since we are very unexperienced in the use of GAP we would
like to know how to deal with the following problem:
We are given a finitly presented group G (we know how to encode
this in GAP) and want GAP to replace each generator by a product
of two new symbols (a representation of G) thus giving us a
new set of relators. Then we would like GAP to give us the
Fox-derivatives of this set of new relators.
Making a trivial example:replace: a -> xv, b -> wy Relator: r= a^-1 b a^3 -> v^-1 x^-1 w y (x v)^3 partial Fox-derivative for x: -> -v^-1 + v^-1 x^-1 w y (1+v+v^2)
Where in the manual shall we turn pages to find how to do this?
Stephan Rosebrock and Cynthia Hog-Angeloni
Irina Kholodna has written a short GAP package for computing a minimal set of
generators for the second homotopy group of the CW-space associated to a finite
presentation of a (finite) group. The package, which includes a function for
computing Fox derivatives, is included as an appendix to a paper in the
Journal of Mathematics and Computation (1999, http://www.lms.ac.uk). The
package is also available from http://hamilton.nuigalway.ie.