Version 0.2 - applied all initial feedback

BNasmith · Feb 4, 2024 · 89c5b8a · 89c5b8a
1 parent a3435da
commit 89c5b8a
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Showing 11 changed files with 324 additions and 334 deletions.
diff --git a/PackageInfo.g b/PackageInfo.g
@@ -7,8 +7,8 @@ SetPackageInfo( rec(
 
   PackageName := "ALCO",
   Subtitle := "Tools for algebraic combinatorics",
-  Version := "0.1",
-  Date := "15/01/2024", # dd/mm/yyyy format
+  Version := "0.2",
+  Date := "04/02/2024", # dd/mm/yyyy format
   License := "GPL-3.0-or-later",
 
   PackageWWWHome := "https://github.com/BNasmith/alco",

diff --git a/doc/ALCO.xml b/doc/ALCO.xml
diff --git a/lib/alco.gd b/lib/alco.gd
@@ -68,7 +68,7 @@ DeclareGlobalFunction( "GoldenIrrationalComponent" );
 
 DeclareGlobalFunction( "GoldenModSigma" );
 
-DeclareGlobalVariable( "IcosianH4Basis" );
+DeclareGlobalVariable( "IcosianH4Generators" );
 
 DeclareOperation("IsIcosian", [ IsQuaternion ] );
 

diff --git a/lib/alco.gi b/lib/alco.gi
@@ -244,7 +244,7 @@ InstallGlobalFunction( GoldenModSigma, function(q)
     return Coefficients(Basis(NF(5,[1,4]), [1, (1-Sqrt(5))/2]), q)[1];
 end );
 
-InstallValue( IcosianH4Basis, Basis(QuaternionAlgebra(Field(Sqrt(5))),
+InstallValue( IcosianH4Generators, Basis(QuaternionAlgebra(Field(Sqrt(5))),
     List([  [ 0, -1, 0, 0 ], 
             [ 0, -1/2*E(5)^2-1/2*E(5)^3, 1/2, -1/2*E(5)-1/2*E(5)^4 ],
             [ 0, 0, -1, 0 ], 
@@ -263,8 +263,8 @@ SetName( IcosianRing, "IcosianRing" );
 SetString( IcosianRing, "IcosianRing" );
 SetIsLeftActedOnByDivisionRing( IcosianRing, false );
 SetSize( IcosianRing, infinity );
-SetGeneratorsOfRing( IcosianRing, AsList(IcosianH4Basis));
-SetGeneratorsOfLeftModule( IcosianRing, AsList(IcosianH4Basis) );
+SetGeneratorsOfRing( IcosianRing, AsList(IcosianH4Generators));
+SetGeneratorsOfLeftModule( IcosianRing, AsList(IcosianH4Generators) );
 SetIsWholeFamily( IcosianRing, false );
 SetIsAssociative( IcosianRing, false );
 
@@ -310,7 +310,7 @@ InstallMethod( CanonicalBasis,
                    rec() );
     SetUnderlyingLeftModule( B, IcosianRing );
     SetIsIntegralBasis( B, true );
-    SetBasisVectors( B, Immutable( BasisVectors(IcosianH4Basis)));
+    SetBasisVectors( B, Immutable( BasisVectors(IcosianH4Generators)));
     # Return the basis.
     return B;
     end );

diff --git a/makedoc.g b/makedoc.g
@@ -28,3 +28,5 @@ AutoDoc(rec(
 ));
 
 # Test("./tst/alco06.tst", rec(transformFunction := NormalizedWhitespace));
+
+FORCE_QUIT_GAP();
diff --git a/tst/alco01.tst b/tst/alco01.tst
@@ -27,7 +27,7 @@ gap> Display(g);
 gap> IsGossetLatticeGramMatrix(g);
 true
 
-# doc/ALCO.xml:45-55
+# doc/ALCO.xml:46-56
 gap> short := Set(ShortestVectors(g,4).vectors, y -> 
 > LinearCombination(Basis(OctavianIntegers), y));;
 gap> s := First(short, x -> x^2 + x + 2*One(x) = Zero(x));
@@ -40,7 +40,7 @@ gap> L := OctonionLatticeByGenerators(gens, One(O)*IdentityMat(3)/2);
 gap> IsLeechLatticeGramMatrix(GramMatrix(L));
 true
 
