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2019-04-18 09:11:40 -0500 commented question Computations in the ring of integers of a number field

@FredericC OK, but how do I do what I've asked to do?

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2019-04-17 16:57:20 -0500 asked a question Computations in the ring of integers of a number field

Suppose I have some number field $K$, with its ring of integers $O_K$ = K.ring_of_integers(). If $I$ is an ideal of $O_K$ (or, if $I$ is a fractional ideal of $K$), I'd like to be able to compute with the ring $O_K/I$. For example, I'd like to be able to ask how big that ring is.

K.<omega> = NumberField(x^2+x+1)
OK = K.ring_of_integers()
R.<a,b> = OK.quo(OK.ideal(9))
R.cardinality()

gives a NotImplementedError. (Even though cardinality shows up as one of the supported methods if I type R.??).

Or, again for example, I'd like to be able to determine the ring structure of $R$, or the structure of its group of units, but none of these methods seem to actually be supported.

The type of R is sage.rings.quotient_ring.QuotientRing_generic_with_category.

What am I missing?

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2019-01-17 22:57:34 -0500 asked a question Extended Sage examples

I'm trying to learn how to use Sage to do algebraic number theory. I've read the thematic tutorials that seem related, but they are pretty bare-bones. The documentation seems to be pretty much a list of methods; I haven't found a higher-level view of what concepts are implemented and how they can be used. Are there any meatier extended examples that are available? Or is there documentation that I'm missing? (So, for example, how would I go about finding in the documentation the answer to "is the square root of two in the field K that I just defined"?)