* Implementation of GiNaC's clifford algebra (Dirac gamma) objects. */
/*
- * GiNaC Copyright (C) 1999-2006 Johannes Gutenberg University Mainz, Germany
+ * GiNaC Copyright (C) 1999-2011 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
* 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))
// 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)
/** 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<idx>(mu));
+}
+
+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)
{
- 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, 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;
}
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
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
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 term
- }
- }
- 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
{
&& 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);
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);
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
ex dirac_ONE(unsigned char rl)
{
static ex ONE = (new diracone)->setflag(status_flags::dynallocated);
- return clifford(ONE, rl, false);
+ return clifford(ONE, rl);
}
-ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl, bool anticommuting)
+static unsigned get_dim_uint(const ex& e)
{
- static ex unit = (new cliffordunit)->setflag(status_flags::dynallocated);
+ 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);
+ 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 ((indices.size() == 2) && is_a<varidx>(indices[0]) && is_a<varidx>(indices[1])) {
- return clifford(unit, mu, metr, 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 if (indices.size() == 0) { // a tensor or other expression without indices
- 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);
+ //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"));
}
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)
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
return e1;
}
-char clifford_max_label(const ex & e, bool ignore_ONE)
+int clifford_max_label(const ex & e, bool ignore_ONE)
{
if (is_a<clifford>(e))
if (ignore_ONE && is_a<diracone>(e.op(0)))
else
return ex_to<clifford>(e).get_representation_label();
else {
- char rl = -1;
+ int 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;
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);
}
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()) {
}
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
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))
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;
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++)
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))))
+ || (! 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 (! 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 (! 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)));
}
}
-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;
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);
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
git://www.ginac.de / ginac.git / blobdiff