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

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   <short_description>This function returns a truncated SAGBI basis of a given standard-graded subalgebra.</short_description>
 
   <short_description>This function returns a truncated SAGBI basis of a given standard-graded subalgebra.</short_description>
 
    
 
    
   <syntax>SB.GetTruncSAGBI(ref S: TAGGED(<quotes>$apcocoa/sagbi.Subalgebra</quotes>), d: INT): LIST of POLY</syntax>
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   <syntax>SB.GetTruncSAGBI(ref S: TAGGED("$apcocoa/sagbi.Subalgebra"), d: INT): LIST of POLY</syntax>
 
   <description>
 
   <description>
 
This function takes a subalgebra <tt>S</tt> generated by homogeneous polynomials as a reference, computes a <tt>d</tt>-truncated SAGBI basis, returns it and saves it into <tt>S</tt> if the function wasn't called previously. If the function was called previously on the same subalgebra with the same or a higher truncation degree <tt>d</tt>, then it just returns the truncated SAGBI basis of <tt>S</tt>.
 
This function takes a subalgebra <tt>S</tt> generated by homogeneous polynomials as a reference, computes a <tt>d</tt>-truncated SAGBI basis, returns it and saves it into <tt>S</tt> if the function wasn't called previously. If the function was called previously on the same subalgebra with the same or a higher truncation degree <tt>d</tt>, then it just returns the truncated SAGBI basis of <tt>S</tt>.
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     </itemize>
 
     </itemize>
 
   
 
   
     <example> </example>
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     <example>
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Use P ::= QQ[x,y,z];
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S := SB.Subalgebra(P,[x^2 -z^2,  x*y +z^2,  y^2 -2*z^2]);
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PrintLn SB.GetTruncSAGBI(S,3);
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-- [y^2 -2*z^2,  x*y +z^2,  x^2 -z^2]</example>
 
   </description>
 
   </description>
  

Latest revision as of 13:21, 29 October 2020

This article is about a function from ApCoCoA-2.

SB.GetTruncSAGBI

This function returns a truncated SAGBI basis of a given standard-graded subalgebra.

Syntax

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

Description

This function takes a subalgebra S generated by homogeneous polynomials as a reference, computes a d-truncated SAGBI basis, returns it and saves it into S if the function wasn't called previously. If the function was called previously on the same subalgebra with the same or a higher truncation degree d, then it just returns the truncated SAGBI basis of S.

  • @param S A subalgebra

  • @param d A positive integer

  • @return A d-truncated SAGBI basis of S

Example

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

See also

HowTo:Call by Reference

HowTo:Term Orderings

Package sagbi/SB.GetTruncDeg

Package sagbi/SB.TruncSAGBI

Package sagbi/SB.GetID

Package sagbi/SB.GetRing

Package sagbi/SB.GetGens

Package sagbi/SB.GetCoeffRing

Package sagbi/SB.GetSAGBI

Package sagbi/SB.GetLTSA

Package sagbi/SB.GetInDeg

Package sagbi/SB.GetHS