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7 Miscellaneous

This chapter describes various aspects of recog that did not fit elsewhere.

7.1 Naming of groups

For non-constructive recognition of classical matrix groups in their natural representation, the following functions are available.

7.1-1 RecogniseClassical

Returns: a record describing the outcome of the non-constructive recognition procedure.

This function implements non-constructive recognition, also called naming, for classical groups in their natural matrix representation over finite fields. The implementation is based on the algorithms described in [NP98], [NP97], and [NP99], and uses further ingredients from [CL97a], [CL97b], and [Pra99].

The input grp must be a matrix group over a finite field. The function is intended for groups that are classical, or close to classical, in their natural representation.

The optional record opt can be used to guide the computation. Its component case may be one of "unknown", "linear", "symplectic", "unitary", "orthogonalplus", or "orthogonalcircle". Furthermore, nrrandels controls how many random elements are inspected, and infoLevel sets the InfoMethSel level used while running the method selection machinery.

The returned record is currently mostly an internal data structure and its full set of components should not be considered a stable public interface. The most useful documented components are the booleans isReducible, isSLContained, isSpContained, isSUContained, and isOmegaContained. The four is*Contained components indicate whether the given group contains the corresponding quasisimple classical group in the natural representation, namely SL(d,q), Sp(d,q), SU(d,q), and Ω of the appropriate type.

To inspect the full internal record for debugging purposes, use DisplayRecog (7.1-2).

7.1-2 DisplayRecog

Returns: nothing

Pretty-print selected information from the record returned by RecogniseClassical (7.1-1). This is mainly intended as a debugging helper for inspecting the internal state accumulated by the recognition procedure.

7.2 Renaming of recog functions and operations

Many of the names in the recog package were found to be unintuitive or inconsistent with other names. For these reasons the names were changed to be more descriptive and to follow the internal consistency of GAP. In this section a dictionary from old to new names is included. The meanings of the old names for components of a recognition node are described in Section 2.6 "Components of the recognition node" of the article [NS06].

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