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Various changes related to documentation #8

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merged 5 commits into from May 8, 2021
Merged

Various changes related to documentation #8

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bdcd2c6
Remove doc/manual.pdf from the repository
fingolfin Aug 1, 2019
54a121a
Add .gitignore to ignore generated documentation
fingolfin Aug 1, 2019
ffe71da
Fix manual.tex to compile again
fingolfin Aug 1, 2019
e71e632
Improve make_doc
fingolfin Aug 1, 2019
a40fd3a
Fix typos in the manual, update examples
fingolfin Aug 1, 2019
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17 changes: 17 additions & 0 deletions .gitignore
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@@ -0,0 +1,17 @@
/doc/manual.aux
/doc/manual.dvi
/doc/manual.example-1.tst
/doc/manual.example-3.tst
/doc/manual.idx
/doc/manual.ilg
/doc/manual.ind
/doc/manual.lab
/doc/manual.log
/doc/manual.pdf
/doc/manual.six
/doc/manual.toc

/htm/

/gh-pages/
/tmp/
145 changes: 76 additions & 69 deletions doc/list.tex
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Open in desktop
Expand Up @@ -13,6 +13,7 @@
true
gap> s := SmallQuandle(6,1);;
gap> IsAffineIndecomposableQuandle(s);
# It contains commuting elements
false
\endexample

Expand All @@ -25,15 +26,15 @@
gap> r := TrivialRack(3);;
gap> Display(r);
rec(
isRack := true,
matrix := [ [ 1, 2, 3 ], [ 1, 2, 3 ], [ 1, 2, 3 ] ],
labels := [ 1 .. 3 ],
size := 3,
aut := "",
basis := "",
comments := "",
env := "",
inn := "",
aut := "",
env := "" )
isRack := true,
labels := [ 1 .. 3 ],
matrix := [ [ 1, 2, 3 ], [ 1, 2, 3 ], [ 1, 2, 3 ] ],
size := 3 )
\endexample

\>AffineCyclicRack( <n>, <x> )
Expand All @@ -46,15 +47,15 @@
gap> r := AffineCyclicRack(3,2);;
gap> Display(r);
rec(
isRack := true,
matrix := [ [ 1, 3, 2 ], [ 3, 2, 1 ], [ 2, 1, 3 ] ],
labels := [ 1 .. 3 ],
size := 3,
aut := "",
basis := "",
comments := "",
env := "",
inn := "",
aut := "",
env := "" )
isRack := true,
labels := [ 1 .. 3 ],
matrix := [ [ 1, 3, 2 ], [ 3, 2, 1 ], [ 2, 1, 3 ] ],
size := 3 )
\endexample

\>AffineRack( <field>, <field_element> )
Expand All @@ -66,15 +67,15 @@
gap> r := AffineRack(GF(3), Z(3));;
gap> Display(r);
rec(
isRack := true,
matrix := [ [ 1, 3, 2 ], [ 3, 2, 1 ], [ 2, 1, 3 ] ],
labels := [ 1 .. 3 ],
size := 3,
aut := "",
basis := "",
comments := "",
env := "",
inn := "",
aut := "",
env := "" )
isRack := true,
labels := [ 1 .. 3 ],
matrix := [ [ 1, 3, 2 ], [ 3, 2, 1 ], [ 2, 1, 3 ] ],
size := 3 )
\endexample

\>AlexanderRack( <n>, <s>, <t> )
Expand All @@ -93,15 +94,15 @@
gap> r := CyclicRack(3);;
gap> Display(r);
rec(
isRack := true,
matrix := [ [ 2, 3, 1 ], [ 2, 3, 1 ], [ 2, 3, 1 ] ],
labels := [ 1 .. 3 ],
size := 3,
aut := "",
basis := "",
comments := "",
env := "",
inn := "",
aut := "",
env := "" )
isRack := true,
labels := [ 1 .. 3 ],
matrix := [ [ 2, 3, 1 ], [ 2, 3, 1 ], [ 2, 3, 1 ] ],
size := 3 )
\endexample

