Add framework and some code for wreath product recognition

.github/workflows/CI.yml

@@ -16,7 +16,6 @@ jobs:
       matrix:
         gap-branch:
           - master
-          - stable-4.11
         HPCGAP: ['no']
 
     steps:

LICENSE

@@ -1,9 +1,9 @@
-WPR is free software; you can redistribute and/or modify
+WPrecog is free software; you can redistribute and/or modify
 it under the terms of the GNU General Public License as published by
 the Free Software Foundation; either version 2 of the License, or (at
 your opinion) any later version.
 
-WPR is distributed in the hope that it will be useful, 
+WPrecog is distributed in the hope that it will be useful, 
 but WITHOUT ANY WARRANTY; without even the implied warranty of 
 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
 General Public License for more details.

PackageInfo.g

@@ -1,5 +1,5 @@
 #
-# WPR: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component
+# WPrecog: WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component
 #
 # This file contains package meta data. For additional information on
 # the meaning and correct usage of these fields, please consult the
@@ -8,7 +8,7 @@
 #
 SetPackageInfo( rec(
 
-PackageName := "WPR",
+PackageName := "WPrecog",
 Subtitle := "WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component",
 Version := "0.1",
 Date := "09/06/2021", # dd/mm/yyyy format
@@ -30,10 +30,10 @@ Persons := [
 
 SourceRepository := rec(
     Type := "git",
-    URL := "https://github.com/FriedrichRober/WPR",
+    URL := "https://github.com/FriedrichRober/WPrecog",
 ),
 IssueTrackerURL := Concatenation( ~.SourceRepository.URL, "/issues" ),
-PackageWWWHome  := "https://FriedrichRober.github.io/WPR/",
+PackageWWWHome  := "https://FriedrichRober.github.io/WPrecog/",
 PackageInfoURL  := Concatenation( ~.PackageWWWHome, "PackageInfo.g" ),
 README_URL      := Concatenation( ~.PackageWWWHome, "README.md" ),
 ArchiveURL      := Concatenation( ~.SourceRepository.URL,
@@ -55,17 +55,17 @@ Status := "dev",
 AbstractHTML   :=  "",
 
 PackageDoc := rec(
-  BookName  := "WPR",
+  BookName  := "WPrecog",
   ArchiveURLSubset := ["doc"],
   HTMLStart := "doc/chap0.html",
   PDFFile   := "doc/manual.pdf",
   SixFile   := "doc/manual.six",
-  LongTitle := "WreathProductRecognition provides constructive recognition algorithms for wreath products with almost simple base component",
+  LongTitle := "WreathProductRecognition provides constructive recognition algorithms for wreath products with an almost simple base component",
 ),
 
 Dependencies := rec(
-  GAP := ">= 4.11",
-  NeededOtherPackages := [ ],
+  GAP := ">= 4.12",
+  NeededOtherPackages := [ ["recog", ">= 1.3.2"] ],
   SuggestedOtherPackages := [ ],
   ExternalConditions := [ ],
 ),

README.md

@@ -1,7 +1,7 @@
-[![CI](https://github.com/FriedrichRober/WPR/workflows/CI/badge.svg)](https://github.com/FriedrichRober/WPR/actions?query=workflow%3ACI+branch%3Amaster)
-[![Code Coverage](https://codecov.io/gh/FriedrichRober/WPR/coverage.svg?branch=master&token=)](https://codecov.io/gh/FriedrichRober/WPR)
+[![CI](https://github.com/FriedrichRober/WPrecog/workflows/CI/badge.svg)](https://github.com/FriedrichRober/WPrecog/actions?query=workflow%3ACI+branch%3Amaster)
+[![Code Coverage](https://codecov.io/gh/FriedrichRober/WPrecog/coverage.svg?branch=master&token=)](https://codecov.io/gh/FriedrichRober/WPrecog)
 
-# The GAP package WPR
+# The GAP package WPrecog
 
 TODO: add a description of your package; perhaps also instructions how how to
 install and use it, resp. where to find out more

