2 Implementation

Sections

Here is the documentation from the package source code. As the package works with matrix groups acting on vector spaces, references to group elements means matrices, ie a list of row vectors, each of which is list of field elements. References to points means row vectors, ie elements of the vector space on which the group acts.

The code tries to avoid the computation of inverse matrices as much as possible, and to accomplish this, the inverse of a group element is stored together with the element in a list of length 2. Each time some computation is made with the element, a similar computation is made with the inverse, so that they are kept consistent. Therefore, in many cases in the code, group element means an immutable list of 2 matrices that are inverses to each other.

2.1 General code

These are the general declarations used by the package. Most notably the attribute StabChainMatrixGroup which is the core of the package functionality.

StabChainMatrixGroup( G ) A

Declare new attribute for storing base, SGS and Schreier trees. The attribute is computed using the Schreier-Sims algorithm for finite matrix groups, which is the main content of the package.

The attribute is a record with two components:

SchreierStructure: the main information structure, see ssInfo.
SGS: a list of the strong generators

The corresponding attribute operations are aware of a few Options.

SimpleSchreierTree: calculate coset representatives at the moment of creation of the Schreier trees, thus making them have height 1. This should make the algorithm significantly faster.
ExtendSchreierTree: Do not recompute Schreier trees at each run of a given level, but extend the Schreier trees from the last run at that level.
AlternatingActions: Always prepend a base point with the line that contains it, using the projective action on the line.
CleverBasePoints: Choose an initial list of base points using BasisVectorsForMatrixAction, which is made by O'Brien and Murray.
ShallowSchreierTree: Create the Schreier trees using the method described by Babai et al (1991) which guarantees logarithmic depth. This Option is only used when the option SimpleSchreierTree is not defined.
Random: Use probabilistic algorithm.
Linear: Use nearly linear-time algorithm. This takes precedence over Random, if it is present.

ssInfo V

Main structure holding information for the algorithm. This is not a global variable, but the same structure is used in all the variants of the algorithm, but all members are not necessarily used.

The structure ssInfo is a list of records, with a record for each level in the algorithm, ie one record for each base point. New base points may of course be added to the base during the execution of the algorithm, and then a new record is added to the end of the list.

The members of the record are:

