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2017-01-01 14:09:29 -0600 asked a question witt index of quadratic form

An important invariant of quadratic forms $(V,q)$ over a field is the Witt index, the dimension of a maximal isotropic subspace of $V$.

Is Sage able to calculate this? I have checked and there does not seem to be anything there to help me (but I may have overlooked it).

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2016-11-10 02:37:22 -0600 asked a question Group of units of number field mod ideal

I am wondering whether Sage has a built-in function that takes an ideal $\mathfrak{a}$ of a number field and returns the unit group of the quotient ring $(\mathcal{O}_K / \mathfrak{a})^{\times}.$

More specifically the problem is to iterate through the characters of $(\mathcal{O}_K / \mathfrak{a})^{\times}$ (essentially Hecke characters) and apply them to a given element of $\mathcal{O}_K$. I am at a bit of a loss as to how to do this in Sage.