groebner::dimension -- the
dimension of the affine variety generated by polynomials
Introductiongroebner::dimension(polys) computes the
dimension of the affine variety generated by the polynomials in the set
or list polys.
Call(s)groebner::dimension(polys <, order>)
Parameterspolys |
- | a list or set of polynomials of the same type. Alternatively, a list or set of polynomial expressions with rational coefficients. |
order |
- | one of the identifiers DegInvLexOrder, DegreeOrder, and LexOrder, or a user-defined term ordering of type
Dom::MonomOrdering.
The default ordering is DegInvLexOrder. |
Returnsa nonnegative integer
Related
Functions
Detailsgroebner package concerning the
polynomial types and the ordering apply.polys must all be of the
same type. In particular, do not mix polynomials created via poly and polynomial
expressions!
Example
1An example from the book of Cox, Little and O'Shea (see below):
>> groebner::dimension([y^2*z^3, x^5*z^4, x^2*y*z^2])
2
Backgroundgroebner::gbasis. This Gröbner
basis is then used to compute the dimension of the affine variety
generated by the polynomials.Dom::MonomOrdering are handled.
The special term orderings from the Gröbner package were moved
there.