Conjugacy class of a tuple in GAP
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I would like to know how to obtain the conjugacy class of some tuple in GAP, or how two know if two tuples are conjugate by an element of some group (permutation group, more especifically).
I know that for unidimensional cases I can use IsConjugate or ConjugacyClass, but I don't know how to do for a list of elements.
gap
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
$endgroup$
add a comment |
$begingroup$
I would like to know how to obtain the conjugacy class of some tuple in GAP, or how two know if two tuples are conjugate by an element of some group (permutation group, more especifically).
I know that for unidimensional cases I can use IsConjugate or ConjugacyClass, but I don't know how to do for a list of elements.
gap
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
$endgroup$
add a comment |
$begingroup$
I would like to know how to obtain the conjugacy class of some tuple in GAP, or how two know if two tuples are conjugate by an element of some group (permutation group, more especifically).
I know that for unidimensional cases I can use IsConjugate or ConjugacyClass, but I don't know how to do for a list of elements.
gap
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
$endgroup$
I would like to know how to obtain the conjugacy class of some tuple in GAP, or how two know if two tuples are conjugate by an element of some group (permutation group, more especifically).
I know that for unidimensional cases I can use IsConjugate or ConjugacyClass, but I don't know how to do for a list of elements.
gap
gap
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
asked Dec 1 '18 at 9:16
MaríaCCMaríaCC
292213
292213
add a comment |
add a comment |
1 Answer
1
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oldest
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To test in GAP whether two tuples are conjugate, first test whether the first entries are conjugate, then map the whole tuple with a conjugator and test for conjugacy of the second component under the centralizer of the first. This is implemented under RepresentativeAction:
RepresentativeAction(group,tuple1,tuple2,OnTuples);
e.g.
gap> g:=SymmetricGroup(10);;
gap> tup:=[ (1,2,5,4,10,3,6,8)(7,9), (1,3,2,10,6,5)(4,9,7), (1,7,2,10,3,4,6)(5,9,8) ];;
gap> tup2:=[ (1,3,5,6,7,9,10,2)(4,8), (1,6,9,3,2,7)(4,8,5), (1,6,7,5,9,2,8)(3,4,10) ];;
gap> RepresentativeAction(g,tup,tup2,OnTuples);
(1,2)(3,7,8,10,6,9,4,5)
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
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$begingroup$
Thanks! So afeter cheking the firs component I just need to see if RepresentativeAction(g,t1,t1,OnTuples)=fail.
$endgroup$
– MaríaCC
Dec 1 '18 at 18:40
1
$begingroup$
@MaríaCC You don't even need to check the first component,RepresentativeActiondoes both.
$endgroup$
– ahulpke
Dec 1 '18 at 19:19
add a comment |
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1 Answer
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active
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1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
To test in GAP whether two tuples are conjugate, first test whether the first entries are conjugate, then map the whole tuple with a conjugator and test for conjugacy of the second component under the centralizer of the first. This is implemented under RepresentativeAction:
RepresentativeAction(group,tuple1,tuple2,OnTuples);
e.g.
gap> g:=SymmetricGroup(10);;
gap> tup:=[ (1,2,5,4,10,3,6,8)(7,9), (1,3,2,10,6,5)(4,9,7), (1,7,2,10,3,4,6)(5,9,8) ];;
gap> tup2:=[ (1,3,5,6,7,9,10,2)(4,8), (1,6,9,3,2,7)(4,8,5), (1,6,7,5,9,2,8)(3,4,10) ];;
gap> RepresentativeAction(g,tup,tup2,OnTuples);
(1,2)(3,7,8,10,6,9,4,5)
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
$endgroup$
$begingroup$
Thanks! So afeter cheking the firs component I just need to see if RepresentativeAction(g,t1,t1,OnTuples)=fail.
$endgroup$
– MaríaCC
Dec 1 '18 at 18:40
1
$begingroup$
@MaríaCC You don't even need to check the first component,RepresentativeActiondoes both.
