* Interface to GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2008 Johannes Gutenberg University Mainz, Germany
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA 02111-1307 USA
+ * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
#ifndef __GINAC_CLIFFORD_H__
clifford(unsigned char rl, const ex & metr, std::auto_ptr<exvector> vp);
// functions overriding virtual functions from base classes
+public:
+ unsigned precedence() const { return 65; }
protected:
ex eval_ncmul(const exvector & v) const;
bool match_same_type(const basic & other) const;
/** Create a Clifford unit object.
*
* @param mu Index (must be of class varidx or a derived class)
- * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix)
+ * @param metr Metric (should be of class tensmetric or a derived class, or a matrix)
* @param rl Representation label
* @return newly constructed Clifford unit object */
ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl = 0);
/** Reversion of the Clifford algebra, coincides with the conjugate(). */
inline ex clifford_star(const ex & e) { return e.conjugate(); }
-ex delete_ONE(const ex &e);
+/** Replaces all dirac_ONE's in e with 1.
+ * Aborts if e contains any clifford_unit.
+ *
+ * @param e Expression to be processed */
+ex remove_dirac_ONE(const ex & e);
+
+/** Replaces dirac_ONE's (with a representation_label no less than rl) in e with 1.
+ * For the default value rl = 0 remove all of them. Aborts if e contains any
+ * clifford_unit with representation_label to be removed.
+ *
+ * @param e Expression to be processed
+ * @param rl Value of representation label */
+ex remove_dirac_ONE(const ex & e, unsigned char rl);
/** Calculation of the norm in the Clifford algebra. */
ex clifford_norm(const ex & e);
*
* @param v List or vector of coordinates
* @param mu Index (must be of class varidx or a derived class)
- * @param metr Metric (should be of class tensmetric or a derived class, or a symmetric matrix)
+ * @param metr Metric (should be of class tensmetric or a derived class, or a matrix)
* @param rl Representation label
* @return Clifford vector with given components */
ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl = 0);
+/** List or vector conversion into the Clifford vector.
+ *
+ * @param v List or vector of coordinates
+ * @param e Clifford unit object
+ * @return Clifford vector with given components */
+ex lst_to_clifford(const ex & v, const ex & e);
+
+/** An inverse function to lst_to_clifford(). For given Clifford vector extracts
+ * its components with respect to given Clifford unit. Obtained components may
+ * contain Clifford units with a different metric. Extraction is based on
+ * the algebraic formula (e * c.i + c.i * e)/ pow(e.i, 2) for non-degenerate cases
+ * (i.e. neither pow(e.i, 2) = 0).
+ *
+ * @param e Clifford expression to be decomposed into components
+ * @param c Clifford unit defining the metric for splitting (should have numeric dimension of indices)
+ * @param algebraic Use algebraic or symbolic algorithm for extractions
+ * @return List of components of a Clifford vector*/
+lst clifford_to_lst(const ex & e, const ex & c, bool algebraic=true);
+
+/** Calculations of Moebius transformations (conformal map) defined by a 2x2 Clifford matrix
+ * (a b\\c d) in linear spaces with arbitrary signature. The expression is
+ * (a * x + b)/(c * x + d), where x is a vector build from list v with metric G.
+ * (see Jan Cnops. An introduction to {D}irac operators on manifolds, v.24 of
+ * Progress in Mathematical Physics. Birkhauser Boston Inc., Boston, MA, 2002.)
+ *
+ * @param a (1,1) entry of the defining matrix
+ * @param b (1,2) entry of the defining matrix
+ * @param c (2,1) entry of the defining matrix
+ * @param d (2,2) entry of the defining matrix
+ * @param v Vector to be transformed
+ * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored
+ * @param rl Representation label
+ * @return List of components of the transformed vector*/
+ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G, unsigned char rl);
+
+/** Same as clifford_moebius_map(a, b, c, d, v, G, 0). */
+ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G);
+
+/** The second form of Moebius transformations defined by a 2x2 Clifford matrix M
+ * This function takes the transformation matrix M as a single entity.
+ *
+ * @param M the defining matrix
+ * @param v Vector to be transformed
+ * @param G Metric of the surrounding space, may be a Clifford unit then the next parameter is ignored
+ * @param rl Representation label
+ * @return List of components of the transformed vector*/
+ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl);
+
+/** Same as clifford_moebius_map(M, v, G, 0). */
+ex clifford_moebius_map(const ex & M, const ex & v, const ex & G);
+
} // namespace GiNaC
#endif // ndef __GINAC_CLIFFORD_H__
git://www.ginac.de / ginac.git / blobdiff