* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*/
+#include <stdexcept>
+
#include "clifford.h"
#include "ex.h"
return m;
}
-clifford::clifford() : representation_label(0), metric(default_metric())
+clifford::clifford() : representation_label(0), metric(default_metric()), anticommuting(false)
{
tinfo_key = TINFO_clifford;
}
/** 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, bool anticommut) : inherited(b), representation_label(rl), metric(0), anticommuting(anticommut)
{
tinfo_key = TINFO_clifford;
}
* 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, bool anticommut) : inherited(b, mu), representation_label(rl), metric(metr), anticommuting(anticommut)
{
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, bool anticommut, const exvector & v, bool discardable) : inherited(not_symmetric(), v, discardable), representation_label(rl), metric(metr), anticommuting(anticommut)
{
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, bool anticommut, std::auto_ptr<exvector> vp) : inherited(not_symmetric(), vp), representation_label(rl), metric(metr), anticommuting(anticommut)
{
tinfo_key = TINFO_clifford;
}
n.find_unsigned("label", rl);
representation_label = rl;
n.find_ex("metric", metric, sym_lst);
+ n.find_bool("anticommuting", anticommuting);
}
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);
}
DEFAULT_UNARCHIVE(clifford)
// functions overriding virtual functions from base classes
//////////
-ex clifford::get_metric(const ex & i, const ex & j) const
+ex clifford::get_metric(const ex & i, const ex & j, bool symmetrised) const
{
- return indexed(metric, symmetric2(), i, j);
+ 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 indexed(metric.op(0), ex_to<symmetry>(ex_to<indexed>(metric).get_symmetry()), i, j);
+ }
+ } else {
+ // should not really happen since all constructors but clifford() make the metric an indexed object
+ return indexed(metric, i, j);
+ }
}
bool clifford::same_metric(const ex & other) const
{
if (is_a<clifford>(other)) {
- return get_metric().is_equal(ex_to<clifford>(other).get_metric());
+ 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
* 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
+ 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 0; //nothing found
+ return -1; //nothing found
}
/** Contraction of a Clifford unit with something else. */
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));
+ 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));
// 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));
+ if (prev_square > -1) {
+ *self = indexed(squared_metric, mu, mu_toggle);
+ v[prev_square] = _ex1;
+ } else {
+ *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) {
+ 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;
+ }
+ } 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) {
+ 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);
+ }
+ } 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;
}
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;
}
}
if (s.empty())
- return clifford(diracone(), representation_label) * sign;
+ return dirac_ONE(representation_label) * sign;
if (something_changed)
return reeval_ncmul(s) * sign;
else
ex clifford::thiscontainer(const exvector & v) const
{
- return clifford(representation_label, get_metric(), v);
+ return clifford(representation_label, get_metric(), is_anticommuting(), v);
}
ex clifford::thiscontainer(std::auto_ptr<exvector> vp) const
{
- return clifford(representation_label, get_metric(), vp);
+ return clifford(representation_label, get_metric(), is_anticommuting(), vp);
}
ex diracgamma5::conjugate() const
ex dirac_ONE(unsigned char rl)
{
static ex ONE = (new diracone)->setflag(status_flags::dynallocated);
- return clifford(ONE, rl);
+ return clifford(ONE, rl, false);
}
-ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl)
+ex clifford_unit(const ex & mu, const ex & metr, unsigned char rl, bool anticommuting)
{
static 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))
- return clifford(unit, mu, metr, rl);
- else
- throw(std::invalid_argument("metric for Clifford unit must be of type indexed, tensormetric or matrix"));
+ 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)"));
+
+ 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<tensmetric>(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);
+ } 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),
+ chi((new symbol)->setflag(status_flags::dynallocated), n);
+ if ((n == M.cols()) && (n == ex_to<varidx>(mu).get_dim())) {
+ for (unsigned i = 0; i < n; i++) {
+ for (unsigned j = i+1; j < n; j++) {
+ if (M(i, j) != 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);
+ } 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, tensormetric or matrix"));
+ }
}
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(default_metric(), symmetric2(), xi, chi), rl, true);
