Spracherkennung für: .tst vermutete Sprache: Unknown {[0] [0] [0]} [Methode: Schwerpunktbildung, einfache Gewichte, sechs Dimensionen]
gap> START_TEST("omput.tst");
########################################################
## May also call `DrawHasse(diagram)` to produce html
########################################################
## Bruhat order on permutations
########################################################
# return {(i,j) | i < j and p(i) > p(j)}
gap> inv := function(p)
> local n, i, j, res;
>
> res := [];
> n := Length(ListPerm(p));
>
> for j in [
1 .. n] do
> for i in [
1 .. j-
1] do
> if i^p > j^p then
> Append(res, [[i,j]]);
> fi;
> od;
> od;
> return res;
> end;
function( p ) ... end
gap>
gap> le := function(p,t)
> return IsSubset(inv(t), inv(p));
> end;
function( p, t ) ... end
gap>
gap> s := SymmetricGroup(
4);
Sym( [
1 ..
4 ] )
gap> l := AsSet(s);
[ (), (
3,
4), (
2,
3), (
2,
3,
4), (
2,
4,
3), (
2,
4), (
1,
2), (
1,
2)(
3,
4), (
1,
2,
3),
(
1,
2,
3,
4), (
1,
2,
4,
3), (
1,
2,
4), (
1,
3,
2), (
1,
3,
4,
2), (
1,
3), (
1,
3,
4),
(
1,
3)(
2,
4), (
1,
3,
2,
4), (
1,
4,
3,
2), (
1,
4,
2), (
1,
4,
3), (
1,
4), (
1,
4,
2,
3),
(
1,
4)(
2,
3) ]
gap> h := CreateHasseDiagram(l,le);;
gap> OMPrint(h);
<OMOBJ xmlns="
http://www.openmath.org/OpenMath" version="
2.
0">
<OMBIND>
<OMS cd="fns2" name="constant"/>
<OMBVAR>
<OMV name="()"/>
<OMV name="(
3,
4)"/>
<OMV name="(
2,
3)"/>
<OMV name="(
2,
3,
4)"/>
<OMV name="(
2,
4,
3)"/>
<OMV name="(
2,
4)"/>
<OMV name="(
1,
2)"/>
<OMV name="(
1,
2)(
3,
4)"/>
<OMV name="(
1,
2,
3)"/>
<OMV name="(
1,
2,
3,
4)"/>
<OMV name="(
1,
2,
4,
3)"/>
<OMV name="(
1,
2,
4)"/>
<OMV name="(
1,
3,
2)"/>
<OMV name="(
1,
3,
4,
2)"/>
<OMV name="(
1,
3)"/>
<OMV name="(
1,
3,
4)"/>
<OMV name="(
1,
3)(
2,
4)"/>
<OMV name="(
1,
3,
2,
4)"/>
<OMV name="(
1,
4,
3,
2)"/>
<OMV name="(
1,
4,
2)"/>
<OMV name="(
1,
4,
3)"/>
<OMV name="(
1,
4)"/>
<OMV name="(
1,
4,
2,
3)"/>
<OMV name="(
1,
4)(
2,
3)"/>
</OMBVAR>
<OMA>
<OMS cd="relation2" name="hasse_diagram"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="()"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
3,
4)"/>
<OMV name="(
2,
3)"/>
<OMV name="(
1,
2)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
3,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
3,
4)"/>
<OMV name="(
1,
2)(
3,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
4,
3)"/>
<OMV name="(
1,
2,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
3,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
4)"/>
<OMV name="(
1,
2,
3,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
4,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
4)"/>
<OMV name="(
1,
2,
4,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
2,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2)(
3,
4)"/>
<OMV name="(
1,
3,
2)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2)(
3,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
4,
2)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2,
4,
3)"/>
<OMV name="(
1,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2,
3,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2,
4)"/>
<OMV name="(
1,
3,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2,
4,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3)(
2,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
2,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
2,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
2)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3)"/>
<OMV name="(
1,
4,
3,
2)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
4,
2)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
4)"/>
<OMV name="(
1,
4,
2)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3)(
2,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
2,
4)"/>
<OMV name="(
1,
4,
2,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
3,
2,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4)(
2,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4,
3,
2)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4,
2)"/>
<OMV name="(
1,
4,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4,
2)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4,
2,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4)(
2,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4,
2,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4)(
2,
3)"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="(
1,
4)(
2,
3)"/>
<OMA>
<OMS cd="list1" name="list"/>
</OMA>
</OMA>
</OMA>
</OMBIND>
</OMOBJ>
gap>
########################################################
## Divisor lattice of a natural number
########################################################
# try these numbers N :=
102,
2618,
282387;
