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asked 5 years ago

rogerl gravatar image

Computations in the ring of integers

Suppose I have some number field K, with its ring of integers OK = K.ring_of_integers(). If I is an ideal of OK (or, if I is a fractional ideal of K), I'd like to be able to compute with the ring OK/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?

Computations in the ring of integers

Suppose I have some number field K, with its ring of integers OK = K.ring_of_integers(). If I is an ideal of OK (or, if I is a fractional ideal of K), I'd like to be able to compute with the ring OK/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?

Computations in the ring of integers

Suppose I have some number field K, with its ring of integers OK = K.ring_of_integers(). If I is an ideal of OK (or, if I is a fractional ideal of K), I'd like to be able to compute with the ring OK/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?