3 * Collection of all flags used through the GiNaC framework. */
6 * GiNaC Copyright (C) 1999-2004 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
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()
50 /** Domain of an object */
59 /** Flags to control series expansion. */
60 class series_options {
63 /** Suppress branch cuts in series expansion. Branch cuts manifest
64 * themselves as step functions, if this option is not passed. If
65 * it is passed and expansion at a point on a cut is performed, then
66 * the analytic continuation of the function is expanded. */
67 suppress_branchcut = 0x0001
71 /** Switch to control algorithm for determinant computation. */
72 class determinant_algo {
75 /** Let the system choose. A heuristics is applied for automatic
76 * determination of a suitable algorithm. */
78 /** Gauss elimination. If \f$m_{i,j}^{(0)}\f$ are the entries of the
79 * original matrix, then the matrix is transformed into triangular
80 * form by applying the rules
82 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}
84 * The determinant is then just the product of diagonal elements.
85 * Choose this algorithm only for purely numerical matrices. */
87 /** Division-free elimination. This is a modification of Gauss
88 * elimination where the division by the pivot element is not
89 * carried out. If \f$m_{i,j}^{(0)}\f$ are the entries of the
90 * original matrix, then the matrix is transformed into triangular
91 * form by applying the rules
93 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}
95 * The determinant can later be computed by inspecting the diagonal
96 * elements only. This algorithm is only there for the purpose of
97 * cross-checks. It is never fast. */
99 /** Laplace elimination. This is plain recursive elimination along
100 * minors although multiple minors are avoided by the algorithm.
101 * Although the algorithm is exponential in complexity it is
102 * frequently the fastest one when the matrix is populated by
103 * complicated symbolic expressions. */
105 /** Bareiss fraction-free elimination. This is a modification of
106 * Gauss elimination where the division by the pivot element is
107 * <EM>delayed</EM> until it can be carried out without computing
108 * GCDs. If \f$m_{i,j}^{(0)}\f$ are the entries of the original
109 * matrix, then the matrix is transformed into triangular form by
112 * 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)}
114 * (We have set \f$m_{-1,-1}^{(-1)}=1\f$ in order to avoid a case
115 * distinction in above formula.) It can be shown that nothing more
116 * than polynomial long division is needed for carrying out the
117 * division. The determinant can then be read of from the lower
118 * right entry. This algorithm is rarely fast for computing
124 /** Switch to control algorithm for linear system solving. */
128 /** Let the system choose. A heuristics is applied for automatic
129 * determination of a suitable algorithm. */
131 /** Gauss elimination. If \f$m_{i,j}^{(0)}\f$ are the entries of the
132 * original matrix, then the matrix is transformed into triangular
133 * form by applying the rules
135 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}
137 * This algorithm is well-suited for numerical matrices but generally
138 * suffers from the expensive division (and computation of GCDs) at
141 /** Division-free elimination. This is a modification of Gauss
142 * elimination where the division by the pivot element is not
143 * carried out. If \f$m_{i,j}^{(0)}\f$ are the entries of the
144 * original matrix, then the matrix is transformed into triangular
145 * form by applying the rules
147 * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}
149 * This algorithm is only there for the purpose of cross-checks.
150 * It suffers from exponential intermediate expression swell. Use it
151 * only for small systems. */
153 /** Bareiss fraction-free elimination. This is a modification of
154 * Gauss elimination where the division by the pivot element is
155 * <EM>delayed</EM> until it can be carried out without computing
156 * GCDs. If \f$m_{i,j}^{(0)}\f$ are the entries of the original
157 * matrix, then the matrix is transformed into triangular form by
160 * 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)}
162 * (We have set \f$m_{-1,-1}^{(-1)}=1\f$ in order to avoid a case
163 * distinction in above formula.) It can be shown that nothing more
164 * than polynomial long division is needed for carrying out the
165 * division. This is generally the fastest algorithm for solving
166 * linear systems. In contrast to division-free elimination it only
167 * has a linear expression swell. For two-dimensional systems, the
168 * two algorithms are equivalent, however. */
173 /** Flags to store information about the state of an object.
174 * @see basic::flags */
178 dynallocated = 0x0001, ///< heap-allocated (i.e. created by new if we want to be clever and bypass the stack, @see ex::construct_from_basic() )
179 evaluated = 0x0002, ///< .eval() has already done its job
180 expanded = 0x0004, ///< .expand(0) has already done its job (other expand() options ignore this flag)
181 hash_calculated = 0x0008, ///< .calchash() has already done its job
182 not_shareable = 0x0010 ///< don't share instances of this object between different expressions unless explicitly asked to (used by ex::compare())
186 /** Possible attributes an object can have. */
190 // answered by class numeric
207 // answered by class relation
212 relation_less_or_equal,
214 relation_greater_or_equal,
216 // answered by class symbol
219 // answered by class lst
222 // answered by class exprseq
225 // answered by classes numeric, symbol, add, mul, power
230 crational_polynomial,
234 // answered by class indexed
235 indexed, // class can carry indices
236 has_indices, // object has at least one index
238 // answered by class idx
248 noncommutative_composite
252 /** Strategies how to clean up the function remember cache.
253 * @see remember_table */
254 class remember_strategies {
257 delete_never, ///< Let table grow undefinitely
258 delete_lru, ///< Least recently used
259 delete_lfu, ///< Least frequently used
260 delete_cyclic ///< First (oldest) one in list
266 #endif // ndef __GINAC_FLAGS_H__