partialSGS: the elements in the current partial SGS that fixes all points at lower levels, or the whole partial SGS for the first level
partialBase: the base point for this level
action: the action (function) at this level
points: the field where the base point partialBase comes from
hash: the hash function for the Schreier tree at this level
schreierTree: the Schreier tree for this level, representing the basic orbit at this level, ie the orbit of partialBase under the action of partialSGS at the previous (lower) level. Thus, the root of the tree is partialBase.
oldSGS: the whole partial SGS at the last call of SchreierSims at this level
IsIdentity: the function to check if a point is the identity at this level
MatrixSchreierSimsInfo V The GAP InfoClass used by the package, for debugging purposes. MATRIXSS_DEBUGLEVEL V The internal debugging level. This is really obsolete and the above info class should be used instead. MATRIXSS_BasePointStore V A list of hopefully good base points, ie base points with small orbits. They are fetched with BasisVectorsForMatrixAction which is due to O'Brien and Murray, and as long as the list is non-empty, new base points will be shifted from it. MatrixGroupOrderStabChain( ssInfo ) F Computes the order of the group defined by the given Schreier trees, see ssInfo. These are the common functions used by all the variants of the Schreier-Sims algorithm implemented in the package. These are the core functions of the package. Size( G ) A A method for Size for finite matrix groups, that uses the implementation of Schreier-Sims algorithm in this package, ie it uses the StabChainMatrixGroup attribute to compute the order of G. This method is only installed if MATRIXSS_TEST is not defined when the package is loaded. MATRIXSS_GetPartialBaseSGS( generators, identity, field ) F Constructs a partial base and a partial SGS given a set of generators for a group. Returns the partial SGS and the ssInfo structure, see ssInfo. beginitems generators given set of generators identity group identity element (the identity matrix) field the vector space on which the group acts
MATRIXSS_DEBUGLEVEL V The internal debugging level. This is really obsolete and the above info class should be used instead. MATRIXSS_BasePointStore V A list of hopefully good base points, ie base points with small orbits. They are fetched with BasisVectorsForMatrixAction which is due to O'Brien and Murray, and as long as the list is non-empty, new base points will be shifted from it. MatrixGroupOrderStabChain( ssInfo ) F Computes the order of the group defined by the given Schreier trees, see ssInfo. These are the common functions used by all the variants of the Schreier-Sims algorithm implemented in the package. These are the core functions of the package. Size( G ) A A method for Size for finite matrix groups, that uses the implementation of Schreier-Sims algorithm in this package, ie it uses the StabChainMatrixGroup attribute to compute the order of G. This method is only installed if MATRIXSS_TEST is not defined when the package is loaded. MATRIXSS_GetPartialBaseSGS( generators, identity, field ) F Constructs a partial base and a partial SGS given a set of generators for a group. Returns the partial SGS and the ssInfo structure, see ssInfo. beginitems generators given set of generators identity group identity element (the identity matrix) field the vector space on which the group acts
MATRIXSS_BasePointStore V A list of hopefully good base points, ie base points with small orbits. They are fetched with BasisVectorsForMatrixAction which is due to O'Brien and Murray, and as long as the list is non-empty, new base points will be shifted from it. MatrixGroupOrderStabChain( ssInfo ) F Computes the order of the group defined by the given Schreier trees, see ssInfo. These are the common functions used by all the variants of the Schreier-Sims algorithm implemented in the package. These are the core functions of the package. Size( G ) A A method for Size for finite matrix groups, that uses the implementation of Schreier-Sims algorithm in this package, ie it uses the StabChainMatrixGroup attribute to compute the order of G. This method is only installed if MATRIXSS_TEST is not defined when the package is loaded. MATRIXSS_GetPartialBaseSGS( generators, identity, field ) F Constructs a partial base and a partial SGS given a set of generators for a group. Returns the partial SGS and the ssInfo structure, see ssInfo. beginitems generators given set of generators identity group identity element (the identity matrix) field the vector space on which the group acts
MatrixGroupOrderStabChain( ssInfo ) F Computes the order of the group defined by the given Schreier trees, see ssInfo. These are the common functions used by all the variants of the Schreier-Sims algorithm implemented in the package. These are the core functions of the package. Size( G ) A A method for Size for finite matrix groups, that uses the implementation of Schreier-Sims algorithm in this package, ie it uses the StabChainMatrixGroup attribute to compute the order of G. This method is only installed if MATRIXSS_TEST is not defined when the package is loaded. MATRIXSS_GetPartialBaseSGS( generators, identity, field ) F Constructs a partial base and a partial SGS given a set of generators for a group. Returns the partial SGS and the ssInfo structure, see ssInfo. beginitems generators given set of generators identity group identity element (the identity matrix) field the vector space on which the group acts
Size( G ) A A method for Size for finite matrix groups, that uses the implementation of Schreier-Sims algorithm in this package, ie it uses the StabChainMatrixGroup attribute to compute the order of G. This method is only installed if MATRIXSS_TEST is not defined when the package is loaded. MATRIXSS_GetPartialBaseSGS( generators, identity, field ) F Constructs a partial base and a partial SGS given a set of generators for a group. Returns the partial SGS and the ssInfo structure, see ssInfo. beginitems generators given set of generators identity group identity element (the identity matrix) field the vector space on which the group acts
MATRIXSS_GetPartialBaseSGS( generators, identity, field ) F Constructs a partial base and a partial SGS given a set of generators for a group. Returns the partial SGS and the ssInfo structure, see ssInfo. beginitems generators given set of generators identity group identity element (the identity matrix) field the vector space on which the group acts
generators: given set of generators
identity: group identity element (the identity matrix)
field: the vector space on which the group acts

MATRIXSS_Membership( ssInfo, element, identity ) F

Check if an element belongs to a group, using sifting

ssInfo: Main information structure about our stabiliser chain. The Schreier trees is used during the sifting.
element: the element to check for membership
identity: group identity

MATRIXSS_NewBasePoint( element, identity, field ) F

Find a point not in base that is moved by the given element (which fixes the base)

element: the bad element that fixes the whole base
identity: the group identity (the identity matrix)
field: the vector space on which the group acts

MATRIXSS_GetSchreierGenerator( schreierTree, generator, point, action, identity, IsIdentity ) F

Creates a Schreier generator for the stabiliser in the group which has generator as one of its generators. The stabiliser fixes point under action.

