Software Specialization as Applied to
Computational Algebra
by wizheart
Software Specialization as Applied to Computational Algebra
,Software Specialization as Applied to Computational Algebra
By
Pouya Larjani, M.Sc.
A Thesis Submitted to the School of Graduate Studies in partial fulfilment of the requirements for the degree
of
Doctor of Philosophy Department of Computing and Software McMaster University
c Copyright by Pouya Larjani, April 22, 2013
,ii DOCTOR OF PHILOSOPHY (2012) (Computer Science) McMaster University Hamilton, Ontario
TITLE:
Software Specialization as Applied to Computational Algebra.
AUTHOR:
Pouya Larjani, M.Sc. (McMaster University)
SUPERVISOR:
Dr. William M. Farmer
NUMBER OF PAGES:
viii, 198
, iii
Abstract
A great variety of algebraic problems can be solved using Gr¨bner bases, and computational commutative
algebra is the branch of mathematics that focuses mainly on such problems. In this thesis we employ
Buchbergers algorithm for finding Gr¨bner o bases by tailoring specialized instances of Buchbergers
algorithm via code generation. We introduce a framework for meta programming and code generation in the
F# programming language that removes the abstraction overhead of generic programs and produces type-
safe and syntactically valid specialized instances of generic programs. Then, we discuss the concept of
modularizing and decomposing the architecture of software products through a multistage design process
and define what specialization of software means in the context of producing special instances. We provide
a domain-specific language for the design of flexible, customizable, multistage programs. Finally, we utilize
the aforementioned techniques and framework to produce a highly parametrized, abstract and generative
program that finds Gr¨bner bases based o on Buchbergers original algorithm, which, given all the proper
definitions and features of a specific problem in computational algebra, produces a specialized instance of a
solver for this problem that can be shown to be correct and perform within the desired time complexity.
Computational Algebra
by wizheart
Software Specialization as Applied to Computational Algebra
,Software Specialization as Applied to Computational Algebra
By
Pouya Larjani, M.Sc.
A Thesis Submitted to the School of Graduate Studies in partial fulfilment of the requirements for the degree
of
Doctor of Philosophy Department of Computing and Software McMaster University
c Copyright by Pouya Larjani, April 22, 2013
,ii DOCTOR OF PHILOSOPHY (2012) (Computer Science) McMaster University Hamilton, Ontario
TITLE:
Software Specialization as Applied to Computational Algebra.
AUTHOR:
Pouya Larjani, M.Sc. (McMaster University)
SUPERVISOR:
Dr. William M. Farmer
NUMBER OF PAGES:
viii, 198
, iii
Abstract
A great variety of algebraic problems can be solved using Gr¨bner bases, and computational commutative
algebra is the branch of mathematics that focuses mainly on such problems. In this thesis we employ
Buchbergers algorithm for finding Gr¨bner o bases by tailoring specialized instances of Buchbergers
algorithm via code generation. We introduce a framework for meta programming and code generation in the
F# programming language that removes the abstraction overhead of generic programs and produces type-
safe and syntactically valid specialized instances of generic programs. Then, we discuss the concept of
modularizing and decomposing the architecture of software products through a multistage design process
and define what specialization of software means in the context of producing special instances. We provide
a domain-specific language for the design of flexible, customizable, multistage programs. Finally, we utilize
the aforementioned techniques and framework to produce a highly parametrized, abstract and generative
program that finds Gr¨bner bases based o on Buchbergers original algorithm, which, given all the proper
definitions and features of a specific problem in computational algebra, produces a specialized instance of a
solver for this problem that can be shown to be correct and perform within the desired time complexity.
