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I would like to define a free group on a custom ordered list of symbols, like say

Frgp=Groups()free([f'a{j}' for j in range (5,10)])

i.e. a5 up to a9 (say). It's important that the list be defined programmatically as above, as the number of generators changes throughout the program run (their labels also need to change).

I would then like to recover elements of the group by evaluating at numbered lists, as in Frgp([1,2]) to get back a5*a6, say, as suggested in the docs. This syntax of Frgp(<numerical list>), however, only works when I define the group via one of the methods

Frgp.<x,y,z> = Groups().free()

or

Frgp=Groups().free(3,'t')

which are not flexible enough to allow me to interpolate strings in variable names (or are they? I have tried all sorts of eval/exec trickery to no avail).

If I define the group as in my preferred style (first code display above), then

sage: Frgp=Groups()free([f'a{j}' for j in range (5,10)])
sage: Frgp([1,2])

results in an error:

TypeError: 'sage.rings.integer.Integer' object is not iterable

I would like to define a free group on a custom ordered list of symbols, like say

Frgp=Groups()free([f'a{j}' Frgp=Groups().free([f'a{j}' for j in range (5,10)])

i.e. a5 up to a9 (say). It's important that the list be defined programmatically as above, as the number of generators changes throughout the program run (their labels also need to change).

I would then like to recover elements of the group by evaluating at numbered lists, as in Frgp([1,2]) to get back a5*a6, say, as suggested in the docs. This syntax of Frgp(<numerical list>), however, only works when I define the group via one of the methods

Frgp.<x,y,z> = Groups().free()

or

Frgp=Groups().free(3,'t')

which are not flexible enough to allow me to interpolate strings in variable names (or are they? I have tried all sorts of eval/exec trickery to no avail).

If I define the group as in my preferred style (first code display above), then

sage: Frgp=Groups()free([f'a{j}' Frgp=Groups().free([f'a{j}' for j in range (5,10)])
sage: Frgp([1,2])

results in an error:

TypeError: 'sage.rings.integer.Integer' object is not iterable

I would like to define a free group on a custom ordered list of symbols, like say

Frgp=Groups().free([f'a{j}' for j in range (5,10)])

i.e. a5 up to a9 (say). It's important that the list be defined programmatically as above, as the number of generators changes throughout the program run (their labels also need to change).

I would then like to recover elements of the group by evaluating at numbered lists, as in Frgp([1,2]) to get back a5*a6, say, as suggested in the docs. This syntax of Frgp(<numerical list>), however, only works when I define the group via one of the methods

Frgp.<x,y,z> = Groups().free()

or

Frgp=Groups().free(3,'t')

which are not flexible enough to allow me to interpolate strings in variable names (or are they? I have tried all sorts of eval/exec trickery to no avail).

If I define the group as in my preferred style (first code display above), then

sage: Frgp=Groups().free([f'a{j}' for j in range (5,10)])
sage: Frgp([1,2])

results in an error:

TypeError: 'sage.rings.integer.Integer' object is not iterable

I would like to define a free group on a custom ordered list of symbols, like say

Frgp=Groups().free([f'a{j}' for j in range (5,10)])

i.e. a5 up to a9 (say). It's important that the list be defined programmatically as above, as the number of generators changes throughout the program run (their labels also need to change).

I would then like to recover elements of the group by evaluating at numbered lists, as in Frgp([1,2]) to get back a5*a6, say, as suggested in the docs. This syntax of Frgp(<numerical list>), however, only works when I define the group via one of the methods

Frgp.<x,y,z> = Groups().free()

or

Frgp=Groups().free(3,'t')

which are not flexible enough to allow me to interpolate strings in variable names (or are they? I have tried all sorts of eval/exec trickery to no avail).

If I define the group as in my preferred style (first code display above), then

sage: Frgp=Groups().free([f'a{j}' for j in range (5,10)])
sage: Frgp([1,2])

results in an error:

TypeError: 'sage.rings.integer.Integer' object is not iterable

sage: Frgp=Groups().free(5,'t')
sage: Frgp([1,2])([var(f'a{j}') for j in range (5,10)])
a5*a6

I would like to define a free group on a custom ordered list of symbols, like say

Frgp=Groups().free([f'a{j}' for j in range (5,10)])

i.e. a5 up to a9 (say). It's important that the list be defined programmatically as above, as the number of generators changes throughout the program run (their labels also need to change).

I would then like to recover elements of the group by evaluating at numbered lists, as in Frgp([1,2]) to get back a5*a6, say, as suggested in the docs. This syntax of Frgp(<numerical list>), however, only works when I define the group via one of the methods

Frgp.<x,y,z> = Groups().free()

or

Frgp=Groups().free(3,'t')

which are not flexible enough to allow me to interpolate strings in variable names (or are they? I have tried all sorts of eval/exec trickery to no avail).

If I define the group as in my preferred style (first code display above), then

sage: Frgp=Groups().free([f'a{j}' for j in range (5,10)])
sage: Frgp([1,2])

results in an error:

TypeError: 'sage.rings.integer.Integer' object is not iterable

Edit:

To clarify, I am aware that the goal I alluded to above can be achieved by other means. For instance, I can do

sage: Frgp=Groups().free(5,'t')
sage: Frgp([1,2])([var(f'a{j}') for j in range (5,10)])
a5*a6

So in other words, I can create a list of symbolic variables and apply a free-group word to that. But this seems like a clumsy workaround. It would be preferable to work in the free group on the desired set of symbolic variables to begin with.

I would like to define a free group on a custom ordered list of symbols, like say

Frgp=Groups().free([f'a{j}' for j in range (5,10)])

i.e. a5 up to a9 (say). It's important that the list be defined programmatically as above, as the number of generators changes throughout the program run (their labels also need to change).

I would then like to recover elements of the group by evaluating at numbered lists, as in Frgp([1,2]) to get back a5*a6, say, as suggested in the docs. This syntax of Frgp(<numerical list>), however, only works when I define the group via one of the methods

Frgp.<x,y,z> = Groups().free()

or

Frgp=Groups().free(3,'t')

which are not flexible enough to allow me to interpolate strings in variable names (or are they? I have tried all sorts of eval/exec trickery to no avail).

If I define the group in my preferred style (first code display above), then

sage: Frgp=Groups().free([f'a{j}' for j in range (5,10)])
sage: Frgp([1,2])

results in an error:

TypeError: 'sage.rings.integer.Integer' object is not iterable

Edit:

To clarify, I am aware that the goal I alluded to above can be achieved by other means. For instance, I can do

sage: Frgp=Groups().free(5,'t')
sage: Frgp([1,2])([var(f'a{j}') for j in range (5,10)])
a5*a6

So in other words, I can create a list of symbolic variables and apply a free-group word to that. But this seems like a clumsy workaround. It would be preferable to work in the free group on the desired set of symbolic variables to begin with.