\>CoreRack( <group> )
Expand All @@ -112,15 +113,15 @@
gap> r := CoreRack(CyclicGroup(3));;
gap> Display(r);
rec(
isRack := true,
matrix := [ [ 1, 3, 2 ], [ 3, 2, 1 ], [ 2, 1, 3 ] ],
labels := [ 1 .. 3 ],
size := 3,
aut := "",
basis := "",
comments := "",
env := "",
inn := "",
aut := "",
env := "" )
isRack := true,
labels := [ 1 .. 3 ],
matrix := [ [ 1, 3, 2 ], [ 3, 2, 1 ], [ 2, 1, 3 ] ],
size := 3 )
\endexample

\>DihedralRack( <n> )
Expand Down Expand Up @@ -160,7 +161,7 @@
of the <group> given. For example:

\beginexample
gap> f := ConjugatorAutomorphism(SymmetricGroup(3), (1,2)));;
gap> f := ConjugatorAutomorphism(SymmetricGroup(3), (1,2));;
gap> r := HomogeneousRack(SymmetricGroup(3), f);;
gap> Display(r.matrix);
[ [ 1, 6, 3, 5, 4, 2 ],
Expand All @@ -171,12 +172,12 @@
[ 5, 3, 2, 4, 1, 6 ] ]
\endexample

\>RackByListOfPermutations( <list> )
\>RackFromPermutations( <list> )

returns the rack given by the list of permutations given in <list>. For example:

\beginexample
gap> r := RackFromListOfPermutations([(2,3),(1,3),(1,2)]);;
gap> r := RackFromPermutations([(2,3),(1,3),(1,2)]);;
gap> Display(r.matrix);
[ [ 1, 3, 2 ],
[ 3, 2, 1 ],
Expand All @@ -192,7 +193,7 @@
returns the group of automorphism of <rack>. For example:

\beginexample
gap> AutomorphismGroup(TrivialRack(3));
gap> AutomorphismGroup(TrivialRack(3));
Group([ (), (2,3), (1,2), (1,2,3), (1,3,2), (1,3) ])
\endexample

Expand All @@ -203,7 +204,7 @@
\beginexample
gap> InnerGroup(DihedralRack(3));
Group([ (2,3), (1,3), (1,2) ])
gap> InnerGroup(TrivialRack(5));
gap> InnerGroup(TrivialRack(5));
Group(())
\endexample

Expand All @@ -215,10 +216,10 @@
\beginexample
gap> a := Rack(AlternatingGroup(4), (1,2,3));;
gap> b := Rack(AlternatingGroup(4), (1,3,2));;
gap> c := AbelianRack(4);
gap> c := AbelianRack(4);;
gap> IsomorphismRacks(a,b);
(3,4)
gap> IsomosphismRacks(a,c);
gap> IsomorphismRacks(a,c);
fail
\endexample

Expand Down Expand Up @@ -266,7 +267,7 @@
\beginexample
gap> a := AbelianRack(2);;
gap> b := Rack([[1,2],[1,2]]);;
gap> Display(b.matrix);
gap> Display(b.matrix);
[ [ 1, 2 ],
[ 1, 2 ] ]
gap> a=b;
Expand Down Expand Up @@ -311,11 +312,11 @@
\beginexample
gap> RackCohomology(DihedralRack(3),2);
[ 1, [ ] ]
gap> RackCohomology(TrivialRack(3),2);
gap> RackCohomology(TrivialRack(3),2);
[ 9, [ ] ]
gap> RackHomology(TrivialRack(2),2);
[ 4, [ ] ]
gap> RackHomology(DihedralRack(4),2);
gap> RackHomology(DihedralRack(4),2);
[ 4, [ 2, 2 ] ]
\endexample

Expand All @@ -325,17 +326,17 @@

\> Dimension( <nichols_datum>, <n> )

computes the dimension in degree <n> of the Nichols algebra <nichols_datum> In
the following example we compute all dimensions of a known 12-dimensional
computes the dimension in degree <n> of the Nichols algebra <nichols_datum>.
In the following example we compute all dimensions of a known 12-dimensional
Nichols algebra.

