=ADD=
=reftype=
14
=number=
03-01
=url=
ftp://ftp.risc.uni-linz.ac.at/pub/techreports/2003/03-01.ps.gz
=year=
2003
=month=
01
=author=
Caruso; Fabrizio
=title=
Polynomial Arithmetic and Linear Systems in Symbolic Summation
=abstract=
The object of the thesis is twofold. Firstly we improve
Zeilberger's algorithm for symbolic definite hypergeometric
summation by interpolating the solutions of the related system
of linear equations with rational function coefficients.
Secondly we develop a
C++/Mathematica program library
for polynomial arithmetic that implements
fast multiplication of sparse polynomials and some of
the operations related to homogeneous linear diophantine
inequalities and equations as studied in MacMahon's
partition analysis and in its algorithmic version ($\Omega$-calculus),
namely exponentiation
of low degree polynomials and division by powers of low
degree polynomials.
=note=
PhD Thesis
=sponsor=
.     
=keywords=
polynomial arithmetic, Zeilberger's algorithm, Gosper's algorithm, interpolation