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2020-04-17 14:18:47 -0500 asked a question Error with rational input in IntegerVectors

I discovered the following unexpected behavior of IntegerVectors:

sage: IntegerVectors(2,3).list()
[[2, 0, 0], [1, 1, 0], [1, 0, 1], [0, 2, 0], [0, 1, 1], [0, 0, 2]]
sage: IntegerVectors(2,3/1).list()
[[2, 0, 0], [1, 1, 0]]

The relevant code block in the implementation of IntegerVectors seems to be the following:

    try:
        return IntegerVectors_nnondescents(n, tuple(k))
    except TypeError:
        pass

    return IntegerVectors_nk(n, k)

For k=3/1 one has that tuple(k) does not give a TypeError (as opposed to tuple(3)) and thus the code never tries to interpret k as an integer.

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2014-01-27 00:12:44 -0500 asked a question Linear subspace of polynomial ring

I am trying to compute a QQ-linear subspace W of a polynomial ring R over QQ. However, R does not seem to have a method like subspace. So what I would like to do is

R=PolynomialRing(QQ,'x',3)
x=R.gens()
W=R.subspace([x[0]^2,3*x[1]+x[0]])

For further purposes I still want to apply functions defined on the ring R to elements of W but also apply linear algebra methods (linear maps, eigenspaces, ...) to W.

I am sorry to bother you with this, it should be very easy, but I did not find a way to do it.