Hi All,
Long ago I posted a public Sage notebook in connection with a course I was
teaching -- http://sagenb.org/home/pub/3914/ . The link no longer works
(no surprise!). My colleague who is teaching the course this year would
like to see the notebook. Is there some way to retrieve it? (I
Thanks to everyone for the explanation of why my comparison of rational
numbers did not work. I'd like to make two comments:
1. I got into this mess by trying to count points above and below the line
in the standard textbook proof of quadratic reciprocity. You have two odd
primes p and q,
On Thursday, March 22, 2012 2:44:43 PM UTC-7, William wrote:
On Thu, Mar 22, 2012 at 5:22 PM, Kenneth A. Ribet wrote:
Consider this short sage transcript:
sage: E=EllipticCurve(GF(3),[1,1])
sage: for i in range(3):
... print i,E.order(extension_degree=i)
0 4
1 4
2 16
I'll add here is that sage, when asked to find gcd(Mod(5,6),5), will
just echo back 5. Of course it then gives the same answer when asked
to find gcd(Mod(11,6),5). In number theory courses, students are told
that these quantities don't make any sense.
Ken
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The key trick is:
sage: R = Integers(2010)
sage: # Make Sage think that R is a field
I'm stunned. Thanks!
Ken
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Thank you for your help responses. I draw from them the lesson is
that even beginning users need to learn about the inheritance tree
and about the difference between top level and other functions. On
the other hand, it's gratifying to know that the strange behavior that
I encountered is
Thank you for your helpful responses. I draw from them the lesson
that even beginning users need to learn about the inheritance tree
and about the difference between top level and other functions. On
the other hand, it's gratifying to know that the strange behavior
that
I encountered is
