>
> My name is Adityan. I am 18 years old. I am currently pursuing an
> integrated MSc. in Mathematics and Computer Science at BITS Pilani, India.
> I have been interested in programming and algorithms code in C++.
>
> I have studied linear algebra, graph theory, series and sequences (like
> taylor series), integral and differential calculus, elementary number
> theory, geometry. Currently I am studying a course based on probability and
> statistics. I have a good experience in C++ with knowledge about stacks,
> queues. Apart from that I am involved in solving problems on Project Euler.
> I am interested in doing a Google summer of Code project. I am very eager
> to work on FriCAS. Can anyone help me?
I wonder what you think about modular methods. If one tries
do calculations in naive way, then growth of intermetiate
expression may be substantial problem. If final result is
big then problem is unavoidable. But evan if final result
is small in naive calculation intermediate parts may be quite
big. Typical example is greatest common divisor (GCD) for integer
polynomials or solving system of linear equations with integer
coefficients. For example Gaussian elimination on integer
matrices produces fractions which may have quite large
numerators and denominators. OTOH when one performs
computation in finite field all field elements have
small fixed size and there is no growth. Of course
performing computation in finite field looses some
information (and may fail), but using several finite
fields it is possible to recover true answer. My
point is that cost of modular computation depends
mainly on answer size and avoid large size of intermediate
expressions. Modular computations are now basis
of several fast algorithms. In particular GCD
is used by other functions. FriCAS already uses
modular (and related p-adic) methods in polynomial
calculations, but the "Zippel style" idea is about
using variant which FriCAS do not have, but could
help for sparse polynomials.
--
Waldek Hebisch
[email protected]
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