Prettified source code.
[ginac.git] / ginac / clifford.cpp
index 0a1f8a4..3b4684c 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */
 
 /*
- *  GiNaC Copyright (C) 1999-2004 Johannes Gutenberg University Mainz, Germany
+ *  GiNaC Copyright (C) 1999-2009 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
@@ -17,7 +17,7 @@
  *
  *  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
  */
 
 #include "clifford.h"
@@ -38,6 +38,8 @@
 #include "archive.h"
 #include "utils.h"
 
+#include <stdexcept>
+
 namespace GiNaC {
 
 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(clifford, indexed,
@@ -72,15 +74,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracgammaR, tensor,
 // default constructors
 //////////
 
-static ex default_metric()
+clifford::clifford() : representation_label(0), metric(0), commutator_sign(-1)
 {
-       static ex m = (new minkmetric)->setflag(status_flags::dynallocated);
-       return m;
-}
-
-clifford::clifford() : representation_label(0), metric(default_metric())
-{
-       tinfo_key = TINFO_clifford;
 }
 
 DEFAULT_CTOR(diracone)
@@ -97,75 +92,141 @@ DEFAULT_CTOR(diracgammaR)
 /** Construct object without any indices. This constructor is for internal
  *  use only. Use the dirac_ONE() function instead.
  *  @see dirac_ONE */
-clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0)
+clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0), commutator_sign(-1)
 {
-       tinfo_key = TINFO_clifford;
 }
 
 /** Construct object with one Lorentz index. This constructor is for internal
  *  use only. Use the clifford_unit() or dirac_gamma() functions instead.
  *  @see clifford_unit
  *  @see dirac_gamma */
-clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl) : inherited(b, mu), representation_label(rl), metric(metr)
+clifford::clifford(const ex & b, const ex & mu, const ex & metr, unsigned char rl, int comm_sign) : inherited(b, mu), representation_label(rl), metric(metr), commutator_sign(comm_sign)
 {
        GINAC_ASSERT(is_a<varidx>(mu));
-       tinfo_key = TINFO_clifford;
 }
 
-clifford::clifford(unsigned char rl, const ex & metr, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr)
+clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), commutator_sign(comm_sign)
 {
-       tinfo_key = TINFO_clifford;
 }
 
-clifford::clifford(unsigned char rl, const ex & metr, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr)
+clifford::clifford(unsigned char rl, const ex & metr, int comm_sign, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), commutator_sign(comm_sign)
 {
-       tinfo_key = TINFO_clifford;
+}
+
+return_type_t clifford::return_type_tinfo() const
+{
+       return make_return_type_t<clifford>(representation_label);
 }
 
 //////////
 // archiving
 //////////
 
-clifford::clifford(const archive_node &n, lst &sym_lst) : inherited(n, sym_lst)
+void clifford::read_archive(const archive_node& n, lst& sym_lst)
 {
+       inherited::read_archive(n, sym_lst);
        unsigned rl;
        n.find_unsigned("label", rl);
        representation_label = rl;
        n.find_ex("metric", metric, sym_lst);
+       n.find_unsigned("commutator_sign+1", rl);
+       commutator_sign = rl - 1;
 }
 
-void clifford::archive(archive_node &n) const
+void clifford::archive(archive_node & n) const
 {
        inherited::archive(n);
        n.add_unsigned("label", representation_label);
        n.add_ex("metric", metric);
+       n.add_unsigned("commutator_sign+1", commutator_sign+1);
+}
+
+GINAC_BIND_UNARCHIVER(clifford);
+GINAC_BIND_UNARCHIVER(diracone);
+GINAC_BIND_UNARCHIVER(diracgamma);
+GINAC_BIND_UNARCHIVER(diracgamma5);
+GINAC_BIND_UNARCHIVER(diracgammaL);
+GINAC_BIND_UNARCHIVER(diracgammaR);
+
+
+ex clifford::get_metric(const ex & i, const ex & j, bool symmetrised) const
+{
+       if (is_a<indexed>(metric)) {
+               if (symmetrised && !(ex_to<symmetry>(ex_to<indexed>(metric).get_symmetry()).has_symmetry())) {
+                       if (is_a<matrix>(metric.op(0))) {
+                               return indexed((ex_to<matrix>(metric.op(0)).add(ex_to<matrix>(metric.op(0)).transpose())).mul(numeric(1, 2)),
+                                              symmetric2(), i, j);
+                       } else {
+                               return simplify_indexed(indexed(metric.op(0)*_ex1_2, i, j) + indexed(metric.op(0)*_ex1_2, j, i));
+                       }
+               } else {
+                       return metric.subs(lst(metric.op(1) == i, metric.op(2) == j), subs_options::no_pattern);
+               }
+       } else {
+               exvector indices = metric.get_free_indices();
+               if (symmetrised)
+                       return _ex1_2*simplify_indexed(metric.subs(lst(indices[0] == i, indices[1] == j), subs_options::no_pattern)
+                                                                       + metric.subs(lst(indices[0] == j, indices[1] == i), subs_options::no_pattern));
+               else
+                       return metric.subs(lst(indices[0] == i, indices[1] == j), subs_options::no_pattern);
+       }
 }
 
-DEFAULT_UNARCHIVE(clifford)
-DEFAULT_ARCHIVING(diracone)
-DEFAULT_ARCHIVING(cliffordunit)
-DEFAULT_ARCHIVING(diracgamma)
-DEFAULT_ARCHIVING(diracgamma5)
-DEFAULT_ARCHIVING(diracgammaL)
-DEFAULT_ARCHIVING(diracgammaR)
+bool clifford::same_metric(const ex & other) const
+{
+       ex metr;
+       if (is_a<clifford>(other)) 
+               metr = ex_to<clifford>(other).get_metric();
+       else 
+               metr = other;
+
+       if (is_a<indexed>(metr))
+               return metr.op(0).is_equal(get_metric().op(0));
+       else {
+               exvector indices = metr.get_free_indices();
+               return  (indices.size() == 2) 
+                       && simplify_indexed(get_metric(indices[0], indices[1])-metr).is_zero();
+       }
+}
 