\beginexample
gap> r := DihedralRack(3);;
gap> q := [ [ -1, -1, -1 ], [ -1, -1, -1 ], [ -1, -1, -1 ] ];;
gap> n := NicholsDatum(r, q, Rationals);;
gap> for i in [0..5] do
Print("Degree ", i, ", dimension=", Dimension(n,i), "\n");
od;
> Print("Degree ", i, ", dimension=", Dimension(n,i), "\n");
> od;
Degree 0, dimension=1
Degree 1, dimension=3
Degree 2, dimension=4
Expand All @@ -351,7 +352,6 @@
all relations in degree two of a 12-dimensional Nichols algebra.

\beginexample
gap> LoadPackage("gbnp");
gap> r := DihedralRack(3);;
gap> q := [ [ -1, -1, -1 ], [ -1, -1, -1 ], [ -1, -1, -1 ] ];;
gap> rels := Relations4GAP(r, q, 2);;
Expand All @@ -370,7 +370,7 @@
\beginexample
gap> r := DihedralRack(4);;
gap> RackOrbit(r, 1);
[1, 3]
[ 1, 3 ]
\endexample

\>Nr_k ( <rack>, <n> )
Expand All @@ -391,27 +391,27 @@
> else
> return fail;
> fi;
> end;
> end;;
gap> a4 := AlternatingGroup(4);;
gap> s4 := SymmetricGroup(4);;
gap> s5 := SymmetricGroup(5);;
gap> Check(RackFromAConjugacyClass(a4, (1,2,3)));
1/2
gap> Check(RackFromAConjugacyClass(s4, (1,2)));
gap> Check(RackFromAConjugacyClass(s4, (1,2)));
2/3
gap> Check(RackFromAConjugacyClass(s4, (1,2,3,4));
gap> Check(RackFromAConjugacyClass(s4, (1,2,3,4)));
2/3
gap> Check(RackFromAConjugacyClass(s5, (1,2)));
gap> Check(RackFromAConjugacyClass(s5, (1,2)));
1
gap> Check(AffineCyclicRack(5,2));
gap> Check(AffineCyclicRack(5,2));
1
gap> Check(AffineCyclicRack(5,3));
1
gap> Check(AffineCyclicRack(7,5));
gap> Check(AffineCyclicRack(7,5));
1
gap> Check(AffineCyclicRack(7,3));
1
gap> Check(DihedralRack(3));
gap> Check(DihedralRack(3));
1/3
\endexample

Expand All @@ -425,7 +425,7 @@
returns the braiding given by <rack>.

\beginexample
gap> Display(Braiding(TrivialRack(2)));
gap> Display(Braiding(TrivialRack(2)));
[ [ 1, 0, 0, 0 ],
[ 0, 0, 1, 0 ],
[ 0, 1, 0, 0 ],
Expand Down Expand Up @@ -470,12 +470,12 @@
\>IsHomologous( <rack>, <q1>, <q2> )
\>TorsionGenerators( <rack>, <n> )
\>SecondCohomologyTorsionGenerators( <rack> )
\>LocalExponent
\>LocalExponents
\>Degree
\>RackAction
\>InverseRackAction
\>Hom
\>LocalExponent( <rack>, <i>, <j> )
\>LocalExponents( <rack> )
\>Degree( <rack> )
\>RackAction( <rack>, <i>, <j> )
\>InverseRackAction( <rack>, <i>, <j> )
\>Hom( <rack1>, <rack2> )

\>Permutations( <rack> )

Expand All @@ -492,11 +492,12 @@
computes the Hurwitz orbit of the <vector>

\beginexample
gap> r := DihedralRack(3);
gap> HurwitzOrbit(r, [1,1,1]);
gap> r := DihedralRack(3);;
gap> HurwitzOrbit(r, [1,1,1]);
[ [ 1, 1, 1 ] ]
gap> HurwitzOrbit(r, [1,2,3]);
[ [ 1, 2, 3 ], [ 3, 1, 3 ], [ 1, 1, 2 ], [ 2, 3, 3 ], [ 3, 2, 1 ], [ 1, 3, 1 ], [ 3, 3, 2 ], [ 2, 1, 1 ] ]
[ [ 1, 2, 3 ], [ 3, 1, 3 ], [ 1, 1, 2 ], [ 2, 3, 3 ], [ 3, 2, 1 ],
[ 1, 3, 1 ], [ 3, 3, 2 ], [ 2, 1, 1 ] ]
\endexample

