Simple roots from weights in type A

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Hi everyone,

I ran into the following strange issue. Running

for a in RootSystem('A3').root_lattice().simple_roots():
    a.to_ambient()

gives the expected formulas for the simple roots in type A.

However, if you run instead

for a in RootSystem('A3').weight_lattice().simple_roots():
    a.to_ambient()

then the last root looks like

(1,1,2,0)

which differs from the first output by the "determinant weight" (1,1,1,1).

Anyone came across this before? This behaviour can easily cause some trouble...

Best, Maxim