ic2 SciMax Toolbox icc1

SciMax Toolbox >> ic_convert

ic_convert

Maxima Function

Calling Sequence

ic_convert (eqn)

Description

Converts the itensor equation eqn to a ctensor assignment statement. Implied sums over dummy indices are made explicit while indexed objects are transformed into arrays (the array subscripts are in the order of covariant followed by contravariant indices of the indexed objects). The derivative of an indexed object will be replaced by the noun form of diff taken with respect to ct_coords subscripted by the derivative index. The Christoffel symbols ichr1 and ichr2 will be translated to lcs and mcs, respectively and if metricconvert is true then all occurrences of the metric with two covariant (contravariant) indices will be renamed to lg (ug). In addition, do loops will be introduced summing over all free indices so that the transformed assignment statement can be evaluated by just doing ev. The following examples demonstrate the features of this function.

(%i1) load(itensor);
(%o1)      /share/tensor/itensor.lisp
(%i2) eqn:ishow(t([i,j],[k])=f([],[])*g([l,m],[])*a([],[m],j)
      *b([i],[l,k]))$
                             k        m   l k
(%t2)                       t    = f a   b    g
                             i j      ,j  i    l m
(%i3) ic_convert(eqn);
(%o3) for i thru dim do (for j thru dim do (
       for k thru dim do
        t        : f sum(sum(diff(a , ct_coords ) b
         i, j, k                   m           j   i, l, k
 g    , l, 1, dim), m, 1, dim)))
  l, m
(%i4) imetric(g);
(%o4)                                done
(%i5) metricconvert:true;
(%o5)                                true
(%i6) ic_convert(eqn);
(%o6) for i thru dim do (for j thru dim do (
       for k thru dim do
        t        : f sum(sum(diff(a , ct_coords ) b
         i, j, k                   m           j   i, l, k
 lg    , l, 1, dim), m, 1, dim)))
   l, m
ic2 SciMax Toolbox icc1