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( | + | <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
