Hi,

I'm running 

SageMath version 9.3, Release Date: 2021-05-09

on Mac OS, but the bug I encountered also occurred on a Windows machine.

The code

R = RootSystem(['D',4,1])
L = R.weight_lattice(extended = True)
R.root_space().positive_real_roots()
L.positive_real_roots()[12]

leads to a long error message, the final line of which is

TypeError: unsupported operand parent(s) for *: 'Rational Field' and 
'Extended weight lattice of the Root system of type ['D', 4, 1]'

Note that the positive root [12] is the first one at grade 1.

One can get around the bug by accessing the positive roots in L first, but 
it would still be nice if this could be fixed. Thanks.

Amir

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