 //////////
 // functions overriding virtual functions from base classes
 //////////
 
-ex clifford::get_metric(const ex & i, const ex & j) const
+ex clifford::op(size_t i) const
 {
-       return indexed(metric, symmetric2(), i, j);
+       GINAC_ASSERT(i<nops());
+       if (nops()-i == 1)
+               return representation_label;
+       else 
+               return inherited::op(i);
 }
 
-bool clifford::same_metric(const ex & other) const
+ex & clifford::let_op(size_t i)
 {
-       if (is_a<clifford>(other)) {
-               return get_metric().is_equal(ex_to<clifford>(other).get_metric());
-       } else if (is_a<indexed>(other)) {
-               return get_metric(other.op(1), other.op(2)).is_equal(other);
-       } else
-               return false;
+        GINAC_ASSERT(i<nops());
+
+       static ex rl = numeric(representation_label);
+        ensure_if_modifiable();
+       if (nops()-i == 1)
+               return rl;
+       else 
+               return inherited::let_op(i);
+}
+
+ex clifford::subs(const exmap & m, unsigned options) const
+{
+       ex subsed = inherited::subs(m, options);
+       if(is_a<clifford>(subsed)) {
+               ex prevmetric = ex_to<clifford>(subsed).metric;
+               ex newmetric = prevmetric.subs(m, options);
+               if(!are_ex_trivially_equal(prevmetric, newmetric)) {
+                       clifford c = ex_to<clifford>(subsed);
+                       c.metric = newmetric;
+                       subsed = c;
+               }
+       }
+       return subsed;
 }
 
 int clifford::compare_same_type(const basic & other) const
@@ -186,7 +247,7 @@ bool clifford::match_same_type(const basic & other) const
        GINAC_ASSERT(is_a<clifford>(other));
        const clifford &o = static_cast<const clifford &>(other);
 
-       return (representation_label == o.representation_label) && same_metric(o);
+       return ((representation_label == o.representation_label) && (commutator_sign == o.get_commutator_sign()) && same_metric(o));
 }
 
 static bool is_dirac_slash(const ex & seq0)
@@ -200,10 +261,23 @@ void clifford::do_print_dflt(const print_dflt & c, unsigned level) const
 {
        // dirac_slash() object is printed differently
        if (is_dirac_slash(seq[0])) {
-               seq[0].print(c, level);
+               seq[0].print(c, precedence());
                c.s << "\\";
-       } else
-               this->print_dispatch<inherited>(c, level);
+       } else { // We do not print representation label if it is 0
+               if (representation_label == 0) {
+                       this->print_dispatch<inherited>(c, level);
+               } else { // otherwise we put it before indices in square brackets; the code is borrowed from indexed.cpp 
+                       if (precedence() <= level) {
+                               c.s << '(';
+                       }
+                       seq[0].print(c, precedence());
+                       c.s << '[' << int(representation_label) << ']';
+                       printindices(c, level);
+                       if (precedence() <= level) {
+                               c.s << ')';
+                       }
+               }
+       }
 }
 
 void clifford::do_print_latex(const print_latex & c, unsigned level) const
@@ -211,10 +285,12 @@ void clifford::do_print_latex(const print_latex & c, unsigned level) const
        // dirac_slash() object is printed differently
        if (is_dirac_slash(seq[0])) {
                c.s << "{";
-               seq[0].print(c, level);
+               seq[0].print(c, precedence());
                c.s << "\\hspace{-1.0ex}/}";
-       } else
+       } else {
+               c.s << "\\clifford[" << int(representation_label) << "]";
                this->print_dispatch<inherited>(c, level);
+       }
 }
 
 DEFAULT_COMPARE(diracone)
@@ -224,7 +300,7 @@ DEFAULT_COMPARE(diracgamma5)
 DEFAULT_COMPARE(diracgammaL)
 DEFAULT_COMPARE(diracgammaR)
 
-DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbb{1}")
+DEFAULT_PRINT_LATEX(diracone, "ONE", "\\mathbf{1}")
 DEFAULT_PRINT_LATEX(cliffordunit, "e", "e")
 DEFAULT_PRINT_LATEX(diracgamma, "gamma", "\\gamma")
 DEFAULT_PRINT_LATEX(diracgamma5, "gamma5", "{\\gamma^5}")
@@ -235,7 +311,7 @@ DEFAULT_PRINT_LATEX(diracgammaR, "gammaR", "{\\gamma_R}")
 static void base_and_index(const ex & c, ex & b, ex & i)
 {
        GINAC_ASSERT(is_a<clifford>(c));
-       GINAC_ASSERT(c.nops() == 2);
+       GINAC_ASSERT(c.nops() == 2+1);
 
        if (is_a<cliffordunit>(c.op(0))) { // proper dirac gamma object or clifford unit
                i = c.op(1);
@@ -369,21 +445,6 @@ bool diracgamma::contract_with(exvector::iterator self, exvector::iterator other
        return false;
 }
 
-/** An utility function looking for a given metric within an exvector,
- *  used in cliffordunit::contract_with(). */
-static int find_same_metric(exvector & v, ex & c)
-{
-       for (int i=0; i<v.size();i++) {
-               if (!is_a<clifford>(v[i]) && is_a<indexed>(v[i])
-                   && ex_to<clifford>(c).same_metric(v[i]) 
-                   && (ex_to<varidx>(c.op(1)) == ex_to<indexed>(v[i]).get_indices()[0]
-                       || ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[0])) {
-                       return ++i; // next to found
-               }
-       }
-       return 0; //nothing found
-}
-
 /** Contraction of a Clifford unit with something else. */
 bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
@@ -400,71 +461,52 @@ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator oth
                    && unit.same_metric(*other))
                        return false;
 
