Prettified source code.
[ginac.git] / ginac / clifford.cpp
index e306be8..3b4684c 100644 (file)
@@ -3,7 +3,7 @@
  *  Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */
 
 /*
- *  GiNaC Copyright (C) 1999-2006 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
@@ -20,8 +20,6 @@
  *  Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA  02110-1301  USA
  */
 
-#include <stdexcept>
-
 #include "clifford.h"
 
 #include "ex.h"
 #include "archive.h"
 #include "utils.h"
 
+#include <stdexcept>
+
 namespace GiNaC {
 
 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(clifford, indexed,
   print_func<print_dflt>(&clifford::do_print_dflt).
   print_func<print_latex>(&clifford::do_print_latex))
 
-const tinfo_static_t clifford::return_type_tinfo_static[256] = {{}};
-
 GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracone, tensor,
   print_func<print_dflt>(&diracone::do_print).
   print_func<print_latex>(&diracone::do_print_latex))
@@ -76,9 +74,8 @@ GINAC_IMPLEMENT_REGISTERED_CLASS_OPT(diracgammaR, tensor,
 // default constructors
 //////////
 
-clifford::clifford() : representation_label(0), metric(0), anticommuting(true), commutator_sign(-1)
+clifford::clifford() : representation_label(0), metric(0), commutator_sign(-1)
 {
-       tinfo_key = &clifford::tinfo_static;
 }
 
 DEFAULT_CTOR(diracone)
@@ -95,42 +92,43 @@ 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, bool anticommut) : inherited(b), representation_label(rl), metric(0), anticommuting(anticommut), commutator_sign(-1)
+clifford::clifford(const ex & b, unsigned char rl) : inherited(b), representation_label(rl), metric(0), commutator_sign(-1)
 {
-       tinfo_key = &clifford::tinfo_static;
 }
 
 /** 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, bool anticommut, int comm_sign) : inherited(b, mu), representation_label(rl), metric(metr), anticommuting(anticommut), commutator_sign(comm_sign)
+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 = &clifford::tinfo_static;
 }
 
-clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, int comm_sign, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), anticommuting(anticommut), commutator_sign(comm_sign)
+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)
+{
+}
+
+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 = &clifford::tinfo_static;
 }
 
-clifford::clifford(unsigned char rl, const ex & metr, bool anticommut, int comm_sign, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), anticommuting(anticommut), commutator_sign(comm_sign)
+return_type_t clifford::return_type_tinfo() const
 {
-       tinfo_key = &clifford::tinfo_static;
+       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_bool("anticommuting", anticommuting);
        n.find_unsigned("commutator_sign+1", rl);
        commutator_sign = rl - 1;
 }
@@ -140,17 +138,15 @@ void clifford::archive(archive_node & n) const
        inherited::archive(n);
        n.add_unsigned("label", representation_label);
        n.add_ex("metric", metric);
-       n.add_bool("anticommuting", anticommuting);
        n.add_unsigned("commutator_sign+1", commutator_sign+1);
 }
 
-DEFAULT_UNARCHIVE(clifford)
-DEFAULT_ARCHIVING(diracone)
-DEFAULT_ARCHIVING(cliffordunit)
-DEFAULT_ARCHIVING(diracgamma)
-DEFAULT_ARCHIVING(diracgamma5)
-DEFAULT_ARCHIVING(diracgammaL)
-DEFAULT_ARCHIVING(diracgammaR)
+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
@@ -158,29 +154,39 @@ 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)),
+                               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 indexed(metric.op(0), ex_to<symmetry>(ex_to<indexed>(metric).get_symmetry()), i, j);
                        return metric.subs(lst(metric.op(1) == i, metric.op(2) == j), subs_options::no_pattern);
                }
        } else {
-               // should not really happen since all constructors but clifford() make the metric an indexed object
-               return indexed(metric, i, j);
+               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);
        }
 }
 
 bool clifford::same_metric(const ex & other) const
 {
-       if (is_a<clifford>(other)) {
-               return same_metric(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;
+       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();
+       }
 }
 
 //////////
@@ -257,8 +263,21 @@ void clifford::do_print_dflt(const print_dflt & c, unsigned level) const
        if (is_dirac_slash(seq[0])) {
                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
@@ -426,22 +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 (size_t i=0; i<v.size(); i++) {
-               if (is_a<indexed>(v[i]) && !is_a<clifford>(v[i])
-                   && ((ex_to<varidx>(c.op(1)) == ex_to<indexed>(v[i]).get_indices()[0]
-                   && ex_to<varidx>(c.op(1)) == ex_to<indexed>(v[i]).get_indices()[1])
-                   || (ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[0]
-                   && ex_to<varidx>(c.op(1)).toggle_variance() == ex_to<indexed>(v[i]).get_indices()[1]))) {
-                       return i; // the index of the found
-               }
-       }
-       return -1; //nothing found
-}
-
 /** Contraction of a Clifford unit with something else. */
 bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator other, exvector & v) const
 {
@@ -458,53 +461,25 @@ 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);
-               const varidx d((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim()),
-                       in1((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim()),
-                       in2((new symbol)->setflag(status_flags::dynallocated), ex_to<idx>(self->op(1)).get_dim());
-               ex squared_metric;
-               if (prev_square > -1)
-                       squared_metric = simplify_indexed(indexed(v[prev_square].op(0), in1, d) 
-                                                                                         * unit.get_metric(d.toggle_variance(), in2, true)).op(0);
-
                exvector::iterator before_other = other - 1;
-               const varidx & mu = ex_to<varidx>(self->op(1));
-               const varidx & mu_toggle = ex_to<varidx>(other->op(1));
-               const varidx & alpha = ex_to<varidx>(before_other->op(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 > -1) {
-                               *self = indexed(squared_metric, mu, mu_toggle);
-                               v[prev_square] = _ex1;
-                       } else {
-                               *self = unit.get_metric(mu, mu_toggle, true);
-                       }
+                       *self = unit.get_metric(mu, mu_toggle, true);
                        *other = dirac_ONE(rl);
                        return true;
 