# the number lattice is basically boring, just a concatenation of cubes...
gap> leq := function(x,y) return y mod x =
0; end;
function( x, y ) ... end
gap> N :=
102;
102
gap> h := CreateHasseDiagram(Filtered([
1..N],i->N mod i =
0), leq);;
gap> OMPrint(h);
<OMOBJ xmlns="
http://www.openmath.org/OpenMath" version="
2.
0">
<OMBIND>
<OMS cd="fns2" name="constant"/>
<OMBVAR>
<OMV name="
1"/>
<OMV name="
2"/>
<OMV name="
3"/>
<OMV name="
6"/>
<OMV name="
17"/>
<OMV name="
34"/>
<OMV name="
51"/>
<OMV name="
102"/>
</OMBVAR>
<OMA>
<OMS cd="relation2" name="hasse_diagram"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
1"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
2"/>
<OMV name="
3"/>
<OMV name="
17"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
2"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
6"/>
<OMV name="
34"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
3"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
6"/>
<OMV name="
51"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
6"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
102"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
17"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
34"/>
<OMV name="
51"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
34"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
102"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
51"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
102"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
102"/>
<OMA>
<OMS cd="list1" name="list"/>
</OMA>
</OMA>
</OMA>
</OMBIND>
</OMOBJ>
gap>
#########################################################################
## Some semigroups examples #############################################
#########################################################################
gap> s1 := Transformation([
1,
1,
3,
4]);
Transformation( [
1,
1 ] )
gap> s2 := Transformation([
1,
2,
2,
4]);
Transformation( [
1,
2,
2 ] )
gap> s3 := Transformation([
1,
2,
3,
3]);
Transformation( [
1,
2,
3,
3 ] )
gap> t1 := Transformation([
2,
2,
3,
4]);
Transformation( [
2,
2 ] )
gap> t2 := Transformation([
1,
3,
3,
4]);
Transformation( [
1,
3,
3 ] )
gap> t3 := Transformation([
1,
2,
4,
4]);
Transformation( [
1,
2,
4,
4 ] )
gap> o4 := Semigroup([s1,s2,s3,t1,t2,t3]);
<transformation semigroup of degree
4 with
6 generators>
gap> rcl := GreensRClasses( o4 );
[ <Green's R-class: Transformation( [
1,
1,
1,
1 ] )>,
<Green's R-class: Transformation( [
1,
1,
1,
2 ] )>,
<Green's R-class: Transformation( [
1,
1,
2,
2 ] )>,
<Green's R-class: Transformation( [
1,
1,
2,
3 ] )>,
<Green's R-class: Transformation( [
1,
2,
2,
2 ] )>,
<Green's R-class: Transformation( [
1,
2,
2,
3 ] )>,
<Green's R-class: Transformation( [
1,
2,
3,
3 ] )> ]
gap> h := CreateHasseDiagram(rcl, IsGreensLessThanOrEqual);;
gap> OMPrint(h);
<OMOBJ xmlns="
http://www.openmath.org/OpenMath" version="
2.
