1############################################################################ 2## 3## recognize.gd IRREDSOL Burkhard Höfling 4## 5## Copyright © 2003–2016 Burkhard Höfling 6## 7 8 9############################################################################ 10## 11#F IsAvailableIdIrreducibleSolubleMatrixGroup(<G>) 12## 13## see the IRREDSOL manual 14## 15DECLARE_IRREDSOL_FUNCTION("IsAvailableIdIrreducibleSolubleMatrixGroup"); 16 17 18############################################################################ 19## 20#F IsAvailableIdAbsolutelyIrreducibleSolubleMatrixGroup(<G>) 21## 22## see the IRREDSOL manual 23## 24DECLARE_IRREDSOL_FUNCTION("IsAvailableIdAbsolutelyIrreducibleSolubleMatrixGroup"); 25 26 27############################################################################ 28## 29#F FingerprintDerivedSeries(<n>) 30## 31DeclareAttribute("FingerprintDerivedSeries", IsGroup); 32 33 34############################################################################ 35## 36#A FingerprintMatrixGroup(<G>) 37## 38## construct some data which is invariant under conjugation by an element 39## of the containing GL 40## 41DeclareAttribute("FingerprintMatrixGroup", IsMatrixGroup); 42DECLARE_IRREDSOL_SYNONYMS_ATTR("FingerprintMatrixGroup"); 43 44 45############################################################################ 46## 47#F ConjugatingMatIrreducibleRepOrFail(repG, repH, q, linonly, maxcost, limit) 48## 49DeclareGlobalFunction("ConjugatingMatIrreducibleRepOrFail"); 50 51 52############################################################################ 53## 54#F ConjugatingMatIrreducibleOrFail(G, H, F) 55## 56DeclareGlobalFunction("ConjugatingMatIrreducibleOrFail"); 57 58 59############################################################################ 60## 61#F ConjugatingMatImprimitiveOrFail(G, H, d, F) 62## 63## G and H must be irreducible matrix groups over the finite field F 64## H must be block monomial with block dimension d 65## 66## computes a matrix x such that G^x = H or returns fail if no such x exists 67## 68## The function works best if d is small. Irreducibility is only requried 69## if ConjugatingMatIrreducibleOrFail is used 70## 71DeclareGlobalFunction("ConjugatingMatImprimitiveOrFail"); 72 73 74############################################################################ 75## 76#F RecognitionAISMatrixGroup(G, inds, wantmat, wantgroup) 77## 78## version of RecognitionIrreducibleSolubleMatrixGroupNC which 79## only works for absolutely irreducible groups G. This version 80## allows to prescribe a set of absolutely irreducible subgroups 81## to which G is compared. This set is described as a subset <inds> of 82## IndicesAbsolutelyIrreducibleSolubleMatrixGroups(n, q), where n is the 83## degree of G and q is the order of the trace field of G. if inds is fail, 84## all groups in the IRREDSOL library are considered. 85## 86## WARNING: The result may be wrong if G is not among the groups 87## described by <inds>. 88## 89DeclareGlobalFunction("RecognitionAISMatrixGroup"); 90 91 92############################################################################ 93## 94#F RecognitionIrreducibleSolubleMatrixGroup(G, wantmat, wantgroup) 95## 96## Let G be an irreducible soluble matrix group over a finite field. 97## This function identifies a conjugate H of G group in the library. 98## 99## It returns a record which has the following entries: 100## id: contains the id of H (and thus of G), 101## cf. IdIrreducibleSolubleMatrixGroup 102## mat: (optional) a matrix x such that G^x = H 103## group: (optional) the group H 104## 105## The entries mat and group are only present if the booleans wantmat and/or 106## wantgroup are true, respectively. 107## 108## Currently, wantmat may only be true if G is absolutely irreducible. 109## 110## Note that in most cases, the function will be much slower if wantmat 111## is set to true. 112## 113DECLARE_IRREDSOL_FUNCTION("RecognitionIrreducibleSolubleMatrixGroup"); 114 115 116############################################################################ 117## 118#F RecognitionIrreducibleSolubleMatrixGroupNC(G, wantmat, wantgroup) 119## 120## version of RecognitionIrreducibleSolubleMatrixGroup which does not check 121## its arguments and returns fail if G is not within the scope of the 122## IRREDSOL library 123## 124DECLARE_IRREDSOL_FUNCTION("RecognitionIrreducibleSolubleMatrixGroupNC"); 125 126 127############################################################################ 128## 129#A IdIrreducibleSolubleMatrixGroup(<G>) 130## 131## see the IRREDSOL manual 132## 133DeclareAttribute("IdIrreducibleSolubleMatrixGroup", IsMatrixGroup); 134DECLARE_IRREDSOL_SYNONYMS_ATTR("IdIrreducibleSolubleMatrixGroup"); 135 136 137############################################################################ 138## 139#F IdIrreducibleSolubleMatrixGroupIndexMS(<n>, <p>, <k>) 140## 141## see the IRREDSOL manual 142## 143DECLARE_IRREDSOL_FUNCTION("IdIrreducibleSolubleMatrixGroupIndexMS"); 144 145 146############################################################################ 147## 148#F IndexMSIdIrreducibleSolubleMatrixGroup(<n>, <q>, <d>, <k>) 149## 150## see the IRREDSOL manual 151## 152DECLARE_IRREDSOL_FUNCTION("IndexMSIdIrreducibleSolubleMatrixGroup"); 153 154 155############################################################################ 156## 157#E 158## 159