                } else if (other - self == 2) {
                        if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
-                               if (ex_to<clifford>(*self).is_anticommuting()) {
-                                       // e~mu e~alpha e.mu = (2*pow(e~alpha, 2) -Tr(B)) e~alpha
-                                       if (prev_square > -1) {
-                                               *self = 2 * indexed(squared_metric, alpha, alpha)
-                                                       - indexed(squared_metric, mu, mu_toggle);
-                                               v[prev_square] = _ex1;
-                                       } else {
-                                               *self = 2 * unit.get_metric(alpha, alpha, true) - unit.get_metric(mu, mu_toggle, true);
-                                       }
-                                       *other = _ex1;
-                                       return true;
-
-                               } else {
-                                       // 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;
-                               }
+                               // 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);
@@ -522,16 +497,7 @@ bool cliffordunit::contract_with(exvector::iterator self, exvector::iterator oth
                        ex S = ncmul(exvector(self + 1, before_other), true);
 
                        if (is_a<clifford>(*before_other) && ex_to<clifford>(*before_other).get_representation_label() == rl) {
-                               if (ex_to<clifford>(*self).is_anticommuting()) {
-                                       if (prev_square > -1) {
-                                               *self = 2 * (*before_other) * S * indexed(squared_metric, alpha, alpha)
-                                                       - (*self) * S * (*other) * (*before_other);
-                                       } else {
-                                               *self = 2 * (*before_other) * S * unit.get_metric(alpha, alpha, true) - (*self) * S * (*other) * (*before_other);
-                                       }
-                               } else {
-                                       *self = 2 * (*self) * S * unit.get_metric(alpha, mu_toggle, true) - (*self) * S * (*other) * (*before_other);
-                               }
+                               *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);
@@ -715,12 +681,12 @@ ex clifford::eval_ncmul(const exvector & v) const
 
 ex clifford::thiscontainer(const exvector & v) const
 {
-       return clifford(representation_label, metric, anticommuting, commutator_sign, v);
+       return clifford(representation_label, metric, commutator_sign, v);
 }
 
 ex clifford::thiscontainer(std::auto_ptr<exvector> vp) const
 {
-       return clifford(representation_label, metric, anticommuting, commutator_sign, vp);
+       return clifford(representation_label, metric, commutator_sign, vp);
 }
 
 ex diracgamma5::conjugate() const
@@ -745,56 +711,61 @@ ex diracgammaR::conjugate() const
 ex dirac_ONE(unsigned char rl)
 {
        static ex ONE = (new diracone)->setflag(status_flags::dynallocated);
-       return clifford(ONE, rl, false);
+       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, bool anticommuting)
+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<idx>(mu))
                throw(std::invalid_argument("clifford_unit(): index of Clifford unit must be of type idx or varidx"));
 
-       if (ex_to<idx>(mu).is_symbolic() && !is_a<varidx>(mu))
-               throw(std::invalid_argument("clifford_unit(): symbolic index of Clifford unit must be of type varidx (not idx)"));
+       exvector indices = metr.get_free_indices();
 
-       if (is_a<indexed>(metr)) {
-               exvector indices = ex_to<indexed>(metr).get_indices();
-               if ((indices.size() == 2) && is_a<varidx>(indices[0]) && is_a<varidx>(indices[1])) {
-                       return clifford(unit, mu, metr, rl, anticommuting);
-               } else {
-                       throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be indexed exactly by two indices of same type as the given index"));
-               }
-       } else if (is_a<tensor>(metr)) {
-               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(unit, mu, indexed(metr, xi, chi), rl, anticommuting);
+       if (indices.size() == 2) {
+               return clifford(unit, mu, metr, rl);
        } else if (is_a<matrix>(metr)) {
                matrix M = ex_to<matrix>(metr);
                unsigned n = M.rows();
                bool symmetric = true;
-               anticommuting = true;
 