-               // Find if a previous contraction produces the square of self
-               int prev_square = find_same_metric(v, self[0]);
-               varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim());
-               ex squared_metric = unit.get_metric(self->op(1), d) * unit.get_metric(d.toggle_variance(), other->op(1));
+               exvector::iterator before_other = other - 1;
+               ex mu = self->op(1);
+               ex mu_toggle = other->op(1);
+               ex alpha = before_other->op(1);
 
                // e~mu e.mu = Tr ONE
                if (other - self == 1) {
-                       if (prev_square != 0) {
-                               *self = squared_metric;
-                               v[prev_square-1] = _ex1;
-                       } else
-                               *self = unit.get_metric(self->op(1), other->op(1));
+                       *self = unit.get_metric(mu, mu_toggle, true);
                        *other = dirac_ONE(rl);
                        return true;
 
-               // e~mu e~alpha e.mu = (2e~alpha^2-Tr) e~alpha
-               } else if (other - self == 2
-                       && is_a<clifford>(self[1])) {
-
-                       const ex & ia = self[1].op(1);
-                       const ex & ib = self[1].op(1);
-                       if (is_a<tensmetric>(unit.get_metric()))
-                               *self = 2 - unit.get_metric(self->op(1), other->op(1));
-                       else if (prev_square != 0) {
-                               *self = 2-squared_metric;
-                               v[prev_square-1] = _ex1;
-                       } else 
-                               *self = 2*unit.get_metric(ia, ib) - unit.get_metric(self->op(1), other->op(1));
-                       *other = _ex1;
-                       return true;
-
-               // e~mu S e~alpha e.mu = 2 e~alpha^3 S - e~mu S e.mu e~alpha
+               } else if (other - self == 2) {
+                       if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
+                               // e~mu e~alpha e.mu = 2*e~mu B(alpha, mu.toggle_variance())-Tr(B) e~alpha
+                               *self = 2 * (*self) * unit.get_metric(alpha, mu_toggle, true) - unit.get_metric(mu, mu_toggle, true) * (*before_other);
+                               *before_other = _ex1;
+                               *other = _ex1;
+                               return true;
+
+                       } else {
+                               // e~mu S e.mu = Tr S ONE
+                               *self = unit.get_metric(mu, mu_toggle, true);
+                               *other = dirac_ONE(rl);
+                               return true;
+                       }
+               } else {
+               // e~mu S e~alpha e.mu = 2 e~mu S B(alpha, mu.toggle_variance()) - e~mu S e.mu e~alpha
                // (commutate contracted indices towards each other, simplify_indexed()
                // will re-expand and re-run the simplification)
-               } else {
-                       exvector::iterator it = self + 1, next_to_last = other - 1;
-                       while (it != other) {
-                               if (!is_a<clifford>(*it))
-                                       return false;
-                               ++it;
+                       if (std::find_if(self + 1, other, is_not_a_clifford()) != other) {
+                               return false;
                        }
-
-                       it = self + 1;
-                       ex S = _ex1;
-                       while (it != next_to_last) {
-                               S *= *it;
-                               *it++ = _ex1;
+                       
+                       ex S = ncmul(exvector(self + 1, before_other), true);
+
+                       if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
+                               *self = 2 * (*self) * S * unit.get_metric(alpha, mu_toggle, true) - (*self) * S * (*other) * (*before_other);
+                       } else {
+                               // simply commutes
+                               *self = (*self) * S * (*other) * (*before_other);
                        }
-
-                       const ex & ia = next_to_last->op(1);
-                       const ex & ib = next_to_last->op(1);
-                       if (is_a<tensmetric>(unit.get_metric()))
-                               *self = 2 * (*next_to_last) * S - (*self) * S * (*other) * (*next_to_last);
-                       else if (prev_square != 0) {
-                               *self = 2 * (*next_to_last) * S  - (*self) * S * (*other) * (*next_to_last)*unit.get_metric(self->op(1),self->op(1));
-                               v[prev_square-1] = _ex1;
-                       } else 
-                               *self = 2 * (*next_to_last) * S* unit.get_metric(ia,ib) - (*self) * S * (*other) * (*next_to_last);
-                       *next_to_last = _ex1;
-                       *other = _ex1;
+                               
+                       std::fill(self + 1, other + 1, _ex1);
                        return true;
                }
-
-       } 
-
+       }
        return false;
 }
 
@@ -573,12 +615,14 @@ ex clifford::eval_ncmul(const exvector & v) const
                        bool a_is_cliffordunit = is_a<cliffordunit>(ag);
                        bool b_is_cliffordunit =  is_a<cliffordunit>(bg);
 
-                       if (a_is_cliffordunit && b_is_cliffordunit && ex_to<clifford>(a).same_metric(b)) {
-
+                       if (a_is_cliffordunit && b_is_cliffordunit && ex_to<clifford>(a).same_metric(b)
+                               && (ex_to<clifford>(a).get_commutator_sign() == -1)) {
+                               // This is done only for Clifford algebras 
+                               
                                const ex & ia = a.op(1);
                                const ex & ib = b.op(1);
                                if (ia.is_equal(ib)) { // gamma~alpha gamma~alpha -> g~alpha~alpha
-                                       a = ex_to<clifford>(a).get_metric(ia, ib);
+                                       a = ex_to<clifford>(a).get_metric(ia, ib, true);
                                        b = dirac_ONE(representation_label);
                                        something_changed = true;
                                }
@@ -628,7 +672,7 @@ ex clifford::eval_ncmul(const exvector & v) const
        }
 
        if (s.empty())
-               return clifford(diracone(), representation_label) * sign;
+               return dirac_ONE(representation_label) * sign;
        if (something_changed)
                return reeval_ncmul(s) * sign;
        else
@@ -637,12 +681,12 @@ ex clifford::eval_ncmul(const exvector & v) const
 
 ex clifford::thiscontainer(const exvector & v) const
 {
-       return clifford(representation_label, get_metric(), v);
+       return clifford(representation_label, metric, commutator_sign, v);
 }
 
 ex clifford::thiscontainer(std::auto_ptr<exvector> vp) const
 {
-       return clifford(representation_label, get_metric(), vp);
+       return clifford(representation_label, metric, commutator_sign, vp);
 }
 
 ex diracgamma5::conjugate() const
@@ -670,19 +714,58 @@ ex dirac_ONE(unsigned char rl)
        return clifford(ONE, rl);
 }
 
