An alternative way of taking quotient avoiding the "is_principal" call
sage: Q = sage.rings.quotient_ring.QuotientRing_generic(R, I, 'a')
Vincent
On 06/06/2017 18:14, Joel Ornstein wrote:
Hi,
For more correct context, I'm taking the quotient of the ring of integers
in my worksheet.
f = QQ['t']({16:1, 0:262})
K.<s> = NumberField(f)
R = K.ring_of_integers()
QuotientRing(R, Ideal(263,s+1))
I forgot to include that when simplifying the example.
On Monday, June 5, 2017 at 1:26:18 PM UTC-6, William wrote:
On Mon, Jun 5, 2017 at 12:17 PM, Vincent Delecroix
<20100.d...@gmail.com <javascript:>> wrote:
On 05/06/2017 22:15, William Stein wrote:
On Mon, Jun 5, 2017 at 11:48 AM, Joel Ornstein
<joel.o...@colorado.edu <javascript:>> wrote:
Hi all,
I'm trying to work with several quotient rings and occasionally
creating
the
quotient ring takes an extremely long time:
f = QQ['t']({16:1, 0:262})
K.<s> = NumberField(f)
QuotientRing(K, Ideal(263,s+1))
Question: What are you really trying to do exactly? The quotient of a
number field by absolutely any nonzero ideal is just 0.
That's a good point. However, it would still be useful if Sage had the
same
answer straight! Don't you think?
I believe the OP was interested in the ring of integers of such number
field
Probably. Even then it would be very relevant to know what the OP
actually wants to do with this quotient ring... Just arithmetic?
Something harder?
Here's a little worksheet working with the quotient as a module, which
shows the quotient is cyclic of order 263:
https://cocalc.com/projects/4a5f0542-5873-4eed-a85c-a18c706e8bcd/files/support/quotient-ring.ipynb?fullscreen
It would be easy to build on that to do arithmetic quickly at least
(without ever worrying about is_principal).
William
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