-# doc/ALCO.xml:55-78
+# doc/ALCO.xml:56-79
 gap> J := AlbertAlgebra(Rationals);
 <algebra-with-one of dimension 27 over Rationals>
 gap> SemiSimpleType(Derivations(Basis(J)));
@@ -53,8 +53,8 @@ gap> k := Basis(J){[17..24]};
 [ k1, k2, k3, k4, k5, k6, k7, k8 ]
 gap> e := Basis(J){[25..27]};
 [ ei, ej, ek ]
-gap> List(e, IsIdempotent);
-[ true, true, true ]
+gap> ForAll(e, IsIdempotent);
+true
 gap> Set(i, x -> x^2);
 [ ej+ek ]
 gap> Set(j, x -> x^2);

diff --git a/tst/alco02.tst b/tst/alco02.tst
@@ -10,7 +10,7 @@
 #
 gap> START_TEST("alco02.tst");
 
-# doc/ALCO.xml:137-154
+# doc/ALCO.xml:140-157
 gap> O := OctonionAlgebra(Rationals);
 <algebra-with-one of dimension 8 over Rationals>
 gap> LeftActingDomain(O);
@@ -30,7 +30,7 @@ gap> Derivations(Basis(O));
 gap> SemiSimpleType(last);
 "G2"
 
-# doc/ALCO.xml:167-180
+# doc/ALCO.xml:171-184
 gap> a := BasisVectors(Basis(OctavianIntegers));;
 gap> for x in a do Display(x); od;
 (-1/2)*e1+(1/2)*e5+(1/2)*e6+(1/2)*e7
@@ -46,44 +46,43 @@ true
 gap> ForAll(a/2, IsOctavianInt);
 false
 
-# doc/ALCO.xml:190-196
+# doc/ALCO.xml:195-200
 gap> BasisVectors(OctonionE8Basis) = BasisVectors(Basis(OctavianIntegers));
 true
-gap> g := List(OctonionE8Basis, x -> 
-> List(OctonionE8Basis, y -> 
+gap> g := List(OctonionE8Basis, x -> List(OctonionE8Basis, y -> 
 > Norm(x+y) - Norm(x) - Norm(y)));;
 gap> IsGossetLatticeGramMatrix(g);
 true
 
-# doc/ALCO.xml:230-235
+# doc/ALCO.xml:218-223
 gap> Oct := OctonionAlgebra(Rationals);;
 gap> List(Basis(Oct), Norm);
 [ 1, 1, 1, 1, 1, 1, 1, 1 ]
 gap> x := Random(Oct);; y := Random(Oct);;
 gap> Norm(x*y) = Norm(x)*Norm(y);
 true
 
-# doc/ALCO.xml:244-249
+# doc/ALCO.xml:236-241
 gap> e := BasisVectors(Basis(OctonionAlgebra(Rationals)));
 [ e1, e2, e3, e4, e5, e6, e7, e8 ]
 gap> List(e, Trace);
 [ 0, 0, 0, 0, 0, 0, 0, 2 ]
 gap> List(e, RealPart);
 [ 0*e1, 0*e1, 0*e1, 0*e1, 0*e1, 0*e1, 0*e1, e8 ]
 
-# doc/ALCO.xml:258-261
+# doc/ALCO.xml:250-253
 gap> e := BasisVectors(Basis(OctonionAlgebra(Rationals)));
 [ e1, e2, e3, e4, e5, e6, e7, e8 ]
 gap> List(e, ComplexConjugate);
 [ (-1)*e1, (-1)*e2, (-1)*e3, (-1)*e4, (-1)*e5, (-1)*e6, (-1)*e7, e8 ]
 