+static unsigned get_dim_uint(const ex& e)
+{
+       if (!is_a<idx>(e))
+               throw std::invalid_argument("get_dim_uint: argument is not an index");
+       ex dim = ex_to<idx>(e).get_dim();
+       if (!dim.info(info_flags::posint))
+               throw std::invalid_argument("get_dim_uint: dimension of index should be a positive integer");
+       unsigned d = ex_to<numeric>(dim).to_int();
+       return d;
+}
+
 ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
 {
-       static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
+       //static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
+       ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
 
-       if (!is_a<varidx>(mu))
-               throw(std::invalid_argument("index of Clifford unit must be of type varidx"));
+       if (!is_a<idx>(mu))
+               throw(std::invalid_argument("clifford_unit(): index of Clifford unit must be of type idx or varidx"));
 
-       if (is_a<indexed>(metr))
-               return clifford(unit, mu, metr.op(0), rl);
-       else if(is_a<tensmetric>(metr) || is_a<matrix>(metr)) 
+       exvector indices = metr.get_free_indices();
+
+       if (indices.size() == 2) {
                return clifford(unit, mu, metr, rl);
-       else
-               throw(std::invalid_argument("metric for Clifford unit must be of type indexed, tensormetric or matrix"));
+       } else if (is_a<matrix>(metr)) {
+               matrix M = ex_to<matrix>(metr);
+               unsigned n = M.rows();
+               bool symmetric = true;
+
+               //static idx xi((new symbol)->setflag(status_flags::dynallocated), n),
+               //      chi((new symbol)->setflag(status_flags::dynallocated), n);
+               idx xi((new symbol)->setflag(status_flags::dynallocated), n),
+                       chi((new symbol)->setflag(status_flags::dynallocated), n);
+               if ((n ==  M.cols()) && (n == get_dim_uint(mu))) {
+                       for (unsigned i = 0; i < n; i++) {
+                               for (unsigned j = i+1; j < n; j++) {
+                                       if (!M(i, j).is_equal(M(j, i))) {
+                                               symmetric = false;
+                                       }
+                               }
+                       }
+                       return clifford(unit, mu, indexed(metr, symmetric?symmetric2():not_symmetric(), xi, chi), rl);
+               } else {
+                       throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be a square matrix with the same dimensions as index"));
+               }
+       } else if (indices.size() == 0) { // a tensor or other expression without indices
+               //static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim()),
+               //      chi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim());
+               varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim()),
+                       chi((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(mu).get_dim());
+               return clifford(unit, mu, indexed(metr, xi, chi), rl);
+       }  else 
+               throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type tensor, matrix or an expression with two free indices"));
 }
 
 ex dirac_gamma(const ex & mu, unsigned char rl)
@@ -690,9 +773,11 @@ ex dirac_gamma(const ex & mu, unsigned char rl)
        static ex gamma = (new diracgamma)->setflag(status_flags::dynallocated);
 
        if (!is_a<varidx>(mu))
-               throw(std::invalid_argument("index of Dirac gamma must be of type varidx"));
+               throw(std::invalid_argument("dirac_gamma(): index of Dirac gamma must be of type varidx"));
 
-       return clifford(gamma, mu, default_metric(), rl);
+       static varidx xi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim()),
+               chi((new symbol)->setflag(status_flags::dynallocated), ex_to<varidx>(mu).get_dim());
+       return clifford(gamma, mu, indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl);
 }
 
 ex dirac_gamma5(unsigned char rl)
@@ -718,28 +803,17 @@ ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
        // Slashed vectors are actually stored as a clifford object with the
        // vector as its base expression and a (dummy) index that just serves
        // for storing the space dimensionality
-       return clifford(e, varidx(0, dim), default_metric(), rl);
-}
 
-/** Check whether a given tinfo key (as returned by return_type_tinfo()
- *  is that of a clifford object with the specified representation label. */
-static bool is_clifford_tinfo(unsigned ti, unsigned char rl)
-{
-       return ti == (TINFO_clifford + rl);
-}
-
-/** Check whether a given tinfo key (as returned by return_type_tinfo()
- *  is that of a clifford object (with an arbitrary representation label). */
-static bool is_clifford_tinfo(unsigned ti)
-{
-       return (ti & ~0xff) == TINFO_clifford;
+       static varidx xi((new symbol)->setflag(status_flags::dynallocated), dim),
+               chi((new symbol)->setflag(status_flags::dynallocated), dim);
+   return clifford(e, varidx(0, dim), indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl);
 }
 
 /** Extract representation label from tinfo key (as returned by
  *  return_type_tinfo()). */
-static unsigned char get_representation_label(unsigned ti)
+static unsigned char get_representation_label(const return_type_t& ti)
 {
-       return ti & 0xff;
+       return (unsigned char)ti.rl;
 }
 
 /** Take trace of a string of an even number of Dirac gammas given a vector
@@ -937,59 +1011,70 @@ ex dirac_trace(const ex & e, unsigned char rl, const ex & trONE)
 }
 
