Dimension of the affine variety generated by polynomials
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groebner::dimension(polys) computes the dimension
of the affine variety generated by the polynomials in the set or list
The rules laid down in the introduction to the groebner package concerning the polynomial types and the ordering apply.
The polynomials in the list
polys must all
be of the same type. In particular, do not mix polynomials created
An 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])
A list or set of polynomials or polynomial expressions of the same type. The coefficients in these polynomials and polynomial expressions can be arbitrary arithmetical expressions.
One of the identifiers
The implemented algorithm is described in Cox, Little, O'Shea: “Ideals, Varieties and Algorithms”, Springer, 1992, Chapter 9.
First, the Gröbner basis of the given polynomials with
respect to the given monomial ordering is computed using
Gröbner basis is then used to compute the dimension of the affine
variety generated by the polynomials.