_dev/aut.g

@@ -0,0 +1,142 @@
+
+################################
+##                            ##
+##          SL(n, q)          ##
+##                            ##
+################################
+
+# parameters of classical group
+n := 4;
+p := 3;
+e := 2;
+q := p ^ e;
+
+# classical groups
+P := GL(n,q); # parent
+M := SL(n,q); # matrix group in parent
+
+# simple group, factoring scalar matrices out
+ZP := Centre(P);
+ZM := Centre(M);
+quo := NaturalHomomorphismByNormalSubgroup(P, ZP);
+T := Image(quo, M);
+
+# automorphism group
+# A = <I, D, G, F> = I ><| (<D, G> x F)
+# I = T  and  F = C_e
+# D = C_d, d = (n, q - 1)
+# if n > 2  =>  G = C_2  and  <D, G> = D_{2 d}
+# if n = 2  =>  G = C_1  and  <D, G> = C_{d}
+A := AutomorphismGroup(T);
+nice := NiceMonomorphism(A);
+
+# inner automorphisms
+Print("-------------------------------------------", "\n");
+Print(" I  : Inner Automorphisms", "\n");
+Print("|I| = ", Order(T), "\n");
+emb_I := GroupHomomorphismByFunction(T, A, x -> ConjugatorAutomorphism(T, x));;
+I := Image(emb_I); # = T
+
+# diagonal automorphism
+Print("-------------------------------------------", "\n");
+Print(" D  : Diagonal Automorphisms", "\n");
+d := Gcd(n, q - 1);
+Print("|D| = ", d, "\n");
+psi := NaturalHomomorphismByNormalSubgroup(Image(quo), T);
+x := First(GeneratorsOfGroup(Image(psi)), x -> Order(x) = d);
+y := PreImagesRepresentative(psi, x);
+diag := y ^ (Order(y) / d);
+diag_aut := ConjugatorAutomorphism(T, diag);
+D := Group(diag_aut); # = C_d = F_q^* / F_q^{*n} = PGL(n, q) / PSL(n, q)
+# C := Group(Z(q));
+# lambda := GroupHomomorphismByFunction(C, C, c -> c ^ n);
+# Cn := Image(lambda);
+# rho := NaturalHomomorphismByNormalSubgroup(C, Cn);
+
+# graph automorphisms
+Print("-------------------------------------------", "\n");
+Print(" G  : Graph Automorphisms", "\n");
+# trivial
+if n = 2 then
+    Print("|G| = ", 1, "\n");
+    G := Group(One(A)); # = C_1
+# duality automorphism
+else
+    Print("|G| = ", 2, "\n");
+    duality_aut := GroupHomomorphismByFunction(T, T, x -> (TransposedMat(PreImagesRepresentative(quo, x) ^ -1)) ^ quo);
+    G := Group(duality_aut); # = C_2
+fi;
+
+# field automorphisms
+Print("-------------------------------------------", "\n");
+Print(" F  : Field Automorphisms", "\n");
+Print("|F| = ", e, "\n");
+frobenius := FrobeniusAutomorphism(GF(q));
+frobenius_aut := GroupHomomorphismByFunction(T, T, x -> (PreImagesRepresentative(quo, x) ^ frobenius) ^ quo);
+F := Group(frobenius_aut); # = C_e
+
+# random element generator in A
+sample_size := 100;
+data := rec(
+    emb_I := emb_I,
+    frobenius_aut := frobenius_aut,
+    diag_aut := diag_aut,
+    G := G,
+);;
+opts := rec(
+
+);;
+RandomA := function(data, opts)
+    local emb_I, frobenius_aut, diag_aut, G, T,
+          elm_I, elm_F, elm_D, elm_G, exp_F, exp_D, exp_G, gen_G;
+    emb_I := data.emb_I;
+    frobenius_aut := data.frobenius_aut;
+    diag_aut := data.diag_aut;
+    G := data.G;
+    # I
+    T := Source(emb_I);
+    elm_I := PseudoRandom(T) ^ emb_I;
+    # F
+    if IsBound(opts.exp_F) then
+        exp_F := opts.exp_F;
+    else
+        exp_F := PseudoRandom([0 .. e - 1]);
+    fi;
+    elm_F := frobenius_aut ^ exp_F;
+    # D
+    if IsBound(opts.exp_D) then
+        exp_D := opts.exp_D;
+    else
+        exp_D := PseudoRandom([0 .. d - 1]);
+    fi;
+    elm_D := diag_aut ^ exp_D;
+    # G
+    gen_G := GeneratorsOfGroup(G)[1];
+    if IsBound(opts.exp_G) then
+        exp_G := opts.exp_G;
+    elif n = 2 then
+        exp_G := 0;
+    else
+        exp_G := PseudoRandom([0, 1]);
+    fi;
+    elm_G := gen_G ^ exp_G;
+
+    return rec(
+        elm := elm_I * elm_F * elm_D * elm_G,
+        elm_I := elm_I,
+        exp_F := exp_F,
+        elm_F := elm_F,
+        exp_D := exp_D,
+        elm_D := elm_D,
+        exp_G := exp_G,
+        elm_G := elm_G,
+    );
+end;;
+
+sample := EmptyPlist(sample_size);
+for i in [1 .. sample_size] do
+    r := RandomA(data, opts);
+    r.order := Order(r.elm);
+    Add(sample, r);
+    Print(r.order, ", ");
+od;