 
-ex canonicalize_clifford(const ex & e)
+ex canonicalize_clifford(const ex & e_)
 {
-       // Scan for any ncmul objects
-       exmap srl;
-       ex aux = e.to_rational(srl);
-       for (exmap::iterator i = srl.begin(); i != srl.end(); ++i) {
-
-               ex lhs = i->first;
-               ex rhs = i->second;
-
-               if (is_exactly_a<ncmul>(rhs)
-                && rhs.return_type() == return_types::noncommutative
-                && is_clifford_tinfo(rhs.return_type_tinfo())) {
-
-                       // Expand product, if necessary
-                       ex rhs_expanded = rhs.expand();
-                       if (!is_a<ncmul>(rhs_expanded)) {
-                               i->second = canonicalize_clifford(rhs_expanded);
-                               continue;
-
-                       } else if (!is_a<clifford>(rhs.op(0)))
-                               continue;
-
-                       exvector v;
-                       v.reserve(rhs.nops());
-                       for (size_t j=0; j<rhs.nops(); j++)
-                               v.push_back(rhs.op(j));
-
-                       // Stupid recursive bubble sort because we only want to swap adjacent gammas
-                       exvector::iterator it = v.begin(), next_to_last = v.end() - 1;
-                       if (is_a<diracgamma5>(it->op(0)) || is_a<diracgammaL>(it->op(0)) || is_a<diracgammaR>(it->op(0)))
-                               ++it;
-                       while (it != next_to_last) {
-                               if (it[0].compare(it[1]) > 0) {
-                                       ex save0 = it[0], save1 = it[1];
-                                       ex b1, i1, b2, i2;
-                                       base_and_index(it[0], b1, i1);
-                                       base_and_index(it[1], b2, i2);
-                                       it[0] = (ex_to<clifford>(save0).get_metric(i1, i2) * b1 * b2).simplify_indexed();
-                                       it[1] = v.size() == 2 ? _ex2 * dirac_ONE(ex_to<clifford>(it[1]).get_representation_label()) : _ex2;
-                                       ex sum = ncmul(v);
-                                       it[0] = save1;
-                                       it[1] = save0;
-                                       sum -= ncmul(v, true);
-                                       i->second = canonicalize_clifford(sum);
-                                       goto next_sym;
+       pointer_to_map_function fcn(canonicalize_clifford);
+
+       if (is_a<matrix>(e_)    // || is_a<pseries>(e) || is_a<integral>(e)
+               || e_.info(info_flags::list)) {
+               return e_.map(fcn);
+       } else {
+               ex e=simplify_indexed(e_);
+               // Scan for any ncmul objects
+               exmap srl;
+               ex aux = e.to_rational(srl);
+               for (exmap::iterator i = srl.begin(); i != srl.end(); ++i) {
+
+                       ex lhs = i->first;
+                       ex rhs = i->second;
+
+                       if (is_exactly_a<ncmul>(rhs)
+                                       && rhs.return_type() == return_types::noncommutative
+                                       && is_clifford_tinfo(rhs.return_type_tinfo())) {
+
+                               // Expand product, if necessary
+                               ex rhs_expanded = rhs.expand();
+                               if (!is_a<ncmul>(rhs_expanded)) {
+                                       i->second = canonicalize_clifford(rhs_expanded);
+                                       continue;
+
+                               } else if (!is_a<clifford>(rhs.op(0)))
+                                       continue;
+
+                               exvector v;
+                               v.reserve(rhs.nops());
+                               for (size_t j=0; j<rhs.nops(); j++)
+                                       v.push_back(rhs.op(j));
+
+                               // Stupid recursive bubble sort because we only want to swap adjacent gammas
+                               exvector::iterator it = v.begin(), next_to_last = v.end() - 1;
+                               if (is_a<diracgamma5>(it->op(0)) || is_a<diracgammaL>(it->op(0)) || is_a<diracgammaR>(it->op(0)))
+                                       ++it;
+
+                               while (it != next_to_last) {
+                                       if (it[0].compare(it[1]) > 0) {
+
+                                               ex save0 = it[0], save1 = it[1];
+                                               ex b1, i1, b2, i2;
+                                               base_and_index(it[0], b1, i1);
+                                               base_and_index(it[1], b2, i2);
+                                               // for Clifford algebras (commutator_sign == -1) metric should be symmetrised
+                                               it[0] = (ex_to<clifford>(save0).get_metric(i1, i2, ex_to<clifford>(save0).get_commutator_sign() == -1) * b1 * b2).simplify_indexed();
+                                               it[1] = v.size() ? _ex2 * dirac_ONE(ex_to<clifford>(save0).get_representation_label()) : _ex2;
+                                               ex sum = ncmul(v);
+                                               it[0] = save1;
+                                               it[1] = save0;
+                                               sum += ex_to<clifford>(save0).get_commutator_sign() * ncmul(v, true);
+                                               i->second = canonicalize_clifford(sum);
+                                               goto next_sym;
+                                       }
+                                       ++it;
                                }
-                               ++it;
-                       }
 next_sym:      ;
+                       }
                }
+               return aux.subs(srl, subs_options::no_pattern).simplify_indexed();
        }
-       return aux.subs(srl, subs_options::no_pattern).simplify_indexed();
 }
 
 ex clifford_prime(const ex & e)
@@ -997,9 +1082,8 @@ ex clifford_prime(const ex & e)
        pointer_to_map_function fcn(clifford_prime);
        if (is_a<clifford>(e) && is_a<cliffordunit>(e.op(0))) {
                return -e;
-       } else if (is_a<add>(e)) {
-               return e.map(fcn);
-       } else if (is_a<ncmul>(e)) {
+       } else if (is_a<add>(e) || is_a<ncmul>(e) || is_a<mul>(e) //|| is_a<pseries>(e) || is_a<integral>(e)
+                          || is_a<matrix>(e) || e.info(info_flags::list)) {
                return e.map(fcn);
        } else if (is_a<power>(e)) {
                return pow(clifford_prime(e.op(0)), e.op(1));
@@ -1007,70 +1091,124 @@ ex clifford_prime(const ex & e)
                return e;
 }
 
