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

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   <short_description>This function computes a vector space basis of a homogeneous component of a given degree of a given standard-graded subalgebra.</short_description>
 
   <short_description>This function computes a vector space basis of a homogeneous component of a given degree of a given standard-graded subalgebra.</short_description>
 
    
 
    
   <syntax>SB.GetInDeg(S: TAGGED(<quotes>$apcocoa/sagbi.Subalgebra</quotes>),d: INT): LIST of POLY</syntax>
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   <syntax>SB.GetInDeg(S: TAGGED("$apcocoa/sagbi.Subalgebra"),d: INT): LIST of POLY</syntax>
 
   <description>
 
   <description>
 
This function computes a vector space basis of the set <tt>{f in S | deg(t) = d for all t in the support of f}</tt>, i.e. the set of all homogeneous polynomials in <tt>S</tt> of degree <tt>d</tt>.
 
This function computes a vector space basis of the set <tt>{f in S | deg(t) = d for all t in the support of f}</tt>, i.e. the set of all homogeneous polynomials in <tt>S</tt> of degree <tt>d</tt>.

Latest revision as of 13:21, 29 October 2020

This article is about a function from ApCoCoA-2.

SB.GetInDeg

This function computes a vector space basis of a homogeneous component of a given degree of a given standard-graded subalgebra.

Syntax

SB.GetInDeg(S: TAGGED("$apcocoa/sagbi.Subalgebra"),d: INT): LIST of POLY

Description

This function computes a vector space basis of the set {f in S | deg(t) = d for all t in the support of f}, i.e. the set of all homogeneous polynomials in S of degree d.

  • @param S A standard graded subalgebra, i.e. a subalgebra generated by homogeneous polynomials

  • @param d The desired degree

  • @return A vector space basis of S_d

Example

Use R ::= QQ[x,y,z];
S := SB.Subalgebra(R,[x^2,y+z]);
PrintLn SB.GetInDeg(S,3);
-- [y^3 +3*y^2*z +3*y*z^2 +z^3,  x^2*y +x^2*z]

See also

Package sagbi/SB.GetID

Package sagbi/SB.GetRing

Package sagbi/SB.GetGens

Package sagbi/SB.GetCoeffRing

Package sagbi/SB.GetSAGBI

Package sagbi/SB.GetTruncSAGBI

Package sagbi/SB.GetTruncDeg

Package sagbi/SB.GetLTSA

Package sagbi/SB.GetHS