Difference between revisions of "Package sagbi/SB.SDA"
From ApCoCoAWiki
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>...") |
Andraschko (talk | contribs) (added term ordering and fixed see link) |
||
| Line 14: | Line 14: | ||
<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]; | ||
Revision as of 17:10, 27 October 2020
| This article is about a function from ApCoCoA-2. |
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
