Extended test files for Chapter 4

Author: Leo

doc/intro.tex

@@ -70,7 +70,7 @@
 isomorphism problem. 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\Section{The Modular Isomorphism Problem}
+\Section{The Modular Isomorphism Problem (MIP)}
 
 The modular isomorphism problem asks whether an isomorphism of algebras $\F_p G \cong \F_p H$ implies
 an isomorphism of groups $G \cong H$ for two $p$-groups $G$ and $H$ and $\F_p$ the field with $p$

tst/manexamples.tst

@@ -92,15 +92,78 @@ gap> C.cano.tab;
 #####################################################################
 # Chapter 4
 #####################################################################
+## classical way to find bins
 gap> bins := BinsByGT(2,6);
 [ [ 156, 158, 160 ], [ 155, 157 ], [ 173, 176 ], [ 179, 180 ] ]
 
 #####################################################################
+# split the bins by algebras
 gap> MIPSplitGroupsByAlgebras(2,6,[156,158,160]).bins;
 [  ]
 gap> MIPSplitGroupsByAlgebras(2,6,[156,158,160]).splits;
 [ [ 7, [ 156, 158, 160 ] ] ]
 
+#########################################################################
+# variations if bin splitting. These involve all the funcions in detbins
+gap> L := AllGroups(2^6);;
+gap> binsNC := MIPSplitGroupsByGroupTheoreticalInvariantsNoCohomology(L);;
+gap> binsAF := MIPSplitGroupsByGroupTheoreticalInvariantsAllFields(L);;
+gap> binsAFNC := MIPSplitGroupsByGroupTheoreticalInvariantsAllFieldsNoCohomology(L);;
+gap> List(binsNC, x -> List(x, y -> IdGroup(y)[2]));
+[ [ 156, 158, 160 ], [ 155, 157, 159 ], [ 173, 176 ], [ 179, 180, 181 ] ]
+gap> List(binsAF, x -> List(x, y -> IdGroup(y)[2]));
+[ [ 172, 182 ], [ 156, 158, 160 ], [ 168, 179, 180 ], [ 175, 181 ], 
+  [ 167, 173, 176 ], [ 142, 155, 157 ], [ 238, 239 ], [ 65, 70 ], 
+  [ 104, 105 ], [ 13, 14 ] ]
+gap> List(binsAFNC, x -> List(x, y -> IdGroup(y)[2]));
+[ [ 172, 182 ], [ 170, 178 ], [ 143, 156, 158, 160 ], [ 142, 155, 157, 159 ], 
+  [ 168, 175, 179, 180, 181 ], [ 167, 173, 176 ], [ 76, 79 ], [ 74, 80 ], 
+  [ 238, 239 ], [ 236, 240 ], [ 208, 212 ], [ 65, 70 ], [ 63, 68 ], 
+  [ 104, 105 ], [ 13, 14 ] ]
+
+##########################################################
+# splitting algebras over different fields
+gap> MIPSplitGroupsByAlgebras(2,6,[142,155]).splits;
+[ [ 2, [ 142, 155 ] ] ]
+gap> MIPSplitGroupsByAlgebras(2,6,[142,155],2).splits;
+[ [ 3, [ 142, 155 ] ] ]
+
+#########################################################
+# kernel sizes
+gap> G := SmallGroup(64, 20);;
+gap> H := SmallGroup(64, 22);;
+gap> TG := ModIsomTable(G, 5);;
+gap> TH := ModIsomTable(H, 5);;
+gap> KernelSizePowerMap(TG, 1, 1, 2);
+3
+gap> KernelSizePowerMap(TH, 1, 1, 2);
+1
+gap> TG := ModIsomTable(G, 5, 2);;
+gap> TH := ModIsomTable(H, 5, 2);;
+gap> KernelSizePowerMap(TG, 1, 1, 2);
+7
+gap> KernelSizePowerMap(TH, 1, 1, 2);
+7
+
+################
+## table generation
+gap> G := DihedralGroup(8);;
+gap> TG := ModIsomTable(G, 3);;
+gap> TG.powwords;
+[ [  ], [ [ Z(2)^0, [ [ 3, 1 ] ] ] ], [  ] ]
+gap> TG.pre.exps;
+[ [ 1, 0, 0 ], [ 0, 1, 0 ], [ 1, 1, 0 ], [ 0, 0, 1 ], [ 1, 0, 1 ], 
+  [ 0, 1, 1 ], [ 1, 1, 1 ] ]
+gap> TG.pre.jen.coms;
+[ [ [ 1, 2 ], [ 0, 0, 1 ] ], [ [ 1, 3 ], [ 0, 0, 0 ] ], 
+  [ [ 2, 3 ], [ 0, 0, 0 ] ] ]
+gap> TG.pre.jen.weights;
+[ 1, 1, 2 ]
+gap> TG.wds;
+[ ,, [ 1, 2 ],, [ 1, 4 ], [ 2, 4 ] ]
+gap> TG.wgs;
+[ 1, 1, 2, 2, 3, 3 ]
+
 #####################################################################
 # Chapter 5
 #####################################################################