Hi,

i don't really know whether this is a bug, but at least it seems a bit
odd to me (are alphacheck supposed to have different meanings in the
spaces?):

R = RootSystem(['A',3])
wgtsp = R.weight_space()
rootsp = R.root_space()

a = wgtsp.simple_roots()[1]
b = rootsp.simple_roots()[1]

a.associated_coroot()
>> 4/5*alphacheck[1] - 2/5*alphacheck[2]
b.associated_coroot()
>> alphacheck[1]

In general is there a way to specify a basis of a ?free module?
(whatever is behind the spaces) and make sage express everything in
this basis?

Best regards
Matthias

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