
D.2.6 modular_lib
 Library:
 modular.lib
 Purpose:
 An abstraction layer for modular techniques
 Author:
 Andreas Steenpass, email: steenpass@mathematik.unikl.de
 Overview:
 This library is an abstraction layer for modular techniques which are
wellknown to speed up many computations and to be easy parallelizable.
The basic idea is to execute some computation modulo several primes and then
to lift the result back to characteristic zero via the farey rational map and
chinese remaindering. It is thus possible to overcome the often problematic
coefficient swell and to run the modular computations in parallel.
In Singular, modular techniques have been quite successfully employed for
several applications. A first implementation was done for Groebner bases in
Singular's modstd_lib, a pioneering work by Stefan Steidel. Since the
algorithm is basically the same for all applications, this library aims at
preventing library authors from writing the same code over and over again by
providing an appropriate abstraction layer. It also offers oneline commands
for ordinary Singular users who want to take advantage of modular techniques
for their own calculations. Thus modular techniques can be regarded as
a parallel skeleton of their own.
The terminology (such as 'pTest' and 'finalTest') follows Singular's
modstd_lib and [1].
 References:
 [1] Nazeran Idrees, Gerhard Pfister, Stefan Steidel: Parallelization of
Modular Algorithms. Journal of Symbolic Computation 46, 672684 (2011).
http://arxiv.org/abs/1005.5663
Procedures:
D.2.6.1 modular   execute a command modulo several primes and lift the result back to characteristic zero 
See also:
assprimeszerodim_lib;
link;
modstd_lib;
parallel_lib;
tasks_lib.