}
ex dirac_gamma5(unsigned char rl)
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[0] = (ex_to<clifford>(save0).get_metric(i1, i2, true) * 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;
return e;
}
-ex remove_dirac_ONE(const ex & e, unsigned char rl)
+ex remove_dirac_ONE(const ex & e, unsigned char rl, unsigned options)
{
- pointer_to_map_function_1arg<unsigned char> fcn(remove_dirac_ONE, rl);
- if (is_a<clifford>(e) && ex_to<clifford>(e).get_representation_label() >= rl) {
- if (is_a<diracone>(e.op(0)))
+ 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) || is_a<lst>(e1)) {
+ if (options & 3) // is a child or was already expanded
+ return e1.map(fcn);
else
- throw(std::invalid_argument("Expression is a non-scalar Clifford number!"));
- } 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) || is_a<lst>(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;
+ 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)
+ex lst_to_clifford(const ex & v, const ex & mu, const ex & metr, unsigned char rl, bool anticommuting)
{
if (!ex_to<idx>(mu).is_dim_numeric())
- throw(std::invalid_argument("Index should have a numeric dimension"));
- ex e = clifford_unit(mu, metr, rl);
+ throw(std::invalid_argument("lst_to_clifford(): Index should have a numeric dimension"));
+ ex e = clifford_unit(mu, metr, rl, anticommuting);
return lst_to_clifford(v, e);
}
if (dim == max)
return indexed(v, ex_to<varidx>(mu).toggle_variance()) * e;
else
- throw(std::invalid_argument("Dimensions of vector and clifford unit mismatch"));
+ throw(std::invalid_argument("lst_to_clifford(): dimensions of vector and clifford unit mismatch"));
} else
- throw(std::invalid_argument("First argument should be a vector vector"));
+ throw(std::invalid_argument("lst_to_clifford(): 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()) * e;
else
- throw(std::invalid_argument("List length and dimension of clifford unit mismatch"));
+ throw(std::invalid_argument("lst_to_clifford(): list length and dimension of clifford unit mismatch"));
} else
- throw(std::invalid_argument("Cannot construct from anything but list or vector"));
+ throw(std::invalid_argument("lst_to_clifford(): cannot construct from anything but list or vector"));
} else
- throw(std::invalid_argument("The second argument should be a Clifford unit"));
+ 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
* from vectors. Used in clifford_to_lst(). */
static ex get_clifford_comp(const ex & e, const ex & c)
if (ind > e.nops())
ind = j;
else
- throw(std::invalid_argument("Expression is a Clifford multi-vector"));
+ 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;
}
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))
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"));
}
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"));
+ throw(std::invalid_argument("clifford_to_lst(): index should have a numeric dimension"));
unsigned int D = ex_to<numeric>(mu.get_dim()).to_int();
if (algebraic) // check if algebraic method is applicable
or (not is_a<numeric>(pow(c.subs(mu == i), 2))))
algebraic = false;
lst V;
- if (algebraic)
+ 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 {
+ } 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)));
+ try {
+ for (unsigned int i = 0; i < D; i++)
+ V.append(get_clifford_comp(e1, c.subs(c.op(1) == i)));
+ } catch (std::exception &p) {
+ /* Try to expand dummy summations to simplify the expression*/
+ e1 = canonicalize_clifford(expand_dummy_sum(e1, true));
+ for (unsigned int i = 0; i < D; i++)
+ V.append(get_clifford_comp(e1, c.subs(c.op(1) == i)));
+ }
}
return V;
}
-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 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 x, D, cu;
if (! is_a<matrix>(v) && ! is_a<lst>(v))
- throw(std::invalid_argument("parameter v should be either vector or list"));
+ throw(std::invalid_argument("clifford_moebius_map(): parameter v should be either vector or list"));
if (is_a<clifford>(G)) {
cu = 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, matrix, or a Clifford unit"));
+ 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);
+ cu = clifford_unit(mu, G, rl, anticommuting);
}
-
+
x = lst_to_clifford(v, cu);
ex e = simplify_indexed(canonicalize_clifford((a * x + b) * clifford_inverse(c * x + d)));
return clifford_to_lst(e, cu, false);
}
-ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl)
+ex clifford_moebius_map(const ex & M, const ex & v, const ex & G, unsigned char rl, bool anticommuting)
{
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);
+ 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);
else
- throw(std::invalid_argument("parameter M should be a matrix"));
+ throw(std::invalid_argument("clifford_moebius_map(): parameter M should be a matrix"));
}
} // namespace GiNaC
git://www.ginac.de / ginac.git / blobdiff