New &GAP; Objects and Utility Functions Provided by the `AtlasRep` Package

This chapter describes &GAP; objects and functions that are provided by the `AtlasRep` package but that might be of general interest.

The new objects are straight line decisions (see Section ) and black box programs (see Section ).

The new functions are concerned with representations of minimal degree, see Section .

Straight Line Decisions
<#Include Label="StraightLineDecisionIntro"> <#Include Label="IsStraightLineDecision"> <#Include Label="LinesOfStraightLineDecision"> <#Include Label="NrInputsOfStraightLineDecision"> <#Include Label="ScanStraightLineDecision"> <#Include Label="StraightLineDecision"> <#Include Label="ResultOfStraightLineDecision"> <#Include Label="Semi-Presentations"> <#Include Label="AsStraightLineDecision"> <#Include Label="StraightLineProgramFromStraightLineDecision">

Black Box Programs
<#Include Label="BBoxIntro"> <#Include Label="IsBBoxProgram"> <#Include Label="ScanBBoxProgram"> <#Include Label="RunBBoxProgram"> <#Include Label="ResultOfBBoxProgram"> <#Include Label="AsBBoxProgram"> <#Include Label="AsStraightLineProgram">

Representations of Minimal Degree

This section deals with minimal degrees of permutation and matrix representations. We do not provide an algorithm that computes these degrees for an arbitrary group, we only provide some tools for evaluating known databases, mainly concerning bicyclic extensions (see ) of simple groups, in order to derive the minimal degrees, see Section .

In the `AtlasRep` package, this information can be used for prescribing minimality conditions in , , and . An overview of the stored minimal degrees can be shown with .

<#Include Label="MinimalRepresentationInfo"> <#Include Label="MinimalRepresentationInfoData"> <#Include Label="SetMinimalRepresentationInfo"> <#Include Label="subsect:minimality-criteria">