> < ^ Date: Mon, 16 Oct 2000 11:39:55 +0100 (BST)
< ^ From: Graham Ellis <0002319S@bodkin.nuigalway.ie >
> < ^ Subject:

Dear GAP-Forum,

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?

Best regards,
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.

Best regards,
Graham Ellis

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