-               static varidx xi((new symbol)->setflag(status_flags::dynallocated), n),
+               //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 == ex_to<varidx>(mu).get_dim())) {
+               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) != M(j, i)) {
+                                       if (!M(i, j).is_equal(M(j, i))) {
                                                symmetric = false;
                                        }
-                                       if (M(i, j) != -M(j, i)) {
-                                               anticommuting = false;
-                                       }
                                }
                        }
-                       return clifford(unit, mu, indexed(metr, symmetric?symmetric2():not_symmetric(), xi, chi), rl, anticommuting);
+                       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 {
-               throw(std::invalid_argument("clifford_unit(): metric for Clifford unit must be of type indexed, tensor or matrix"));
-       }
+       } 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)
@@ -806,7 +777,7 @@ ex dirac_gamma(const ex & mu, unsigned char 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, true);
+       return clifford(gamma, mu, indexed((new minkmetric)->setflag(status_flags::dynallocated), symmetric2(), xi, chi), rl);
 }
 
 ex dirac_gamma5(unsigned char rl)
@@ -835,22 +806,14 @@ ex dirac_slash(const ex & e, const ex & dim, unsigned char rl)
 
        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, true);
-}
-
-/** Check whether a given tinfo key (as returned by return_type_tinfo()
- *  is that of a clifford object (with an arbitrary representation label). */
-bool is_clifford_tinfo(tinfo_t ti)
-{
-       p_int start_loc=(p_int)&clifford::return_type_tinfo_static;
-       return (p_int)ti>=start_loc && (p_int)ti<start_loc+256;
+   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(tinfo_t ti)
+static unsigned char get_representation_label(const return_type_t& ti)
 {
-       return (unsigned char)((p_int)ti-(p_int)&clifford::return_type_tinfo_static);
+       return (unsigned char)ti.rl;
 }
 
 /** Take trace of a string of an even number of Dirac gammas given a vector
@@ -1198,11 +1161,11 @@ ex clifford_inverse(const ex & e)
                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, bool anticommuting)
+ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl)
 {
        if (!ex_to<idx>(mu).is_dim_numeric())
                throw(std::invalid_argument("lst_to_clifford(): Index should have a numeric dimension"));
-       ex e = clifford_unit(mu, metr, rl, anticommuting);
+       ex e = clifford_unit(mu, metr, rl);
        return lst_to_clifford(v, e);
 }
 
@@ -1210,8 +1173,10 @@ ex lst_to_clifford(const ex & v, const ex & e) {
        unsigned min, max;
 
        if (is_a<clifford>(e)) {
-               varidx mu = ex_to<varidx>(e.op(1));
-               unsigned dim = (ex_to<numeric>(mu.get_dim())).to_int();
+               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()) {
@@ -1223,14 +1188,21 @@ ex lst_to_clifford(const ex & v, const ex & e) {
                        }
                        if (min == 1) {
                                if (dim == max)
-                                       return indexed(v, ex_to<varidx>(mu).toggle_variance()) * e;
-                               else
+                                       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)), ex_to<varidx>(mu).toggle_variance()) * e;
+                               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("lst_to_clifford(): list length and dimension of clifford unit mismatch"));
                } else
@@ -1244,7 +1216,7 @@ ex lst_to_clifford(const ex & v, const ex & e) {
 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) || e.info(info_flags::list) // || is_a<pseries>(e) || is_a<integral>(e)
                || is_a<matrix>(e)) 
@@ -1252,42 +1224,54 @@ static ex get_clifford_comp(const ex & e, const ex & c)
        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 
+                               }
+                               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("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;
@@ -1299,10 +1283,10 @@ static ex get_clifford_comp(const ex & e, const ex & c)
 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())
+       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>(mu.get_dim()).to_int();
+       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++) 
@@ -1310,19 +1294,28 @@ lst clifford_to_lst(const ex & e, const ex & c, bool algebraic)
                                or (not is_a<numeric>(pow(c.subs(mu == i, subs_options::no_pattern), 2))))
                                algebraic = false;
        lst V; 
+       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, subs_options::no_pattern) +  c.subs(mu == i, subs_options::no_pattern) * e))
+                                               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 {
-               ex e1 = canonicalize_clifford(e);
                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(e1, true));
+                       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)));
                }
@@ -1331,7 +1324,7 @@ lst clifford_to_lst(const ex & e, const ex & c, bool algebraic)
 }
 
 
-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, bool anticommuting)
+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, cu;
        
@@ -1341,14 +1334,16 @@ ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d,
        if (is_a<clifford>(G)) {
                cu = G;
        } else {
-               if (is_a<indexed>(G)) 
-                       D = ex_to<varidx>(G.op(1)).get_dim();
-               else if (is_a<matrix>(G)) 
+               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(); 
-               else throw(std::invalid_argument("clifford_moebius_map(): metric should be an indexed object, matrix, or a Clifford unit"));
+                       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);
-               cu = clifford_unit(mu, G, rl, anticommuting);
        }
        
        x = lst_to_clifford(v, cu); 
@@ -1356,13 +1351,12 @@ ex clifford_moebius_map(const ex & a, const ex & b, const ex & c, const ex & d,
        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, unsigned char rl, bool anticommuting)
+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, rl, anticommuting);
+       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("clifford_moebius_map(): parameter M should be a matrix"));
+               throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a 2x2 matrix"));
 }
 
 } // namespace GiNaC