-# doc/ALCO.xml:269-272
+# doc/ALCO.xml:261-264
 gap> e := BasisVectors(Basis(OctonionAlgebra(Rationals)));
 [ e1, e2, e3, e4, e5, e6, e7, e8 ]
 gap> List(e, RealPart);
 [ 0*e1, 0*e1, 0*e1, 0*e1, 0*e1, 0*e1, 0*e1, e8 ]
 
-# doc/ALCO.xml:292-301
+# doc/ALCO.xml:284-293
 gap> O := UnderlyingLeftModule(OctonionE8Basis);
 <algebra-with-one of dimension 8 over Rationals>
 gap> BasisVectors(CanonicalBasis(O));
@@ -95,7 +94,7 @@ gap> y := OctonionToRealVector(CanonicalBasis(O), x);
 gap> RealToOctonionVector(CanonicalBasis(O), y);
 [ (-1)*e1+e5+e6+e7, (-1)*e1+(-1)*e2+(-1)*e4+(-1)*e7 ]
 
-# doc/ALCO.xml:310-318
+# doc/ALCO.xml:304-312
 gap> Oct := OctonionAlgebra(Rationals);;
 gap> x := Basis(Oct){[8,1,2]};
 [ e8, e1, e2 ]
@@ -106,11 +105,11 @@ gap> y := VectorToIdempotentMatrix(x);; Display(y);
 gap> IsIdempotent(y);
 true
 
-# doc/ALCO.xml:330-331
+# doc/ALCO.xml:324-325
 gap> WeylReflection([1,0,1],[0,1,1]);
 [ -1, 1, 0 ]
 
-# doc/ALCO.xml:341-360
+# doc/ALCO.xml:335-354
 gap> H := QuaternionAlgebra(Rationals);
 <algebra-with-one of dimension 4 over Rationals>
 gap> IsQuaternion(Random(H));
@@ -132,7 +131,7 @@ gap> List(b, RealPart);
 gap> List(b, ImaginaryPart);
 [ 0*e, e, k, (-1)*j ]
 
-# doc/ALCO.xml:367-374
+# doc/ALCO.xml:363-370
 gap> H := QuaternionAlgebra(Rationals);;
 gap> b := BasisVectors(CanonicalBasis(H));
 [ e, i, j, k ]
@@ -142,14 +141,14 @@ gap> x := Random(H);; y := Random(H);;
 gap> Norm(x*y) = Norm(x)*Norm(y);
 true
 
-# doc/ALCO.xml:382-386
+# doc/ALCO.xml:379-383
 gap> H := QuaternionAlgebra(Rationals);;
 gap> b := BasisVectors(CanonicalBasis(H));
 [ e, i, j, k ]
 gap> List(b, Trace);
 [ 2, 0, 0, 0 ]
 
-# doc/ALCO.xml:450-459
+# doc/ALCO.xml:397-406
 gap> f := BasisVectors(Basis(HurwitzIntegers));;
 gap> for x in f do Display(x); od;
 (-1/2)*e+(-1/2)*i+(-1/2)*j+(1/2)*k
@@ -161,15 +160,15 @@ true
 gap> ForAll(f/2, IsHurwitzInt);
 false
 
-# doc/ALCO.xml:469-474
+# doc/ALCO.xml:416-421
 gap> B := QuaternionD4Basis;;
 gap> for x in BasisVectors(B) do Display(x); od;
 (-1/2)*e+(-1/2)*i+(-1/2)*j+(1/2)*k
 (-1/2)*e+(-1/2)*i+(1/2)*j+(-1/2)*k
 (-1/2)*e+(1/2)*i+(-1/2)*j+(-1/2)*k
 e
 
-# doc/ALCO.xml:526-543
+# doc/ALCO.xml:452-469
 gap> f := BasisVectors(Basis(IcosianRing));;
 gap> for x in f do Display(x); od;
 (-1)*i
@@ -189,15 +188,15 @@ true
 gap> ForAll(f*(1+Sqrt(5))/2, IsIcosian);
 true
 
