The course material will consist of the pdf files for the slides,
handouts (copies of Chapters of books) and exercises sets that will
be handed out and posted here as well.
The first week we got started, found a suitable time and
looked briefly at what computer algebra really is; in the second week
(February 10 and 11)
we had a look at some general issues, representation and complexity,
and considered the Pollard-rho method as an example algorithm. Here are the
notes.
I also handed out copies of Chapter 0 of Yap.
Here are some additional notes on
complexity and number theory.
And the
first set of exercises.
In the third week (February 24 and 25) we looked at some ring
essentials and at the Fourier transform (see these
notes).
And the second set of exercises.
In the fourth week (March 3 and 4) we considered the (extended) Euclidean
algorithm (in a general context) and continued fractions (of reals),
using these
notes. See also
this chapter on continued fractions.
The (easy) exercises in the third set of exercises
and the (harder) one
in the fourth set of exercises refer to this
chapter too.
In the fifth week, the first lecture (March 10)
had to be cancelled, and the second (March 11) was used for a
practical session with Magma.
In the sixth week (March 17 and 18) was used for the Chinese
remainder theorem (constructively), and Polynomial Remainder Sequences.
Here are notes. I used some examples
from Geddes et al.
In the seventh week (March 24) we did a practical Magma session,
mainly on the continued fraction exercises; the second lecture (March 25)
was cancelled.
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