A term-rewriting system for computer quantum algebra

Existing computer algebra packages do not fully support quantum mechanics calculations in Dirac's notation. I present the foundation for building such support: a mathematical system for the symbolic manipulation of expressions used in the invariant formalism of quantum mechanics. I first describe the essential mathematical features of the Hilbert-space invariant formalism. This is followed by a formal characterisation of all possible algebraic expressions in this formalism. This characterisation is provided in the form of a set of terms. Rewrite rules over this set of terms are then developed that correspond to allowed manipulations of the algebraic expressions. This approach is contrasted with current attempts to build invariant quantum mechanics calculations into computer algebra systems.Comment: 16 pages, 1 tabl

Development of a Java Package for Matrix Programming

We had assembled a Java package, known as MatrixPak, of four classes for the purpose of numerical matrix computation. The classes are matrix, matrix_operations, StrToMatrix, and MatrixToStr; all of which are inherited from java.lang.Object class. Class matrix defines a matrix as a two-dimensional array of float types, and contains the following mathematical methods: transpose, adjoint, determinant, inverse, minor and cofactor. Class matrix_operations contains the following mathematical methods: matrix addition, matrix subtraction, matrix multiplication, and matrix exponential. Class StrToMatrix contains methods necessary to parse a string representation (for example, [[2 3 4]-[5 6 7]]) of a matrix into a matrix definition, whereas class MatrixToStr does the reverse.Comment: Secondary school (high school) student project report. Foundation for JMaths projec