Difference between revisions of "Package sagbi/SB.TorRingHS"

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   <short_description>This function computes the Hilbert series of the subalgebra generated by a given set of terms.</short_description>
 
   <short_description>This function computes the Hilbert series of the subalgebra generated by a given set of terms.</short_description>
 
    
 
    
   <syntax>SB.TorRingHS(G: LIST of POLY): TAGGED(<quotes>$hp.PSeries</quotes>)</syntax>
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   <syntax>SB.TorRingHS(G: LIST of POLY): TAGGED("$hp.PSeries")</syntax>
 
   <description>
 
   <description>
 
This function takes a list of terms <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 standard-graded subalgebra <tt>S = K[g|g in G]</tt> of <tt>R</tt>.
 
This function takes a list of terms <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 standard-graded subalgebra <tt>S = K[g|g in G]</tt> of <tt>R</tt>.

Latest revision as of 13:23, 29 October 2020

This article is about a function from ApCoCoA-2.

SB.TorRingHS

This function computes the Hilbert series of the subalgebra generated by a given set of terms.

Syntax

SB.TorRingHS(G: LIST of POLY): TAGGED("$hp.PSeries")

Description

This function takes a list of terms G all of the same polynomial ring R over the field K and computes the Hilbert series of the standard-graded subalgebra S = K[g|g in G] of R.

  • @param G A list of terms in R

  • @return The Hilbert series of the subalgebra K[g|g in G] of R

Example

Use QQ[x,y];
G := [x^2*y,  y^2,  x^2*y^2,  x^2*y^4];
SB.TorRingHS(G);
-----------------------------------------------------------------------------
---  Non-simplified HilbertPoincare' Series  ---
(1 - t^6 - t^8 + t^14) / ( (1-t^3)*(1-t^2)*(1-t^4)*(1-t^6) )

See also

Package sagbi/SB.GetHS

Package sagbi/SB.IsGraded

Package sagbi/SB.SubalgebraHS