# Package sagbi/SB.TruncSAGBI

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This article is about a function in ApCoCoA-2.0. |

## SB.TruncSAGBI

Computes a truncated SAGBI-basis of a 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 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[1..3]]; S := SB.TruncSAGBI([x[1]^2-x[3]^2,x[1]*x[2]+x[3]^2,x[2]^2-2*x[3]^2],2); indent(S,2); ----------------------------------------------------------------------------- [ [ x[2]^2 -2*x[3]^2, x[1]*x[2] +x[3]^2, x[1]^2 -x[3]^2, x[1]^2*x[3]^2 +x[1]*x[2]*x[3]^2 +(1/2)*x[2]^2*x[3]^2 +(-1/2)*x[3]^4 ], true ]

#### Example

Use QQ[x,y]; S := SB.TruncSAGBI([x+y,x*y,x*y^2],10); -- K[x+y,xy,xy^2] doesn't have a finite SAGBI basis indent(S,2); ----------------------------------------------------------------------------- [ [ x +y, x*y, x*y^2, x*y^3, x*y^4 ], false ]