-# doc/ALCO.xml:553-558
-gap> f := BasisVectors(IcosianH4Basis);;
+# doc/ALCO.xml:479-484
+gap> f := BasisVectors(IcosianH4Generators);;
 gap> for x in f do Display(x); od;
 (-1)*i
 (-1/2*E(5)^2-1/2*E(5)^3)*i+(1/2)*j+(-1/2*E(5)-1/2*E(5)^4)*k
 (-1)*j
 (-1/2*E(5)-1/2*E(5)^4)*e+(1/2)*j+(-1/2*E(5)^2-1/2*E(5)^3)*k
 
-# doc/ALCO.xml:566-572
+# doc/ALCO.xml:494-500
 gap> sigma := (1-Sqrt(5))/2;; tau := (1+Sqrt(5))/2;;
 gap> x := 5 + 3*sigma;; GoldenModSigma(x);
 5
@@ -206,15 +205,15 @@ gap> GoldenModSigma(sigma);
 gap> GoldenModSigma(tau);
 1
 
-# doc/ALCO.xml:591-596
+# doc/ALCO.xml:521-526
 gap> f := BasisVectors(Basis(EisensteinIntegers));
 [ 1, E(3) ]
 gap> IsEisenInt(E(4));
 false
 gap> IsEisenInt(1+E(3)^2);
 true
 
-# doc/ALCO.xml:606-611
+# doc/ALCO.xml:538-543
 gap> f := BasisVectors(Basis(KleinianIntegers));
 [ 1, E(7)+E(7)^2+E(7)^4 ]
 gap> IsKleinInt(E(4));

diff --git a/tst/alco03.tst b/tst/alco03.tst
@@ -10,7 +10,7 @@
 #
 gap> START_TEST("alco03.tst");
 
-# doc/ALCO.xml:713-727
+# doc/ALCO.xml:657-671
 gap> J := AlbertAlgebra(Rationals);;
 gap> x := Sum(Basis(J){[4,5,6,25,26,27]});
 i4+i5+i6+ei+ej+ek
@@ -27,13 +27,13 @@ gap> Determinant(x);
 gap> Norm(x);
 9/2
 
-# doc/ALCO.xml:758-761
+# doc/ALCO.xml:716-719
 gap> J := SimpleEuclideanJordanAlgebra(3,8);
 <algebra-with-one of dimension 27 over Rationals>
 gap> Derivations(Basis(J));; SemiSimpleType(last);
 "F4"
 
-# doc/ALCO.xml:770-787
+# doc/ALCO.xml:729-746
 gap> J := JordanSpinFactor(IdentityMat(8));
 <algebra-with-one of dimension 9 over Rationals>
 gap> One(J);
@@ -53,13 +53,13 @@ gap> p := GenericMinimalPolynomial(x);
 gap> ValuePol(p,x);
 0*v.1
 
-# doc/ALCO.xml:794-797
+# doc/ALCO.xml:754-757
 gap> J := HermitianSimpleJordanAlgebra(3,QuaternionD4Basis);
 <algebra-with-one of dimension 15 over Rationals>
 gap> [JordanRank(J), JordanDegree(J)];
 [ 3, 4 ]
 
-# doc/ALCO.xml:813-824
+# doc/ALCO.xml:775-786
 gap> J := SimpleEuclideanJordanAlgebra(2,7);
 <algebra-with-one of dimension 9 over Rationals>
 gap> u := Sum(Basis(J){[1,2,7,8]});
@@ -73,7 +73,7 @@ gap> H := JordanHomotope(J, u, "w.");
 gap> One(H);
 (-1/2)*w.1+(1/2)*w.2+(1/2)*w.7+(1/2)*w.8
 
-# doc/ALCO.xml:848-858
+# doc/ALCO.xml:813-823
 gap> A := AlbertAlgebra(Rationals);
 <algebra-with-one of dimension 27 over Rationals>
 gap> i := Basis(A){[1..8]};;
@@ -86,7 +86,7 @@ gap> Display(i); Display(j); Display(k); Display(e);
 [ k1, k2, k3, k4, k5, k6, k7, k8 ]
 [ ei, ej, ek ]
 