-ex remove_dirac_ONE(const ex & e)
+ex remove_dirac_ONE(const ex & e, unsigned char rl, unsigned options)
 {
-       pointer_to_map_function fcn(remove_dirac_ONE);
-       if (is_a<clifford>(e) && is_a<diracone>(e.op(0))) {
-               return 1;
-       } else if (is_a<add>(e)) {
-               return e.map(fcn);
-       } else if (is_a<ncmul>(e)) {
-               return e.map(fcn);
-       } else if (is_a<mul>(e)) {
-               return e.map(fcn);
-       } else if (is_a<power>(e)) {
-               return pow(remove_dirac_ONE(e.op(0)), e.op(1));
-       } else
-               return e;
+       pointer_to_map_function_2args<unsigned char, unsigned> fcn(remove_dirac_ONE, rl, options | 1);
+       bool need_reevaluation = false;
+       ex e1 = e;
+       if (! (options & 1) )  { // is not a child
+               if (options & 2)
+                       e1 = expand_dummy_sum(e, true);
+               e1 = canonicalize_clifford(e1);
+       }
+       
+       if (is_a<clifford>(e1) && ex_to<clifford>(e1).get_representation_label() >= rl) {
+               if (is_a<diracone>(e1.op(0)))
+                       return 1;
+               else 
+                       throw(std::invalid_argument("remove_dirac_ONE(): expression is a non-scalar Clifford number!"));
+       } else if (is_a<add>(e1) || is_a<ncmul>(e1) || is_a<mul>(e1)  
+                          || is_a<matrix>(e1) || e1.info(info_flags::list)) {
+               if (options & 3) // is a child or was already expanded
+                       return e1.map(fcn);
+               else
+                       try {
+                               return e1.map(fcn);
+                       } catch (std::exception &p) {
+                               need_reevaluation = true;
+                       }
+       } else if (is_a<power>(e1)) {
+               if (options & 3) // is a child or was already expanded
+                       return pow(remove_dirac_ONE(e1.op(0), rl, options | 1), e1.op(1));
+               else
+                       try {
+                               return pow(remove_dirac_ONE(e1.op(0), rl, options | 1), e1.op(1));
+                       } catch (std::exception &p) {
+                               need_reevaluation = true;
+                       }
+       } 
+       if (need_reevaluation)
+               return remove_dirac_ONE(e, rl, options | 2);
+       return e1;
 }
 
-ex clifford_norm(const ex & e)
+char clifford_max_label(const ex & e, bool ignore_ONE)
 {
-       return sqrt(remove_dirac_ONE(canonicalize_clifford(e * clifford_bar(e)).simplify_indexed()));
+       if (is_a<clifford>(e))
+               if (ignore_ONE && is_a<diracone>(e.op(0)))
+                       return -1;
+               else
+                       return ex_to<clifford>(e).get_representation_label();
+       else {
+               char rl = -1;
+               for (size_t i=0; i < e.nops(); i++) 
+                       rl = (rl > clifford_max_label(e.op(i), ignore_ONE)) ? rl : clifford_max_label(e.op(i), ignore_ONE);
+               return rl;
+       }
 }
 
+ex clifford_norm(const ex & e)
+{
+       return sqrt(remove_dirac_ONE(e * clifford_bar(e)));
+}
+       
 ex clifford_inverse(const ex & e)
 {
        ex norm = clifford_norm(e);
        if (!norm.is_zero())
                return clifford_bar(e) / pow(norm, 2);
        else 
-               throw(std::invalid_argument("Cannot find inverse of Clifford number with zero norm!"));
+               throw(std::invalid_argument("clifford_inverse(): cannot find inverse of Clifford number with zero norm!"));
 }
 
 ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl)
 {
-       unsigned min, max;
        if (!ex_to<idx>(mu).is_dim_numeric())
-               throw(std::invalid_argument("Index should have a numeric dimension"));
-       unsigned dim = (ex_to<numeric>(ex_to<idx>(mu).get_dim())).to_int();
-       ex c = clifford_unit(mu, metr, rl);
-
-       if (is_a<matrix>(v)) {
-               if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) {
-                       min = ex_to<matrix>(v).rows();
-                       max = ex_to<matrix>(v).cols();
-               } else {
-                       min = ex_to<matrix>(v).cols();
-                       max = ex_to<matrix>(v).rows();
-               }
-               if (min == 1) {
-                       if (dim == max)
-                               if (is_a<varidx>(mu)) // need to swap variance
-                                       return indexed(v, ex_to<varidx>(mu).toggle_variance()) * c;
-                               else
-                                       return indexed(v, mu) * c;
+               throw(std::invalid_argument("lst_to_clifford(): Index should have a numeric dimension"));
+       ex e = clifford_unit(mu, metr, rl);
+       return lst_to_clifford(v, e);
+}
+
+ex lst_to_clifford(const ex & v, const ex & e) {
+       unsigned min, max;
+
+       if (is_a<clifford>(e)) {
+               ex mu = e.op(1);
+               ex mu_toggle
+                       = is_a<varidx>(mu) ? ex_to<varidx>(mu).toggle_variance() : mu;
+               unsigned dim = get_dim_uint(mu);
+
+               if (is_a<matrix>(v)) {
+                       if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows()) {
+                               min = ex_to<matrix>(v).rows();
+                               max = ex_to<matrix>(v).cols();
+                       } else {
+                               min = ex_to<matrix>(v).cols();
+                               max = ex_to<matrix>(v).rows();
+                       }
+                       if (min == 1) {
+                               if (dim == max)
+                                       return indexed(v, mu_toggle) * e;
+                               else if (max - dim == 1) {
+                                       if (ex_to<matrix>(v).cols() > ex_to<matrix>(v).rows())
+                                               return v.op(0) * dirac_ONE(ex_to<clifford>(e).get_representation_label()) + indexed(sub_matrix(ex_to<matrix>(v), 0, 1, 1, dim), mu_toggle) * e;
+                                       else 
+                                               return v.op(0) * dirac_ONE(ex_to<clifford>(e).get_representation_label()) + indexed(sub_matrix(ex_to<matrix>(v), 1, dim, 0, 1), mu_toggle) * e;
+                               } else
+                                       throw(std::invalid_argument("lst_to_clifford(): dimensions of vector and clifford unit mismatch"));
+                       } else
+                               throw(std::invalid_argument("lst_to_clifford(): first argument should be a vector (nx1 or 1xn matrix)"));
+               } else if (v.info(info_flags::list)) {
+                       if (dim == ex_to<lst>(v).nops())
+                               return indexed(matrix(dim, 1, ex_to<lst>(v)), mu_toggle) * e;
+                       else if (ex_to<lst>(v).nops() - dim == 1)
+                               return v.op(0) * dirac_ONE(ex_to<clifford>(e).get_representation_label()) + indexed(sub_matrix(matrix(dim+1, 1, ex_to<lst>(v)), 1, dim, 0, 1), mu_toggle) * e;
                        else
-                               throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch"));
+                               throw(std::invalid_argument("lst_to_clifford(): list length and dimension of clifford unit mismatch"));
                } else
-                       throw(std::invalid_argument("First argument should be a vector vector"));
-       } else if (is_a<lst>(v)) {
-               if (dim == ex_to<lst>(v).nops())
-                       return indexed(matrix(dim, 1, ex_to<lst>(v)), ex_to<varidx>(mu).toggle_variance()) * c;
-               else
-                       throw(std::invalid_argument("List length and dimension of clifford unit mismatch"));
+                       throw(std::invalid_argument("lst_to_clifford(): cannot construct from anything but list or vector"));
        } else
-               throw(std::invalid_argument("Cannot construct from anything but list or vector"));
+               throw(std::invalid_argument("lst_to_clifford(): the second argument should be a Clifford unit"));
 }
  
