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 subs(). */
41 no_pattern = 0x0001, ///< disable pattern matching
42 subs_no_pattern = 0x0001, // for backwards compatibility
43 algebraic = 0x0002, ///< enable algebraic substitutions
44 subs_algebraic = 0x0002, // for backwards compatibility
45 pattern_is_product = 0x0004, ///< used internally by expairseq::subschildren()
46 pattern_is_not_product = 0x0008, ///< used internally by expairseq::subschildren()
47 no_index_renaming = 0x0010
51 /** Domain of an object */
60 /** Flags to control series expansion. */
61 class series_options {
64 /** Suppress branch cuts in series expansion. Branch cuts manifest
65 * themselves as step functions, if this option is not passed. If
66 * it is passed and expansion at a point on a cut is performed, then
67 * the analytic continuation of the function is expanded. */
68 suppress_branchcut = 0x0001
72 /** Switch to control algorithm for determinant computation. */
73 class determinant_algo {
76 /** Let the system choose. A heuristics is applied for automatic
77 * determination of a suitable algorithm. */
79 /** Gauss elimination. If \f$m_{i,j}^{(0)}\f$ are the entries of the
80 * original matrix, then the matrix is transformed into triangular
81 * form by applying the rules
83 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}
85 * The determinant is then just the product of diagonal elements.
86 * Choose this algorithm only for purely numerical matrices. */
88 /** Division-free elimination. This is a modification of Gauss
89 * elimination where the division by the pivot element is not
90 * carried out. If \f$m_{i,j}^{(0)}\f$ are the entries of the
91 * original matrix, then the matrix is transformed into triangular
92 * form by applying the rules
94 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}
96 * The determinant can later be computed by inspecting the diagonal
97 * elements only. This algorithm is only there for the purpose of
98 * cross-checks. It is never fast. */
100 /** Laplace elimination. This is plain recursive elimination along
101 * minors although multiple minors are avoided by the algorithm.
102 * Although the algorithm is exponential in complexity it is
103 * frequently the fastest one when the matrix is populated by
104 * complicated symbolic expressions. */
106 /** Bareiss fraction-free elimination. This is a modification of
107 * Gauss elimination where the division by the pivot element is
108 * <EM>delayed</EM> until it can be carried out without computing
109 * GCDs. If \f$m_{i,j}^{(0)}\f$ are the entries of the original
110 * matrix, then the matrix is transformed into triangular form by
113 * 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)}
115 * (We have set \f$m_{-1,-1}^{(-1)}=1\f$ in order to avoid a case
116 * distinction in above formula.) It can be shown that nothing more
117 * than polynomial long division is needed for carrying out the
118 * division. The determinant can then be read of from the lower
119 * right entry. This algorithm is rarely fast for computing
125 /** Switch to control algorithm for linear system solving. */
129 /** Let the system choose. A heuristics is applied for automatic
130 * determination of a suitable algorithm. */
132 /** Gauss elimination. If \f$m_{i,j}^{(0)}\f$ are the entries of the
133 * original matrix, then the matrix is transformed into triangular
134 * form by applying the rules
136 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}
138 * This algorithm is well-suited for numerical matrices but generally
139 * suffers from the expensive division (and computation of GCDs) at
142 /** Division-free elimination. This is a modification of Gauss
143 * elimination where the division by the pivot element is not
144 * carried out. If \f$m_{i,j}^{(0)}\f$ are the entries of the
145 * original matrix, then the matrix is transformed into triangular
146 * form by applying the rules
148 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}
150 * This algorithm is only there for the purpose of cross-checks.
151 * It suffers from exponential intermediate expression swell. Use it
152 * only for small systems. */
154 /** Bareiss fraction-free elimination. This is a modification of
155 * Gauss elimination where the division by the pivot element is
156 * <EM>delayed</EM> until it can be carried out without computing
157 * GCDs. If \f$m_{i,j}^{(0)}\f$ are the entries of the original
158 * matrix, then the matrix is transformed into triangular form by
161 * 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)}
163 * (We have set \f$m_{-1,-1}^{(-1)}=1\f$ in order to avoid a case
164 * distinction in above formula.) It can be shown that nothing more
165 * than polynomial long division is needed for carrying out the
166 * division. This is generally the fastest algorithm for solving
167 * linear systems. In contrast to division-free elimination it only
168 * has a linear expression swell. For two-dimensional systems, the
169 * two algorithms are equivalent, however. */
174 /** Flags to store information about the state of an object.
175 * @see basic::flags */
179 dynallocated = 0x0001, ///< heap-allocated (i.e. created by new if we want to be clever and bypass the stack, @see ex::construct_from_basic() )
180 evaluated = 0x0002, ///< .eval() has already done its job
181 expanded = 0x0004, ///< .expand(0) has already done its job (other expand() options ignore this flag)
182 hash_calculated = 0x0008, ///< .calchash() has already done its job
183 not_shareable = 0x0010 ///< don't share instances of this object between different expressions unless explicitly asked to (used by ex::compare())
187 /** Possible attributes an object can have. */
191 // answered by class numeric
208 // answered by class relation
213 relation_less_or_equal,
215 relation_greater_or_equal,
217 // answered by class symbol
220 // answered by class lst
223 // answered by class exprseq
226 // answered by classes numeric, symbol, add, mul, power
231 crational_polynomial,
235 // answered by class indexed
236 indexed, // class can carry indices
237 has_indices, // object has at least one index
239 // answered by class idx
249 noncommutative_composite
253 /** Strategies how to clean up the function remember cache.
254 * @see remember_table */
255 class remember_strategies {
258 delete_never, ///< Let table grow undefinitely
259 delete_lru, ///< Least recently used
260 delete_lfu, ///< Least frequently used
261 delete_cyclic ///< First (oldest) one in list
267 #endif // ndef __GINAC_FLAGS_H__