MATRIXSS_ExtendBase( ssInfo, badElement, identity ) F

Add a new base point to the base, so that the given element is not in the stabiliser of the point

ssInfo: main information structure for the current Schreier-Sims run
badElement: the element that fixes all current base points
identity: the group identity

MATRIXSS_AugmentBase( ssInfo, newPoint, action, hash, identity ) F

Add a new base point to the base, so that the given element is not in the stabiliser of the point

ssInfo: main information structure for the current Schreier-Sims run
newPoint: the point to add to the base
action: the action for the new point
hash: the dictionary info for the new point
identity: the group identity

MATRIXSS_OrbitElement( schreierTree, point, action, identity, IsIdentity ) F

Compute the group element that connects the root of the Schreier tree to a given point. This function assumes that the point actually is in the orbit described by the given Schreier tree.

schreierTree: Schreier tree for the orbit to use
point: the point to check if it is in the orbit
action: the action that was used to create the Schreier tree
identity: the group identity (the identity matrix)
IsIdentity: function to use when checking if a group element is equal to the identity

MATRIXSS_ComputeSchreierTree( tree, generators, action, root, hash, identity ) F

Fill a Schreier tree that contains only the root.

tree: The Schreier tree to fill.
generators: The generators for the group that gives rise to the orbit represented by the Schreier tree.
action: The action of the group on the point set.
root: The root point of the tree.
hash: The dictionary info for the tree, used to create hash function.
identity: the group identity (the identity matrix)

MATRIXSS_ExtendSchreierTree( oldTree, generators, oldGenerators, action, dictinfo ) F

Extends an existing Schreier tree by a given set of generators

oldTree: The Schreier tree to extend, ie a Dictionary.
generators: The generators for the group that gives rise to the orbit represented by the Schreier tree.
oldGenerators: The current generators (edge-labels) of oldTree.
action: The action of the group on the point set.
dictinfo: The Dictionary info used when oldTree was created.

MATRIXSS_OrbitElement_ToddCoxeter( schreierTree, point, action, identity, IsIdentity, freeGroup, genMap ) F

Special version of MATRIXSS_OrbitElement, see MATRIXSS_OrbitElement, that also calculates the Word in the generators of the group element it returns.

More specifically, it computes the Word of the generators of the corresponding free group.

schreierTree: Schreier tree for the orbit to use
point: the point to check if it is in the orbit
action: the action that was used to create the Schreier tree
identity: the group identity (the identity matrix)
IsIdentity: function to use when checking if a group element is equal to the identity
freeGroup: corresponding free group to the group whose generators form the set of edge labels of schreierTree
genMap: list of 2 lists of the same length, the first being the edge labels of schreierTree (the generators of the corresponding group), and the second being the corresponding generators of freeGroup

MATRIXSS_Membership_ToddCoxeter( ssInfo, element, identity, freeGroup ) F

Special version of MATRIXSS_Membership, see MATRIXSS_Membership, that also expresses the sifted group element as a word in the generators of a given free group.

ssInfo: Main information structure about our stabiliser chain. The Schreier trees is used during the sifting.
element: the element to check for membership
identity: group identity
freeGroup: the free group in which the sifted element will be expressed

MATRIXSS_GetSchreierGenerator_ToddCoxeter( schreierTree, generator, point, action, identity, IsIdentity, freeGroup, genMap ) F

Special version of MATRIXSS_GetSchreierGenerator, see MATRIXSS_GetSchreierGenerator, that also returns the Schreier generator as a Word in the generators of freeGroup, using genMap to map the generators to the free group. See MATRIXSS_OrbitElement_ToddCoxeter.

MATRIXSS_CreateShallowSchreierTree( orbitTree, root, generators, labels, action, identity, hash ) F

Create a shallow Schreier tree, ie with at most logarithmic height.

orbitTree: Given tree representing the same orbit as the shallow Schreier to be computed.
root: The root point of the tree.
generators: From this set will any new edge labels be taken.
labels: The elements that, together with its inverses, will form the edge labels of the tree.
action: The action of the group on the point set.
identity: the group identity (the identity matrix)
hash: The dictionary info for the tree, used to create hash function.

MATRIXSS_GetSchreierTree( oldTree, root, generators, oldGenerators, action, hash, identity ) F

Returns a Schreier tree. This routine encapsulates the other Schreier tree functions.

oldTree: The Schreier tree to extend, in case there should be an extension.
root: The root point of the tree.
generators: The generators for the group that gives rise to the orbit represented by the Schreier tree.
oldGenerators: The current generators (edge-labels) of oldTree.
action: The action of the group on the point set.
hash: The dictionary info for the tree, used to create hash function.
identity: the group identity (the identity matrix)

MATRIXSS_MonotoneTree( root, elements, action, identity, dictinfo ) F

Create a monotone Schreier tree with given root and edge labels.

root: The root point of the tree.
elements: The elements that, together with its inverses, will form the edge labels of the tree.
action: The action of the group on the point set.
identity: the group identity (the identity matrix)
dictinfo: The dictionary info for the tree, used to create hash function.

