Let I be an ideal of the polynomial ring
P = K[x_1, ..., x_n]. Let X be the set
{ x_1, ..., x_n } of variables of P.
A subset U of X is called independent modulo I if
I intersect 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 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.[Next] [Prev] [Right] [Left] [Up] [Index] [Root]