 /** Auxiliary structure to define a function for striping one Clifford unit
@@ -1078,113 +1216,147 @@ ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char r
 static ex get_clifford_comp(const ex & e, const ex & c) 
 {
        pointer_to_map_function_1arg<const ex &> fcn(get_clifford_comp, c);
-       int ival = ex_to<numeric>(ex_to<varidx>(c.op(1)).get_value()).to_int();
+       int ival = ex_to<numeric>(ex_to<idx>(c.op(1)).get_value()).to_int();
                
-       if (is_a<add>(e) || is_a<lst>(e) // || is_a<pseries>(e) || is_a<integral>(e)
+       if (is_a<add>(e) || e.info(info_flags::list) // || is_a<pseries>(e) || is_a<integral>(e)
                || is_a<matrix>(e)) 
                return e.map(fcn);
        else if (is_a<ncmul>(e) || is_a<mul>(e)) {
                // find a Clifford unit with the same metric, delete it and substitute its index
                size_t ind = e.nops() + 1;
-               for (size_t j = 0; j < e.nops(); j++) 
-                       if (is_a<clifford>(e.op(j)) && ex_to<clifford>(c).same_metric(e.op(j)))
-                               if (ind > e.nops()) 
+               for (size_t j = 0; j < e.nops(); j++) {
+                       if (is_a<clifford>(e.op(j)) && ex_to<clifford>(c).same_metric(e.op(j))) {
+                               if (ind > e.nops()) {
                                        ind = j;
-                               else 
-                                       throw(std::invalid_argument("Expression is a Clifford multi-vector"));
+                               }
+                               else {
+                                       throw(std::invalid_argument("get_clifford_comp(): expression is a Clifford multi-vector"));
+                               }
+                       }
+               }
                if (ind < e.nops()) {
                        ex S = 1;
                        bool same_value_index, found_dummy;
-                       same_value_index = ( ex_to<varidx>(e.op(ind).op(1)).is_numeric()
-                                                                &&  (ival == ex_to<numeric>(ex_to<varidx>(e.op(ind).op(1)).get_value()).to_int()) );
+                       same_value_index = ( ex_to<idx>(e.op(ind).op(1)).is_numeric()
+                                                                &&  (ival == ex_to<numeric>(ex_to<idx>(e.op(ind).op(1)).get_value()).to_int()) );
                        found_dummy = same_value_index;
-                       for(size_t j=0; j < e.nops(); j++)
-                               if (j != ind) 
-                                       if (same_value_index) 
+                       for (size_t j=0; j < e.nops(); j++) {
+                               if (j != ind) {
+                                       if (same_value_index) {
                                                S = S * e.op(j);
+                                       }
                                        else {
                                                exvector ind_vec = ex_to<indexed>(e.op(j)).get_dummy_indices(ex_to<indexed>(e.op(ind)));
                                                if (ind_vec.size() > 0) {
                                                        found_dummy = true;
                                                        exvector::const_iterator it = ind_vec.begin(), itend = ind_vec.end();
                                                        while (it != itend) {
-                                                               S = S * e.op(j).subs(lst(ex_to<varidx>(*it) == ival, ex_to<varidx>(*it).toggle_variance() == ival), subs_options::no_pattern);
+                                                               ex curridx = *it;
+                                                               ex curridx_toggle = is_a<varidx>(curridx)
+                                                                       ? ex_to<varidx>(curridx).toggle_variance()
+                                                                       : curridx;
+                                                               S = S * e.op(j).subs(lst(curridx == ival,
+                                                                       curridx_toggle == ival), subs_options::no_pattern);
                                                                ++it;
                                                        }
                                                } else
                                                        S = S * e.op(j);
                                        }
+                               }
+                       }
                        return (found_dummy ? S : 0);
                } else
-                       throw(std::invalid_argument("Expression is not a Clifford vector to the given units"));
+                       throw(std::invalid_argument("get_clifford_comp(): expression is not a Clifford vector to the given units"));
        } else if (e.is_zero()) 
                return e;
        else if (is_a<clifford>(e) && ex_to<clifford>(e).same_metric(c))
-               if ( ex_to<varidx>(e.op(1)).is_numeric() &&
-                        (ival != ex_to<numeric>(ex_to<varidx>(e.op(1)).get_value()).to_int()) )
+               if ( ex_to<idx>(e.op(1)).is_numeric() &&
+                        (ival != ex_to<numeric>(ex_to<idx>(e.op(1)).get_value()).to_int()) )
                        return 0;
                else 
                        return 1;
        else
-               throw(std::invalid_argument("Expression is not usable as a Clifford vector"));
+               throw(std::invalid_argument("get_clifford_comp(): expression is not usable as a Clifford vector"));
 }
 
