Difference between revisions of "Package sagbi/SB.SDA"
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Andraschko (talk | contribs) (Created page with "{{Version|2}} <command> <title>SB.SDA</title> <short_description>This function is an implementation of the Subalgebra Division Algorithm.</short_description> <syntax>...") |
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| − | {{Version|2}} | + | {{Version|2|[[ApCoCoA-1:SB.NFS]]}} |
<command> | <command> | ||
<title>SB.SDA</title> | <title>SB.SDA</title> | ||
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<example> | <example> | ||
| − | Use QQ[x,y]; | + | Use QQ[x,y], DegRevLex; |
f := x^4*y^2 + x^2*y^4+1; | f := x^4*y^2 + x^2*y^4+1; | ||
G := [x^2-1, y^2-1]; | G := [x^2-1, y^2-1]; | ||
Latest revision as of 17:50, 27 October 2020
| This article is about a function from ApCoCoA-2. If you are looking for the ApCoCoA-1 version of it, see ApCoCoA-1:SB.NFS. |
SB.SDA
This function is an implementation of the Subalgebra Division Algorithm.
Syntax
SB.SDA(f: POLY, G: LIST of POLY): POLY
Description
The function takes a polynomial f and a list of polynomials G all of the same ring RingOf(f) and performs the Subalgebra Division Algoritm on f and G. Note that this algorithm is different from the Subduction algorithm written by Robbiano and Sweedler, for more informations see Package sagbi.
@param f A polynomial
@param G A list of polynomials
@return A polynomial g such that f Subalgebra reduces (with respect to G) to g and g is irreducible with respect to the rewrite relation defined by G.
Example
Use QQ[x,y], DegRevLex; f := x^4*y^2 + x^2*y^4+1; G := [x^2-1, y^2-1]; SB.SDA(f,G); -- 0
See also
Package sagbi/SB.ReductionStep
Package sagbi/SB.IsInSubalgebra_SAGBI
