Difference between revisions of "Package sagbi/SB.SubalgebraHS"
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<short_description>This function computes the Hilbert series of the subalgebra generated by a given set of homogeneous polynomials.</short_description> | <short_description>This function computes the Hilbert series of the subalgebra generated by a given set of homogeneous polynomials.</short_description> | ||
| − | <syntax>SB.SubalgebraHS(G: LIST of POLY): TAGGED( | + | <syntax>SB.SubalgebraHS(G: LIST of POLY): TAGGED("$hp.PSeries")</syntax> |
<description> | <description> | ||
This function takes a list of polynomials <tt>G</tt> all of the same polynomial ring <tt>R</tt> over the field <tt>K</tt> and computes the Hilbert series of the subalgebra <tt>S = K[g | g in G]</tt> of <tt>R</tt>. Note that the polynomials in <tt>G</tt> all have to be homogeneous such that the subalgebra <tt>S</tt> is standard-graded and its Hilbert series is well-defined. | This function takes a list of polynomials <tt>G</tt> all of the same polynomial ring <tt>R</tt> over the field <tt>K</tt> and computes the Hilbert series of the subalgebra <tt>S = K[g | g in G]</tt> of <tt>R</tt>. Note that the polynomials in <tt>G</tt> all have to be homogeneous such that the subalgebra <tt>S</tt> is standard-graded and its Hilbert series is well-defined. | ||
Latest revision as of 13:23, 29 October 2020
| This article is about a function from ApCoCoA-2. |
SB.SubalgebraHS
This function computes the Hilbert series of the subalgebra generated by a given set of homogeneous polynomials.
Syntax
SB.SubalgebraHS(G: LIST of POLY): TAGGED("$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
