# Package sagbi/SB.GetTruncSAGBI

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< Package sagbi

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This article is about a function from ApCoCoA-2. |

## SB.GetTruncSAGBI

This function returns a truncated SAGBI basis of a given standard-graded subalgebra.

### Syntax

SB.GetTruncSAGBI(ref S: TAGGED("$apcocoa/sagbi.Subalgebra"), d: INT): LIST of POLY

### Description

This function takes a subalgebra `S` generated by homogeneous polynomials as a reference, computes a `d`-truncated SAGBI basis, returns it and saves it into `S` if the function wasn't called previously. If the function was called previously on the same subalgebra with the same or a higher truncation degree `d`, then it just returns the truncated SAGBI basis of `S`.

@param

`S`A subalgebra@param

`d`A positive integer@return A

`d`-truncated SAGBI basis of`S`

#### Example

Use P ::= QQ[x,y,z]; S := SB.Subalgebra(P,[x^2 -z^2, x*y +z^2, y^2 -2*z^2]); PrintLn SB.GetTruncSAGBI(S,3); -- [y^2 -2*z^2, x*y +z^2, x^2 -z^2]

### See also