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Let I be an ideal of the polynomial ring
P = K[x1, ..., xn], where K is a field. Let X be the set
{ x1, ..., xn } of variables of P.
A subset U of X is called independent modulo I if
I ∩K[U] = emptyset.
A subset U of X is called maximally independent modulo I if
U is independent modulo I, and no proper superset of U is
independent modulo I. The dimension of I is defined to
be the maximum of the cardinalities of all the independent sets
modulo I.
Note that the definition given above of zero-dimensionality (as the
case when the quotient of P by I has finite dimension as a vector
space over the coefficient field) coincides with the definition of
zero-dimensionality as dimension 0.
Dimension(I) : RngMPol -> RngIntElt, [ RngIntElt ]
Given an ideal I of a polynomial ring P defined over a field, return the
dimension d of I, together with a (sorted) sequence U of integers
of length d such that the variables of P corresponding to the integers
of U constitute a maximally independent set modulo I.
If I is the full polynomial ring P, the dimension is defined to
be -1, and the second return value is not set.
The algorithm implemented is that given in [BW93, p. 449].
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