$endgroup$
– ahulpke
Dec 1 '18 at 19:19
add a comment |
$begingroup$
To test in GAP whether two tuples are conjugate, first test whether the first entries are conjugate, then map the whole tuple with a conjugator and test for conjugacy of the second component under the centralizer of the first. This is implemented under RepresentativeAction:
RepresentativeAction(group,tuple1,tuple2,OnTuples);
e.g.
gap> g:=SymmetricGroup(10);;
gap> tup:=[ (1,2,5,4,10,3,6,8)(7,9), (1,3,2,10,6,5)(4,9,7), (1,7,2,10,3,4,6)(5,9,8) ];;
gap> tup2:=[ (1,3,5,6,7,9,10,2)(4,8), (1,6,9,3,2,7)(4,8,5), (1,6,7,5,9,2,8)(3,4,10) ];;
gap> RepresentativeAction(g,tup,tup2,OnTuples);
(1,2)(3,7,8,10,6,9,4,5)
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
$endgroup$
$begingroup$
Thanks! So afeter cheking the firs component I just need to see if RepresentativeAction(g,t1,t1,OnTuples)=fail.
$endgroup$
– MaríaCC
Dec 1 '18 at 18:40
1
$begingroup$
@MaríaCC You don't even need to check the first component,RepresentativeActiondoes both.
$endgroup$
– ahulpke
Dec 1 '18 at 19:19
add a comment |
$begingroup$
To test in GAP whether two tuples are conjugate, first test whether the first entries are conjugate, then map the whole tuple with a conjugator and test for conjugacy of the second component under the centralizer of the first. This is implemented under RepresentativeAction:
RepresentativeAction(group,tuple1,tuple2,OnTuples);
e.g.
gap> g:=SymmetricGroup(10);;
gap> tup:=[ (1,2,5,4,10,3,6,8)(7,9), (1,3,2,10,6,5)(4,9,7), (1,7,2,10,3,4,6)(5,9,8) ];;
gap> tup2:=[ (1,3,5,6,7,9,10,2)(4,8), (1,6,9,3,2,7)(4,8,5), (1,6,7,5,9,2,8)(3,4,10) ];;
gap> RepresentativeAction(g,tup,tup2,OnTuples);
(1,2)(3,7,8,10,6,9,4,5)
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
$endgroup$
To test in GAP whether two tuples are conjugate, first test whether the first entries are conjugate, then map the whole tuple with a conjugator and test for conjugacy of the second component under the centralizer of the first. This is implemented under RepresentativeAction:
RepresentativeAction(group,tuple1,tuple2,OnTuples);
e.g.
gap> g:=SymmetricGroup(10);;
gap> tup:=[ (1,2,5,4,10,3,6,8)(7,9), (1,3,2,10,6,5)(4,9,7), (1,7,2,10,3,4,6)(5,9,8) ];;
gap> tup2:=[ (1,3,5,6,7,9,10,2)(4,8), (1,6,9,3,2,7)(4,8,5), (1,6,7,5,9,2,8)(3,4,10) ];;
gap> RepresentativeAction(g,tup,tup2,OnTuples);
(1,2)(3,7,8,10,6,9,4,5)
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
answered Dec 1 '18 at 16:52
ahulpkeahulpke
7,070926
7,070926
$begingroup$
Thanks! So afeter cheking the firs component I just need to see if RepresentativeAction(g,t1,t1,OnTuples)=fail.
$endgroup$
– MaríaCC
Dec 1 '18 at 18:40
1
$begingroup$
@MaríaCC You don't even need to check the first component,RepresentativeActiondoes both.
$endgroup$
– ahulpke
Dec 1 '18 at 19:19
add a comment |
$begingroup$
Thanks! So afeter cheking the firs component I just need to see if RepresentativeAction(g,t1,t1,OnTuples)=fail.
$endgroup$
– MaríaCC
Dec 1 '18 at 18:40
1
$begingroup$
@MaríaCC You don't even need to check the first component,RepresentativeActiondoes both.
$endgroup$
– ahulpke
Dec 1 '18 at 19:19
$begingroup$
Thanks! So afeter cheking the firs component I just need to see if RepresentativeAction(g,t1,t1,OnTuples)=fail.
$endgroup$
– MaríaCC
Dec 1 '18 at 18:40
$begingroup$
Thanks! So afeter cheking the firs component I just need to see if RepresentativeAction(g,t1,t1,OnTuples)=fail.
$endgroup$
– MaríaCC
Dec 1 '18 at 18:40
1
1
$begingroup$
@MaríaCC You don't even need to check the first component,
RepresentativeAction does both.$endgroup$
– ahulpke
Dec 1 '18 at 19:19
$begingroup$
@MaríaCC You don't even need to check the first component,
RepresentativeAction does both.$endgroup$
– ahulpke
Dec 1 '18 at 19:19
add a comment |
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