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### coercion into/from subgroup or Tietze of generator change

Hi there,

do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want):

F.<a,b,c> = FreeGroup()
x=a*b/c

H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]

x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)


I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )

In my use-case I have a free group $F$ and an element $x \in F$ in it. Now I want for a given list of generators (e.g. in above $[ab,b,bc]$) the $x$ as a word of these generators, hence I would like to see $x$ as an element in $H$ and use $Tietze$.

Another solution to my problem would be to swap the generators, but I can't see a way to do that either?

### coercion into/from subgroup or Tietze of generator change

Hi there,

do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want):

F.<a,b,c> = FreeGroup()
x=a*b/c

H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]

x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)


I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )

In my use-case I have a free group $F$ and an element $x \in F$ in it. Now I want for a given list of generators (e.g. in above $[ab,b,bc]$) c] $) the$x$as a word of these generators, hence I would like to see$x$as an element in$H$and use$Tietze$. Another solution to my problem would be to swap the generators, but I can't see a way to do that either? ### coercion into/from subgroup or Tietze of generator change Hi there, do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want): F.<a,b,c> = FreeGroup() x=a*b/c H=F.subgroup([a*b,b,b*c]) y=H.gens()[1]*H.gens()[0] x in H y in F #F(y) #F.coerce(y) #H.coerce(x).Tietze() #H(x)  I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html ) In my use-case I have a free group$F$and an element$x \in F$in it. Now I want for a given list of generators (e.g. in above$[a$[ab,b,bc]$ ) the $x$ as a word of these generators, hence I would like to see $x$ as an element in $H$ and use $Tietze$.

Another solution to my problem would be to swap the generators, but I can't see a way to do that either?

### coercion into/from subgroup or Tietze of generator change

Hi there,

do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want):

F.<a,b,c> = FreeGroup()
x=a*b/c

H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]

x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)


I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )

In my use-case I have a free group $F$ and an element $x \in F$ in it. Now I want for a given list of generators (e.g. in above $[a[ ab,b,bb, b, bc] c ]$ ) the $x$ as a word of these generators, hence I would like to see $x$ as an element in $H$ and use $Tietze$.

Another solution to my problem would be to swap the generators, but I can't see a way to do that either?

### coercion into/from subgroup or Tietze of generator change

Hi there,

do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want):

F.<a,b,c> = FreeGroup()
x=a*b/c

H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]

x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)


I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )

In my use-case I have a free group $F$ and an element $x \in F$ in it. Now I want for a given list of generators (e.g. in above $[ ab, b, bc ]$ ) the $the$x$as a word of these generators, hence I would like to see$x$as an element in$H$and use$Tietze$. Another solution to my problem would be to swap the generators, but I can't see a way to do that either? ### coercion into/from subgroup or Tietze of generator change Hi there, do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want): F.<a,b,c> = FreeGroup() x=a*b/c H=F.subgroup([a*b,b,b*c]) y=H.gens()[1]*H.gens()[0] x in H y in F #F(y) #F.coerce(y) #H.coerce(x).Tietze() #H(x)  I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html ) In my use-case I have a free group$F$and an element$x \in F$in it. Now I want for a given list of generators (e.g. in above$ [ ab, b, bc ] $)$the $x$ as a word of these generators, hence I would like to see $x$ as an element in $H$ and use $Tietze$.x.Tietze().

Another solution to my problem would be to swap the generators, but I can't see a way to do that either?

### coercion into/from subgroup or Tietze of generator change

Hi there,

do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want):

F.<a,b,c> = FreeGroup()
x=a*b/c

H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]

x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)


I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )

In my use-case I have a free group $F$ and an element $x \in F$ in it. Now I want for a given list of generators (e.g. in above $[$[ ab, b, bc ] $]$ ) $the the$x$as a word of these generators, hence I would like to see$x$as an element in$H$and use x.Tietze(). Another solution to my problem would be to swap the generators, but I can't see a way to do that either? ### coercion into/from subgroup or Tietze of generator change Hi there, do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want): F.<a,b,c> = FreeGroup() x=a*b/c H=F.subgroup([a*b,b,b*c]) y=H.gens()[1]*H.gens()[0] x in H y in F #F(y) #F.coerce(y) #H.coerce(x).Tietze() #H(x)  I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html ) In my use-case I have a free group$F$and an element$x \in F$in it. Now I want for a given list of generators (e.g. in above$[ ab, b, bc ]$) the$x$as a word of these generators, hence I would like to see$x$as an element in$H$and use x.Tietze(). Another solution to my problem would be to swap the generators, but I can't see a way to do that either? ### coercion into/from subgroup or Tietze of generator change Hi there, do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want): F.<a,b,c> = FreeGroup() x=a*b/c H=F.subgroup([a*b,b,b*c]) y=H.gens()[1]*H.gens()[0] x in H y in F #F(y) #F.coerce(y) #H.coerce(x).Tietze() #H(x)  I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html ) In my use-case I have a free group$F$and an element$x \in F$in it. Now I want for a given list of generators (e.g. in above$[ $[ ab, b, bc ]$ ) the $x$ as a word of these generators, hence I would like to see $x$ as an element in $H$ and use x.Tietze().

Another solution to my problem would be to swap the generators, but I can't see a way to do that either?

### coercion into/from subgroup or Tietze of generator change

Hi there,

do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want):

F.<a,b,c> = FreeGroup()
x=a*b/c

H=F.subgroup([a*b,b,b*c])
y=H.gens()[1]*H.gens()[0]

x in H
y in F
#F(y)
#F.coerce(y)
#H.coerce(x).Tietze()
#H(x)


I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html )

In my use-case I have a free group $F$ and an element $x \in F$ in it. Now I want for a given list of generators (e.g. in above $\$ [ ab, b, bc ]$) the$x$as a word of these generators, hence I would like to see$x$as an element in$H$and use x.Tietze(). Another solution to my problem would be to swap the generators, but I can't see a way to do that either? ### coercion into/from subgroup or Tietze of generator change Hi there, do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want): F.<a,b,c> = FreeGroup() x=a*b/c H=F.subgroup([a*b,b,b*c]) y=H.gens()[1]*H.gens()[0] x in H y in F #F(y) #F.coerce(y) #H.coerce(x).Tietze() #H(x)  I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html ) In my use-case I have a free group$F$and an element$x \in F$in it. Now I want for a given list of generators (e.g. in above \$ [ $[ ab, b, bc ]$ ) ]$) the$x$as a word of these generators, hence I would like to see$x$as an element in$H$and use x.Tietze(). Another solution to my problem would be to swap the generators, but I can't see a way to do that either? ### coercion into/from subgroup or Tietze of generator change Hi there, do you know of a function, which solves the Tietze for subgroups or converts elements from parentgroup to elements of subgroup and the other way round (if possible)? Neither of the commented codes work (but I hope it is clear what I want): F.<a,b,c> = FreeGroup() x=a*b/c H=F.subgroup([a*b,b,b*c]) y=H.gens()[1]*H.gens()[0] x in H y in F #F(y) #F.coerce(y) #H.coerce(x).Tietze() #H(x)  I am using cocalc, if this is a version thing. I know something like that exists for quotient groups (s. http://doc.sagemath.org/html/en/reference/groups/sage/groups/finitely_presented.html ) In my use-case I have a free group$F$and an element$x \in F$in it. Now I want for a given list of generators (e.g. in above$[ [ ab, b, bc ]$) ]) the$x$as a word of these generators, hence I would like to see$x$as an element in$H\$ and use x.Tietze().

Another solution to my problem would be to swap the generators, but I can't see a way to do that either?