[GiNaC-list] Question

[Vladimir V. Kisil]

		Hi,

>>>>> "JRG" == Javier Ros Ganuza <jros at unavarra.es> writes:
    JRG> I want to do algebra with cartesian (3x1) "vectors". Cartesian
    JRG> "vector"s are to be represented by a 3x1 Ginac vector (3-tuple)
    JRG> and a reference to a basis that tell us in which base the
    JRG> components have physical sense.

  Extension of GiNaC classes is not very difficult and you may implement
  from scratch. 
  However it may be better to do this through the Clifford algebras in
  GiNaC. There are many references (e.g. books of Hestenes) on doing
  geometry with Clifford algebras. 

    JRG> for example (in my particular jargon):
    JRG> vector1.expresion=matrix(3,1,lst(a1,b1,c1));
    JRG> vector1.basis=basis_k;
    JRG> vector2.expresion=matrix(3,1,lst(a2,b2,c2));
    JRG> vector1.basis=basis_l;

	This can be implemented as follows:
	
	varidx nu(symbol("nu", "\\nu"), 3), mu(symbol("mu", "\\mu"), 3);
		xi(symbol("xi", "\\xi"), 3),  rho(symbol("rho", "\\rho"),3);
	basis1 = clifford_unit(mu, diag_matrix(lst(1, 1, 1)));
	basis2 = clifford_unit(nu, diag_matrix(lst(1, 1, 1)));

	vector1 = lst_to_clifford(lst(a1,b1,c1), xi, basis1);
	vector2 = lst_to_clifford(lst(a1,b1,c1), rho, basis2);

	Then the expression

    JRG> result=2*vector1+vector2;

  will be well defined and behave as expected even without reduction to
  the single basis. The reduction is needed only if someone try to
  extract its components in either basis1,  basis2, or even another
  basis3. To this end values of all products like basis1[i]*basis2[j]
  (i.e. transition matrix) should be defined.

  Best wishes,
  Vladimir
-- 
Vladimir V. Kisil     email: kisilv at maths.leeds.ac.uk
--                      www: http://maths.leeds.ac.uk/~kisilv/