+char clifford_max_label(const ex & e, bool ignore_ONE)
+{
+ 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("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)
+{
+ 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);
+ 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("lst_to_clifford(): list length and dimension of clifford unit mismatch"));
+ } else
+ throw(std::invalid_argument("lst_to_clifford(): cannot construct from anything but list or vector"));
+ } else
+ 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)
+{
+ pointer_to_map_function_1arg<const ex &> fcn(get_clifford_comp, c);
+ 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))
+ 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())
+ ind = j;
+ 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<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)
+ 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) {
+ 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<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("get_clifford_comp(): expression is not usable as a Clifford vector"));
+}