Difference between revisions of "Package sagbi/SB.TruncSAGBI"
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<example> | <example> | ||
| − | Use QQ[x | + | Use QQ[x,y,z]; |
| − | S := SB.TruncSAGBI([x | + | S := SB.TruncSAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2],3); |
| − | indent(S | + | indent(S); |
| − | ---- | + | -- [ |
| − | + | -- [y^2 -2*z^2, x*y +z^2, x^2 -z^2], | |
| − | [ | + | -- false |
| − | + | -- ] | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | ] | ||
</example> | </example> | ||
<example> | <example> | ||
Use QQ[x,y]; | Use QQ[x,y]; | ||
| − | S := SB.TruncSAGBI([x+y,x*y,x*y^2], | + | S := SB.TruncSAGBI([x +y, x*y, x*y^2],7); -- K[x+y,xy,xy^2] does not have a finite SAGBI basis |
| − | indent(S | + | indent(S); |
| − | ---- | + | -- [ |
| − | + | -- [x +y, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6], | |
| − | [ | + | -- false |
| − | + | -- ] | |
| − | |||
| − | |||
| − | |||
| − | |||
| − | |||
| − | false | ||
| − | ] | ||
</example> | </example> | ||
</description> | </description> | ||
| − | < | + | <seealso> |
| − | < | + | <see>Package sagbi/SB.SAGBI</see> |
| + | <see>Package sagbi/SB.SAGBITimeout</see> | ||
| + | <see>Package sagbi/SB.IsSAGBIOf</see> | ||
| + | <see>Package sagbi/SB.GetSAGBI</see> | ||
| + | <see>Package sagbi/SB.GetTruncSAGBI</see> | ||
| + | </seealso> | ||
<types> | <types> | ||
<type>sagbi</type> | <type>sagbi</type> | ||
Revision as of 18:03, 27 October 2020
| This article is about a function in ApCoCoA-2.0. |
SB.TruncSAGBI
Computes a truncated SAGBI-basis of a standard-graded subalgebra.
Syntax
SB.SAGBI(G:LIST of POLY,d:RAT):LIST of POLY
Description
This function computes a d-truncated SAGBI-basis of the subalgebra S generated by the polynomials in the list G, i.e. a set of polynomials F such that any term appearing as the leading term of a polynomial in S of degree smaller than or equal to d is a product of terms appearing as leading term of a polynomial in F.
@param G A list of homogeneous polynomials which generates a subalgebra.
@param d An integer specifying the truncation degree.
@return A tuple [L,b] where L is a list of polynomials which form a d-truncated finite SAGBI-basis of the subalgebra generated by G. b is a boolean value which is true if L is already a complete SAGBI basis.
Example
Use QQ[x,y,z]; S := SB.TruncSAGBI([x^2 -z^2, x*y +z^2, y^2 -2*z^2],3); indent(S); -- [ -- [y^2 -2*z^2, x*y +z^2, x^2 -z^2], -- false -- ]
Example
Use QQ[x,y]; S := SB.TruncSAGBI([x +y, x*y, x*y^2],7); -- K[x+y,xy,xy^2] does not have a finite SAGBI basis indent(S); -- [ -- [x +y, x*y, x*y^2, x*y^3, x*y^4, x*y^5, x*y^6], -- false -- ]
See also
Package sagbi/SB.GetTruncSAGBI
