2 research outputs found
Computing with finite groups
The character table of a finite group G is constructed
by computing the eigenvectors of matrix equations determined
by the centre of the group algebra. The numerical character
values are expressed in algebraic form. A variant using a
certain sub-algebra of the centre of the group algebra is
used to ease problems associated with determining the
conjugacy classes of elements of G. The simple group of
order 50,232,960 and its subgroups PSL(2,17) and PSL(2,19)
are constructed using general techniques.
A combination of hand and machine calculation gives the
character tables of the known simple groups of order < 106
excepting Sp(4,4) and PSL(2,q). The characters of the non-
Abelian 2-groups of order < 2 6 are computed.
Miscellaneous computations involving the symmetric
group Sn are given
Design and implementation of a language for manipulating algebraic formulae
This thesis explores the possibilities of doing
mathematical problems involving algebra on a computer. A
language is designed which allows names to occur as unknown
quantities. This language has all the facilities of a
general purpose language such as IMP, but is designed to be
used inter-actively by a user at a console. The language
also includes instructions which cause the usual algebraic
operations to be applied to expressions. These operators
include simplification, differentiation, but not
integration.
A brief survey is given of other languages in the
field, with comments on their capabilities and
restrictions.
The second part of the thesis describes how the
language is implemented. An interpreter is used. Statements
of the language are analysed syntactically and then obeyed.
Algebraic expressions are stored in byte arrays, using a
type of prefix Polish notation.
Finally the language is reviewed in the light of
recent work done in the field, and suggestions are made for
a further version