0">
<OMBIND>
<OMS cd="fns2" name="constant"/>
<OMBVAR>
<OMV name="<object>"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
</OMBVAR>
<OMA>
<OMS cd="relation2" name="hasse_diagram"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMA>
<OMS cd="list1" name="list"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMV name="<object>"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMA>
<OMS cd="list1" name="list"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="<object>"/>
<OMA>
<OMS cd="list1" name="list"/>
</OMA>
</OMA>
</OMA>
</OMBIND>
</OMOBJ>
gap>
###################################################################
## Some basic Hasse Diagrams - for when everything else is broken
###################################################################
gap> d := Domain(["
0","a","b","c","
1"]);;
gap> Elements(d);
[ "
0", "
1", "a", "b", "c" ]
gap> Size(d);
5
gap> r := BinaryRelationByElements(d,
> [ DirectProductElement(["
0","a"]),
> DirectProductElement(["
0","b"]),
> DirectProductElement(["
0","c"]),
> DirectProductElement(["a","
1"]),
> DirectProductElement(["b","
1"]),
> DirectProductElement(["c","
1"])]);;
gap> SetIsHasseDiagram(r, true);
gap> OMPrint(r);
<OMOBJ xmlns="
http://www.openmath.org/OpenMath" version="
2.
0">
<OMBIND>
<OMS cd="fns2" name="constant"/>
<OMBVAR>
<OMV name="
0"/>
<OMV name="a"/>
<OMV name="b"/>
<OMV name="c"/>
<OMV name="
1"/>
</OMBVAR>
<OMA>
<OMS cd="relation2" name="hasse_diagram"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
0"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="a"/>
<OMV name="b"/>
<OMV name="c"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="a"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
1"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="b"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
1"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="c"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
1"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="
1"/>
<OMA>
<OMS cd="list1" name="list"/>
</OMA>
</OMA>
</OMA>
</OMBIND>
</OMOBJ>
gap>
########################################################
## Partitions of a Natural Number
##
## problematic? - writing matrices?
########################################################
# this identifies the holes where the spacers go
gap> sumrep := function(p)
> return List([
1 .. Length(p)], i->Sum([
1 .. i], j->p[j]));
> end;
function( p ) ... end
# a refines b iff sumrep(b) is a subset of sumrep(a)
gap> refines := function(a,b)
> return IsSubset(sumrep(a), sumrep(b));
> end;
function( a, b ) ... end
gap>
gap> p := Partitions(
5);
[ [
1,
1,
1,
1,
1 ], [
2,
1,
1,
1 ], [
2,
2,
1 ], [
3,
1,
1 ], [
3,
2 ],
[
4,
1 ], [
5 ] ]
gap> h := CreateHasseDiagram(p, refines);;
gap> OMPrint(h);
<OMOBJ xmlns="
http://www.openmath.org/OpenMath" version="
2.
0">
<OMBIND>
<OMS cd="fns2" name="constant"/>
<OMBVAR>
<OMV name="[
1,
1,
1,
1,
1 ]"/>
<OMV name="[
2,
1,
1,
1 ]"/>
<OMV name="[
2,
2,
1 ]"/>
<OMV name="[
3,
1,
1 ]"/>
<OMV name="[
3,
2 ]"/>
<OMV name="[
4,
1 ]"/>
<OMV name="[
5 ]"/>
</OMBVAR>
<OMA>
<OMS cd="relation2" name="hasse_diagram"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
1,
1,
1,
1,
1 ]"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
2,
1,
1,
1 ]"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
2,
1,
1,
1 ]"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
2,
2,
1 ]"/>
<OMV name="[
3,
1,
1 ]"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
2,
2,
1 ]"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
4,
1 ]"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
3,
1,
1 ]"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
3,
2 ]"/>
<OMV name="[
4,
1 ]"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
3,
2 ]"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
5 ]"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
4,
1 ]"/>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
5 ]"/>
</OMA>
</OMA>
<OMA>
<OMS cd="list1" name="list"/>
<OMV name="[
5 ]"/>
<OMA>
<OMS cd="list1" name="list"/>
</OMA>
</OMA>
</OMA>
</OMBIND>
</OMOBJ>
#
gap> STOP_TEST("omput.tst");
