62.7 Multivariate Polynomials

  • Value( ratfun, indets, vals[, one] ) O
  • Value( upol, value[, one] ) O

    The first variant takes a rational function ratfun and specializes the indeterminates given in indets to the values given in vals, replacing the i-th indeterminate indets i by vals i. If this specialization results in a constant polynomial, an element of the coefficient ring is returned. If the specialization would specialize the denominator of ratfun to a noninvertible element, fail is returned.

    A variation is the evaluation at elements of another ring R, for which a multiplication with elements of the coefficient ring of ratfun are defined. In this situation the identity element of R may be given by a further argument one which will be used for x0 for any specialized indeterminate x.

    The second version takes an univariate rational function and specializes the value of its indeterminate to val. Again, an optional argument one may be given.

    gap> Value(x*y+y+x^7,[x,y],[5,7]);
    78167
    
    Note that the default values for one can lead to different results than one would expect: For example for a matrix M, the values M+M0 and M+1 are different. As Value defaults to the one of the coefficient ring, when evaluating Matrices in polynomials always the correct one should be given!

  • OnIndeterminates( poly, perm ) F

    A permutation perm acts on the multivariate polynomial poly by permuting the indeterminates as it permutes points.

    gap> OnIndeterminates(x^7*y+x*y^4,(1,17)(2,28)); 
    x_17*x_28^4+x_17^7*x_28
    gap> Stabilizer(Group((1,2,3,4),(1,2)),x*y,OnIndeterminates);
    Group( [ (1,2), (3,4) ] )
    

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    GAP 4 manual
    February 2000