-# doc/ALCO.xml:872-879
+# doc/ALCO.xml:838-845
 gap> j := Basis(AlbertAlgebra(Rationals)){[9..16]};
 [ j1, j2, j3, j4, j5, j6, j7, j8 ]
 gap> mat := AlbertVectorToHermitianMatrix(j[3]);; Display(mat);
@@ -96,7 +96,7 @@ gap> mat := AlbertVectorToHermitianMatrix(j[3]);; Display(mat);
 gap> HermitianMatrixToAlbertVector(mat);
 j3
 
-# doc/ALCO.xml:899-917
+# doc/ALCO.xml:866-886
 gap> J := JordanSpinFactor(IdentityMat(3));
 <algebra-with-one of dimension 4 over Rationals>
 gap> x := [-1,4/3,-1,1]*Basis(J);
@@ -110,14 +110,16 @@ gap> JordanQuadraticOperator(x);; Display(last);
   [  -8/3,   7/9,  -8/3,   8/3 ],
   [     2,  -8/3,  -7/9,    -2 ],
   [    -2,   8/3,    -2,  -7/9 ] ]
-gap> LinearCombination(Basis(J), JordanQuadraticOperator(x)*ExtRepOfObj(y)) = JordanQuadraticOperator(x,y);
+gap> LinearCombination(Basis(J), JordanQuadraticOperator(x)
+> *ExtRepOfObj(y)) = JordanQuadraticOperator(x,y);
 true
-gap> ExtRepOfObj(JordanQuadraticOperator(x,y)) = JordanQuadraticOperator(x)*ExtRepOfObj(y);
+gap> ExtRepOfObj(JordanQuadraticOperator(x,y)) = 
+> JordanQuadraticOperator(x)*ExtRepOfObj(y);
 true
 gap> JordanQuadraticOperator(2*x) = 4*JordanQuadraticOperator(x);
 true
 
-# doc/ALCO.xml:929-946
+# doc/ALCO.xml:899-916
 gap> J := AlbertAlgebra(Rationals);
 <algebra-with-one of dimension 27 over Rationals>
 gap> i := Basis(J){[1..8]};
@@ -137,7 +139,7 @@ gap> List(k, x -> 2*JordanTripleSystem(i[1],i[1],x));
 gap> List(e, x -> JordanTripleSystem(i[1],i[1],x));
 [ 0*i1, ej, ek ]
 
-# doc/ALCO.xml:961-976
+# doc/ALCO.xml:931-946
 gap> H := QuaternionAlgebra(Rationals);;
 gap> for x in HermitianJordanAlgebraBasis(2, Basis(H)) do Display(x); od;
 [ [    e,  0*e ],
@@ -155,7 +157,7 @@ gap> for x in HermitianJordanAlgebraBasis(2, Basis(H)) do Display(x); od;
 gap> AsList(Basis(H));
 [ e, i, j, k ]
 
-# doc/ALCO.xml:993-1012
+# doc/ALCO.xml:963-982
 gap> H := QuaternionAlgebra(Rationals);;
 gap> J := HermitianSimpleJordanAlgebra(2,Basis(H));
 <algebra-with-one of dimension 6 over Rationals>
@@ -177,10 +179,11 @@ gap> JordanMatrixBasis(J);; for x in last do Display(x); od;
 gap> List(JordanMatrixBasis(J), x -> HermitianMatrixToJordanVector(x, J));
 [ v.1, v.2, v.3, v.4, v.5, v.6 ]
 
-# doc/ALCO.xml:1019-1024
+# doc/ALCO.xml:990-996
 gap> J := HermitianSimpleJordanAlgebra(2,OctonionE8Basis);
 <algebra-with-one of dimension 10 over Rationals>
-gap> List(Basis(J), x -> List(Basis(J), y -> Trace(x*y))) = JordanAlgebraGramMatrix(J);
+gap> List(Basis(J), x -> List(Basis(J), y -> Trace(x*y))) = 
+> JordanAlgebraGramMatrix(J);
 true
 gap> DiagonalOfMat(JordanAlgebraGramMatrix(J));
 [ 1, 1, 2, 2, 2, 2, 2, 2, 2, 2 ]