Dear linear algebra specialists,

I am stuck with an elementary linear algebra problem where
Sage is (for now) of no help. I want to compute the rank of
a 30 x 30 dense matrix over a number field of degree 30.

sage: x = polygen(QQ, 'x')
sage: K = NumberField(x^30 - 3, 'a')
sage: M = MatrixSpace(K, 30)
sage: m = M.random_element()
sage: m.rank()

See also

https://ask.sagemath.org/question/50626/compute-dimension-of-vector-subspace/

Any hint?

Best
Vincent

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