 
-lst clifford_to_lst (const ex & e, const ex & c, bool algebraic)
+lst clifford_to_lst(const ex & e, const ex & c, bool algebraic)
 {
        GINAC_ASSERT(is_a<clifford>(c));
-       varidx mu = ex_to<varidx>(c.op(1));
-       if (! mu.is_dim_numeric())
-               throw(std::invalid_argument("Index should have a numeric dimension"));
-       unsigned int D = ex_to<numeric>(mu.get_dim()).to_int();
+       ex mu = c.op(1);
+       if (! ex_to<idx>(mu).is_dim_numeric())
+               throw(std::invalid_argument("clifford_to_lst(): index should have a numeric dimension"));
+       unsigned int D = ex_to<numeric>(ex_to<idx>(mu).get_dim()).to_int();
 
        if (algebraic) // check if algebraic method is applicable
                for (unsigned int i = 0; i < D; i++) 
-                       if (pow(c.subs(mu == i), 2) == 0)
+                       if (pow(c.subs(mu == i, subs_options::no_pattern), 2).is_zero() 
+                               or (not is_a<numeric>(pow(c.subs(mu == i, subs_options::no_pattern), 2))))
                                algebraic = false;
        lst V; 
-       if (algebraic) 
+       ex v0 = remove_dirac_ONE(canonicalize_clifford(e+clifford_prime(e)).normal())/2;
+       if (not v0.is_zero())
+               V.append(v0);
+       ex e1 = canonicalize_clifford(e - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label())); 
+       if (algebraic) {
                for (unsigned int i = 0; i < D; i++) 
                        V.append(remove_dirac_ONE(
-                                               simplify_indexed(canonicalize_clifford(e * c.subs(mu == i) +  c.subs(mu == i) * e))
-                                               / (2*pow(c.subs(mu == i), 2))));
-       else {
-               ex e1 = canonicalize_clifford(e);
-               for (unsigned int i = 0; i < D; i++) 
-                       V.append(get_clifford_comp(e1, c.subs(c.op(1) == i)));
+                                               simplify_indexed(canonicalize_clifford(e1 * c.subs(mu == i, subs_options::no_pattern) +  c.subs(mu == i, subs_options::no_pattern) * e1))
+                                               / (2*pow(c.subs(mu == i, subs_options::no_pattern), 2))));
+       } else {
+               try {
+                       for (unsigned int i = 0; i < D; i++) 
+                               V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern)));
+               } catch  (std::exception &p) {
+                       /* Try to expand dummy summations to simplify the expression*/
+                       e1 = canonicalize_clifford(expand_dummy_sum(e, true));
+                       V.remove_all();
+                       v0 = remove_dirac_ONE(canonicalize_clifford(e1+clifford_prime(e1)).normal())/2;
+                       if (not v0.is_zero()) {
+                               V.append(v0);
+                               e1 = canonicalize_clifford(e1 - v0 * dirac_ONE(ex_to<clifford>(c).get_representation_label())); 
+                       }
+                       for (unsigned int i = 0; i < D; i++) 
+                               V.append(get_clifford_comp(e1, c.subs(c.op(1) == i, subs_options::no_pattern)));
+               }
        }
        return V;
 }
 
 
-ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d, const ex & v, const ex & G)
+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)
 {
-       ex x, D;
-       if (is_a<indexed>(G)) 
-               D = ex_to<varidx>(G.op(1)).get_dim();
-       else if (is_a<matrix>(G)) 
-               D = ex_to<matrix>(G).rows();
-       else
-               throw(std::invalid_argument("metric should be an indexed object or matrix"));
+       ex x, D, cu;
+       
+       if (! is_a<matrix>(v) && ! v.info(info_flags::list))
+               throw(std::invalid_argument("clifford_moebius_map(): parameter v should be either vector or list"));
+       
+       if (is_a<clifford>(G)) {
+               cu = G;
+       } else {
+               if (is_a<indexed>(G)) {
+                       D = ex_to<idx>(G.op(1)).get_dim();
+                       varidx mu((new symbol)->setflag(status_flags::dynallocated), D);
+                       cu = clifford_unit(mu, G, rl);
+               } else if (is_a<matrix>(G)) {
+                       D = ex_to<matrix>(G).rows(); 
+                       idx mu((new symbol)->setflag(status_flags::dynallocated), D);
+                       cu = clifford_unit(mu, G, rl);
+               } else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit"));
+               
+       }
        
-       varidx mu((new symbol)->setflag(status_flags::dynallocated), D);
-                  
-       if (! is_a<matrix>(v) && ! is_a<lst>(v))
-               throw(std::invalid_argument("parameter v should be either vector or list"));
-
-       x = lst_to_clifford(v, mu, G);
-       ex e = simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d)));
-       ex cu = clifford_unit(mu, G);
-       return clifford_to_lst(e, cu, false);
+       x = lst_to_clifford(v, cu); 
+       ex e = clifford_to_lst(simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d))), cu, false);
+       return (is_a<matrix>(v) ? matrix(ex_to<matrix>(v).rows(), ex_to<matrix>(v).cols(), ex_to<lst>(e)) : e);
 }
 
-ex clifford_moebius_map(const ex & M, const ex & v, const ex & G
+ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl)
 {
-       if (is_a<matrix>(M)) 
-               return clifford_moebius_map(ex_to<matrix>(M)(0,0), ex_to<matrix>(M)(0,1), 
-                                               ex_to<matrix>(M)(1,0), ex_to<matrix>(M)(1,1), v, G);
+       if (is_a<matrix>(M) && (ex_to<matrix>(M).rows() == 2) && (ex_to<matrix>(M).cols() == 2)) 
+               return clifford_moebius_map(M.op(0), M.op(1), M.op(2), M.op(3), v, G, rl);
        else
-               throw(std::invalid_argument("parameter M should be a matrix"));
+               throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a 2x2 matrix"));
 }
 
 } // namespace GiNaC