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

From ApCoCoAWiki
(added term ordering and fixed see link)
(added term ordering)
 
Line 14: Line 14:
 
   
 
   
 
     <example>
 
     <example>
Use QQ[x,y];
+
Use QQ[x,y], DegRevLex;
 
f := x^4*y^2 + x^2*y^4;
 
f := x^4*y^2 + x^2*y^4;
 
G := [x^2-1, y^2-1];
 
G := [x^2-1, y^2-1];

Latest revision as of 17:10, 27 October 2020

This article is about a function from ApCoCoA-2.

SB.ReductionStep

This function computes a polynomial to which the given polynomial reduces in one step.

Syntax

SB.ReductionStep(f: POLY, G: LIST of POLY): POLY

Description

This function takes a polynomial f and a list of polynomials G and computes a polynomial g such that f reduces to g in one step with respect to the Subalgebra rewrite relation defined by G, see Package sagbi. If there is no such polynomial g, then f is returned.

  • @param f A polynomial

  • @param G A list of polynomials

  • @return see description above

Example

Use QQ[x,y], DegRevLex;
f := x^4*y^2 + x^2*y^4;
G := [x^2-1, y^2-1];
SB.ReductionStep(f,G);
-- x^4*y^3 +2*x^2*y^2 +y^4 -x^2 -2*y^2 +1

Example

Use QQ[x,y], DegRevLex;
f := x^4*y^3 + x^2*y^3;
G := [x^2-1, y^2-1];
SB.ReductionStep(f,G);
-- x^4*y^3 +x^2*y^3


See also

Package sagbi/SB.SDA

Package sagbi/SB.Interreduced

Package sagbi/SB.FindLTRepr

Package sagbi/SB.FindLTRepr_glpk