MATRIXSS_RandomCosetRepresentative( schreierTree, action, identity ) F

Return a random coset representative from the transversal defined by schreierTree.

MATRIXSS_RandomOrbitPoint( schreierTree ) F

Returns a random point in the orbit given by schreierTree.

MATRIXSS_RandomSchreierGenerator( schreierTree, elements, action, identity ) F

Return a random Schreier generator constructed from the points in schreierTree and the generators in elements.

MATRIXSS_RandomSubproduct( elements, identity ) F

Return a random subproduct of elements.

These are also core function, but of slightly less importance, or mainly of technical nature.

MATRIXSS_SubProdGroups V

A Dictionary of SymmetricGroups, used when permuting random subproducts.

MATRIXSS_CopySchreierTree( tree, dictinfo ) F

Creates a copy of a whole Schreier tree, ie of makes a copy of the Dictionary.

tree: the Dictionary to copy
dictinfo: the dictinfo that was used when creating tree

MATRIXSS_GetOrbitSize( schreierTree ) F

Get size of orbit defined by the given Schreier tree.

MATRIXSS_GetOrbit( schreierTree ) F

Return all points (as a list) in the orbit of the point which is root of the Schreier tree, ie return all keys in the Dictionary. The list is not necessarily sorted, and it is mutable.

MATRIXSS_IsPointInOrbit( schreierTree, point ) F

Check if the given point is in the orbit defined by the given Schreier tree.

MATRIXSS_CreateInitialSchreierTree( root, dictinfo, identity ) F

Create a Schreier tree containing only the root.

root: The base point that is to be the root of the Schreier tree.
dictinfo: Used when creating the Dictionary that is the Schreier tree
identity: the group identity element

MATRIXSS_GetSchreierTreeEdge( schreierTree, point ) F

Get the label of the edge originating at the given point, and directed towards the root of the given Schreier tree.

MATRIXSS_ProjectiveIsIdentity( element, identity ) F

Identity check when using projective action (all scalar matrices are considered equal to the identity)

element: the group element to check if it is equal to identity
identity: the group identity (the identity matrix)

MATRIXSS_IsIdentity( element, identity ) F

Identity check when using normal point action

element: the group element to check if it is equal to identity
identity: the group identity (the identity matrix)

MATRIXSS_PointAction( point, element ) F

The action of a group element (a matrix) on a point (a row vector). The action is from the right

point: The point (row vector) to act on.
element: The group element (matrix) that acts.

MATRIXSS_ProjectiveAction( point, element ) F

The projective action of a matrix on a row vector. The one-dimensional subspace corresponding to the point is represented by the corresponding normed row vector

point: The point to act on. Must be a normed row vector.
element: The group element (matrix) that acts.

MATRIXSS_DebugPrint( level, message ) F

Internal function for printing debug messages. Uses the internal variable MATRIXSS_DEBUGLEVEL, see MATRIXSS_DEBUGLEVEL, to determine if the message should be printed.

2.2 Deterministic algorithm

These are the special routines for the deterministic version of Schreier-Sims algorithm.

StabChainMatrixGroup( G ) A

An implementation of the Schreier-Sims algorithm, for matrix groups, probabilistic version. See StabChainMatrixGroup!general for general information about the attribute.

SchreierSims( ssInfo, partialSGS, level, identity ) F

The main Schreier-Sims function, which is called for each level.

ssInfo: main information structure for the current Schreier-Sims run
partialSGS: given partial strong generating set
level: the level of the call to Schreier-Sims
identity: the group identity

2.3 Probabilistic algorithm

These are the special routines for the probabilistic implementation of Schreier-Sims algorithm.

StabChainMatrixGroup( G ) A

An implementation of the Schreier-Sims algorithm, for matrix groups, probabilistic version. See StabChainMatrixGroup!general for general information about the attribute.

In addition to the general Options of the attribute StabChainMatrixGroup, the probabilistic algorithm is aware of the following:

Probability

(lower bound for) probability of correct solution, which defaults to 3/4

Verify

Boolean parameter which signifies if the base and SGS computed using the random Schreir-Sims algorithm should be verified using the Schreier-Todd-Coxeter-Sims algorithm. Defaults to false.