\>HurwitzOrbits( <rack>, <n> )
Expand All @@ -506,10 +507,14 @@
\beginexample
gap> r := DihedralRack(3);;
gap> HurwitzOrbits(r, 3);
[ [ [ 1, 1, 1 ] ], [ [ 1, 1, 2 ], [ 1, 3, 1 ], [ 2, 1, 1 ], [ 1, 2, 3 ], [ 3, 2, 1 ], [ 3, 1, 3 ], [ 3, 3, 2 ],
[ 2, 3, 3 ] ], [ [ 1, 1, 3 ], [ 1, 2, 1 ], [ 3, 1, 1 ], [ 1, 3, 2 ], [ 2, 3, 1 ], [ 2, 1, 2 ], [ 2, 2, 3 ],
[ 3, 2, 2 ] ], [ [ 1, 2, 2 ], [ 3, 1, 2 ], [ 2, 3, 2 ], [ 3, 3, 1 ], [ 2, 1, 3 ], [ 3, 2, 3 ], [ 2, 2, 1 ],
[ 1, 3, 3 ] ], [ [ 2, 2, 2 ] ], [ [ 3, 3, 3 ] ] ]
[ [ [ 1, 1, 1 ] ],
[ [ 1, 1, 2 ], [ 1, 3, 1 ], [ 2, 1, 1 ], [ 1, 2, 3 ], [ 3, 2, 1 ],
[ 3, 1, 3 ], [ 3, 3, 2 ], [ 2, 3, 3 ] ],
[ [ 1, 1, 3 ], [ 1, 2, 1 ], [ 3, 1, 1 ], [ 1, 3, 2 ], [ 2, 3, 1 ],
[ 2, 1, 2 ], [ 2, 2, 3 ], [ 3, 2, 2 ] ],
[ [ 1, 2, 2 ], [ 3, 1, 2 ], [ 2, 3, 2 ], [ 3, 3, 1 ], [ 2, 1, 3 ],
[ 3, 2, 3 ], [ 2, 2, 1 ], [ 1, 3, 3 ] ], [ [ 2, 2, 2 ] ],
[ [ 3, 3, 3 ] ] ]
\endexample

\>HurwitzOrbitsRepresentatives( <rack>, <n> )
Expand All @@ -519,7 +524,8 @@
\beginexample
gap> r := DihedralRack(3);;
gap> HurwitzOrbitsRepresentatives(r, 3);
[ [ 1, 1, 1 ], [ 1, 1, 2 ], [ 1, 1, 3 ], [ 1, 2, 2 ], [ 2, 2, 2 ], [ 3, 3, 3 ] ]
[ [ 1, 1, 1 ], [ 1, 1, 2 ], [ 1, 1, 3 ], [ 1, 2, 2 ], [ 2, 2, 2 ],
[ 3, 3, 3 ] ]
\endexample

\>HurwitzOrbitsRepresentativesWS( <rack>, <n> )
Expand All @@ -532,7 +538,8 @@
gap> SizesHurwitzOrbits(r, 3);
[ 1, 8 ]
gap> HurwitzOrbitsRepresentativesWS(r, 3);
[ [ [ 1, 1, 1 ], 1 ], [ [ 1, 1, 2 ], 8 ], [ [ 1, 1, 3 ], 8 ], [ [ 1, 2, 2 ], 8 ], [ [ 2, 2, 2 ], 1 ], [ [ 3, 3, 3 ], 1 ] ]
[ [ [ 1, 1, 1 ], 1 ], [ [ 1, 1, 2 ], 8 ], [ [ 1, 1, 3 ], 8 ],
[ [ 1, 2, 2 ], 8 ], [ [ 2, 2, 2 ], 1 ], [ [ 3, 3, 3 ], 1 ] ]
\endexample

\>NrHurwitzOrbits( <rack>, <n>, <size> )
Expand Down