# Difference between revisions of "Package sagbi/SB.GetTruncSAGBI"

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<short_description>This function returns a truncated SAGBI basis of a given standard-graded subalgebra.</short_description> | <short_description>This function returns a truncated SAGBI basis of a given standard-graded subalgebra.</short_description> | ||

− | <syntax>SB.GetTruncSAGBI(ref S: TAGGED( | + | <syntax>SB.GetTruncSAGBI(ref S: TAGGED("$apcocoa/sagbi.Subalgebra"), d: INT): LIST of POLY</syntax> |

<description> | <description> | ||

This function takes a subalgebra <tt>S</tt> generated by homogeneous polynomials as a reference, computes a <tt>d</tt>-truncated SAGBI basis, returns it and saves it into <tt>S</tt> 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 <tt>d</tt>, then it just returns the truncated SAGBI basis of <tt>S</tt>. | This function takes a subalgebra <tt>S</tt> generated by homogeneous polynomials as a reference, computes a <tt>d</tt>-truncated SAGBI basis, returns it and saves it into <tt>S</tt> 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 <tt>d</tt>, then it just returns the truncated SAGBI basis of <tt>S</tt>. |

## Latest revision as of 13:21, 29 October 2020

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