1 | initial version |
The following dialog worked for me...
sage: K.<a> = QuadraticField(5)
sage: OK = K.ring_of_integers()
sage: OK.gens()
(1/2*a + 1/2, a)
sage: g = 1 + 7*(1+a)/2 # can be obviously expressed in terms of OK.gens()
sage: g in OK
True
sage: J = OK.ideal(g) # works
sage: J
Fractional ideal (7/2*a + 9/2)
It was possible to initialize J
, since its generator(s) $\in \mathcal O_K$. But if we try "the same" with some $h$ which is not integral...
sage: h = a/3
sage: h in OK
False
sage: H = OK.ideal(h)
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ValueError Traceback (most recent call last)