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]); 78167Note 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