OrderLowerBound

Lower bound for the order of G, must be geq 1. Defaults to 1.

OrderUpperBound

Upper bound for the order of G, or 0 if unknown. Defaults to 0.

Note that if the order of G is known, so that OrderLowerBound = OrderUpperBound = Size(G) then the randomized algorithm always produces a correct base and SGS, so there is no need of verification. Also, the verification will extend the given base and SGS to a complete base and SGS if needed.

RandomSchreierSims( ssInfo, partialSGS, maxIdentitySifts, identity, low_order, high_order ) F The main random Schreier-Sims function. beginitems ssInfo main information structure for the Schreier-Sims partialSGS given partial strong generating set maxIdentitySifts maximum number of consecutive elements that sifts to identity before the algorithm terminates identity the group identity lowOrder lower bound on the group order (must be geq 1) highOrder upper bound on the group order, or 0 if not available

2.4 STCS algorithm

These are the Schreier-Todd-Coxeter-Sims routines, ie Schreier-Sims algorithm with additional calls to Todd-Coxeter coset enumeration to possibly speed up the process. It is known to be fast when the input is already a base and SGS, and therefore it is good for verifying a proposed base and SGS, for example the output of a probabilistic algorithm.

MATRIXSS_SchreierToddCoxeterSims( ssInfo, partialSGS, level, identity, cosetFactor ) F

The main function for the Schreier-Todd-Coxeter-Sims algorithm. It is very similar to ordinary Schreier-Sims algorithm and has a similar interface.

ssInfo: main information structure for the current Schreier-Sims run
partialSGS: given partial strong generating set
level: the level of the call to Schreier-Sims
identity: the group identity
cosetFactor: the quotient of the maximum number of cosets generated during coset enumeration and the corresponding orbit size

2.5 Nearly linear time algorithm

These are the special routines for the nearly linear-time version, described in Babai et al, 1991.

StabChainMatrixGroup( G ) A

An implementation of the Schreier-Sims algorithm, for matrix groups. This version is inspired by the nearly linear time algorithm, described in seress03. See StabChainMatrixGroup!general for general information about the attribute.

ConstructSGS( ssInfo, partialSGS, identity ) F

The main Schreier-Sims function for the nearly linear-time algorithm.

ssInfo: main information structure for the current Schreier-Sims run
partialSGS: given partial strong generating set
identity: the group identity

CompletePointStabiliserSubgroup( ssInfo, element, level, identity, maxIdentitySifts ) F

The work-horse of the nearly linear-time algorithm, called for each level.

ssInfo: main information structure for the current Schreier-Sims run
element: the element which
partialSGS: given partial strong generating set
identity: the group identity

2.6 Verify routine

MatrixSchreierSimsVerify( ssInfo, SGS, identity ) F

The Verify routine by Sims. Checks whether the given ssInfo and SGS encodes a base and strong generating set, and returns a record with components Residue and Level. In case the verification succeeds, the level is 0 and the residue is the identity. Otherwise the residue is an element that is in the stabiliser of the group at the indicated level, but is not in the group at the next higher level.

ssInfo: proposed structure to check
SGS: proposed SGS to check
identity: the group identity

MATRIXSS_VerifyLevel( ssInfo, partialSGS, level, identity ) F

Checks that the stabiliser of the group at the given level is the same as the group at the next higher level.

ssInfo: proposed structure to check
partialSGS: proposed SGS to check
level: level to check
identity: the group identity

MATRIXSS_VerifyMultipleGenerators( generators, schreierTree, point, action, hash, subGenerators, ssInfo, SGS, identity, points, IsIdentity, field ) F

Verifies that the stabiliser of the group generated by generators, at the point point is the same group as the group generated by generators minus subGenerators. If so, the identity is returned, and otherwise an element that is in the difference is returned.

ssInfo and SGS should be a base and strong generating set for the smaller group.

generators: generators of the bigger group
schreierTree: Schreier tree for the orbit of point under action of the group generated by generators
point: the point to get the stabiliser of
action: the action to use when calculating the stabiliser
hash: the dictionary info of schreierTree
subGenerators: the additional generators of the bigger group
ssInfo: main structure for the base and sgs of the smaller group
SGS: strong generating set for the smaller group
identity: the group identity
points: the point set to which point belong
IsIdentity: the identity check function for the larger group
field: the finite field of the larger group

