+ enum {
+ expand_indexed = 0x0001, ///< expands (a+b).i to a.i+b.i
+ expand_function_args = 0x0002, ///< expands the arguments of functions
+ expand_rename_idx = 0x0004, ///< used internally by mul::expand()
+ expand_transcendental = 0x0008 ///< expands transcendental functions like log and exp
+ };
+};
+
+/** Flags to control the behavior of has(). */
+class has_options {
+public:
+ enum {
+ algebraic = 0x0001 ///< enable algebraic matching
+ };
+};
+
+/** Flags to control the behavior of subs(). */
+class subs_options {
+public:
+ enum {
+ no_pattern = 0x0001, ///< disable pattern matching
+ subs_no_pattern = 0x0001, // for backwards compatibility
+ algebraic = 0x0002, ///< enable algebraic substitutions
+ subs_algebraic = 0x0002, // for backwards compatibility
+ pattern_is_product = 0x0004, ///< used internally by expairseq::subschildren()
+ pattern_is_not_product = 0x0008, ///< used internally by expairseq::subschildren()
+ no_index_renaming = 0x0010,
+ // To indicate that we want to substitute an index by something that
+ // is not an index. Without this flag the index value would be
+ // substituted in that case.
+ really_subs_idx = 0x0020
+ };
+};
+
+/** Domain of an object */
+class domain {
+public:
+ enum {
+ complex,
+ real,
+ positive
+ };
+};
+
+/** Flags to control series expansion. */
+class series_options {
+public:
+ enum {
+ /** Suppress branch cuts in series expansion. Branch cuts manifest
+ * themselves as step functions, if this option is not passed. If
+ * it is passed and expansion at a point on a cut is performed, then
+ * the analytic continuation of the function is expanded. */
+ suppress_branchcut = 0x0001
+ };
+};
+
+/** Switch to control algorithm for determinant computation. */
+class determinant_algo {
+public:
+ enum {
+ /** Let the system choose. A heuristics is applied for automatic
+ * determination of a suitable algorithm. */
+ automatic,
+ /** Gauss elimination. If \f$m_{i,j}^{(0)}\f$ are the entries of the
+ * original matrix, then the matrix is transformed into triangular
+ * form by applying the rules
+ * \f[
+ * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)} / m_{k,k}^{(k)}
+ * \f]
+ * The determinant is then just the product of diagonal elements.
+ * Choose this algorithm only for purely numerical matrices. */
+ gauss,
+ /** Division-free elimination. This is a modification of Gauss
+ * elimination where the division by the pivot element is not
+ * carried out. If \f$m_{i,j}^{(0)}\f$ are the entries of the
+ * original matrix, then the matrix is transformed into triangular
+ * form by applying the rules
+ * \f[
+ * m_{i,j}^{(k+1)} = m_{i,j}^{(k)} m_{k,k}^{(k)} - m_{i,k}^{(k)} m_{k,j}^{(k)}
+ * \f]
+ * The determinant can later be computed by inspecting the diagonal
+ * elements only. This algorithm is only there for the purpose of
+ * cross-checks. It is never fast. */
+ divfree,
+ /** Laplace elimination. This is plain recursive elimination along
+ * minors although multiple minors are avoided by the algorithm.
+ * Although the algorithm is exponential in complexity it is
+ * frequently the fastest one when the matrix is populated by
+ * complicated symbolic expressions. */
+ laplace,
+ /** Bareiss fraction-free elimination. This is a modification of
+ * Gauss elimination where the division by the pivot element is
+ * <EM>delayed</EM> until it can be carried out without computing
+ * GCDs. If \f$m_{i,j}^{(0)}\f$ are the entries of the original
+ * matrix, then the matrix is transformed into triangular form by
+ * applying the rules
+ * \f[
+ * 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)}
+ * \f]
+ * (We have set \f$m_{-1,-1}^{(-1)}=1\f$ in order to avoid a case
+ * distinction in above formula.) It can be shown that nothing more
+ * than polynomial long division is needed for carrying out the
+ * division. The determinant can then be read of from the lower
+ * right entry. This algorithm is rarely fast for computing
+ * determinants. */
+ bareiss
+ };