Package sagbi/SB.SubalgebraHS
From ApCoCoAWiki
| This article is about a function from ApCoCoA-2. |
SB.SubalgebraHS
This function computes the Hilbert series of the subalgebra generated by a given set of homogeneous polynomials.
Syntax
SB.SubalgebraHS(G: LIST of POLY): TAGGED("$hp.PSeries")
Description
This function takes a list of polynomials G all of the same polynomial ring R over the field K and computes the Hilbert series of the subalgebra S = K[g | g in G] of R. Note that the polynomials in G all have to be homogeneous such that the subalgebra S is standard-graded and its Hilbert series is well-defined.
@param G A list of polynomials
@return The Hilbert series of the subalgebra K[g | g in G] of R
Example
Use QQ[x,y]; G := [x^2*y, x^2 -y^2, x^2*y^2 -y^4, x^2*y^4]; SB.SubalgebraHS(G); ----------------------------------------------------------------------------- --- Non-simplified HilbertPoincare' Series --- (1 - t^8 - t^10 - t^12 + t^14 + t^16) / ( (1-t^3)*(1-t^2)*(1-t^4)*(1-t^6) )
See also