MATRIXSS_VerifySingleGenerator( generators, schreierTree, point, action, hash, subGenerator, ssInfo, SGS, identity ) F

Verifies that the stabiliser of the group generated by generators, at the point point is the same group as the group generated by generators minus subGenerator. If so, the identity is returned, and otherwise an element that is in the difference is returned.

ssInfo and SGS should be a base and strong generating set for the smaller group.

generators: generators of the bigger group
schreierTree: Schreier tree for the orbit of point under action of the group generated by generators
point: the point to get the stabiliser of
action: the action to use when calculating the stabiliser
hash: the dictionary info of schreierTree
subGenerator: the additional generator of the bigger group
ssInfo: main structure for the base and sgs of the smaller group
SGS: strong generating set for the smaller group
identity: the group identity

MATRIXSS_StabiliserGens( ssInfo, partialSGS, point, action, dictinfo, identity ) F

Return generators of the stabiliser of the group generated by the strong generators partialSGS at point under action. The ssInfo structure should be a base for the group.

ssInfo: main structure for the base
partialSGS: strong generating set for the given group
point: the point to get stabiliser at
action: the action to use when computing stabiliser
dictinfo: the dictionary info of schreierTree
identity: the group identity

MATRIXSS_IsBlockOfImprimitivity( schreierTree, generators, block, action, identity ) F

Checks whether block is a block of imprimitivity for action of the group given by generators on the set of points given by schreierTree.

schreierTree: Schreier tree for the point set
generators: generators of the acting group
block: the block to check for imprimitivity
action: the action to use
identity: the group identity

MATRIXSS_DecomposeOrbit( schreierTree, root, generators, action, hash, identity ) F

Decompose the orbit given by schreierTree, with root point root, into orbits of the group generated by generators, under action.

schreierTree: Schreier tree for the orbit to decompose
root: root point of schreierTree
generators: generators of the decomposing group
action: the action of the decomposing group
hash: the dictionary info of schreierTree
identity: the group identity

MATRIXSS_BaseChange( ssInfo, partialSGS, level, identity ) F

Flips the base point at level with the next higher base point and update the ssInfo structure.

ssInfo: main structure for the base
partialSGS: strong generating set corresponding to ssInfo
level: the level for the base change
identity: the group identity

2.7 Test and benchmark routines

These are the main routines for testing and benchmarking the package.

MatrixSchreierSimsTest( maxDegree, maxFieldSize ) F

Compares results of the above function with the built-in GAP Size method for a bunch of classical matrix groups. (GL, SL, etc)

maxDegree: maximum matrix size for classical matrix groups to be used for testing
maxFieldSize: maximum finite field size for classical matrix groups to be used for testing

MatrixSchreierSimsBenchmark( maxDegree, maxFieldSize, maxReeSize, maxSuzukiSize ) F

Check speed of package routines against classical matrix groups and the matrix representations of Ree and Suzuki sporadic groups.

maxDegree: maximum matrix size for classical matrix groups to be used for testing
maxFieldSize: maximum finite field size for classical matrix groups to be used for testing
maxReeSize: maximum ReeGroup size, see Ree in the reference manual.
maxSuzukiSize: maximum SuzukiGroup size, see Sz in the reference manual.

These are auxiliary functions for test and benchmark.

MATRIXSS_GetTestGroups( maxDegree, maxFieldSize ) F

Creates a list of classical matrix groups to use when testing the package. The groups are GL, SL, GO, SO, GU and SU.

maxDegree: maximum matrix size for classical matrix groups to be used for testing
maxFieldSize: maximum finite field size for classical matrix groups to be used for testing

MATRIXSS_GetBenchmarkGroups( maxDegree, maxFieldSize ) F

Creates a list of classical matrix groups and sporadic groups to use when benchmarking the package. The classical groups are GL, SL, GO and SO. The sporadic groups are Ree and Sz.

maxDegree: maximum matrix size for classical matrix groups to be used for testing
maxFieldSize: maximum finite field size for classical matrix groups to be used for testing
maxReeSize: maximum ReeGroup size, see Ree in the reference manual.
maxSuzukiSize: maximum SuzukiGroup size, see Sz in the reference manual.

MATRIXSS_TimedCall( call, args ) F

Runs the specified function with arguments and return the running time in milliseconds, as given by Runtime, see Runtime in the reference manual.

call: function to call
args: list of arguments to call

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matrixss manual
september 2004