Symbolic Computing Package for Mathematica for Versatile Manipulation of Mathematical Expressions
Symbolic computing, in contrast to numerical computing, is computation with
variables and constants according to the rules of algebra for manipulation and
evaluation of mathematical expressions. This will lead to dramatic improvement
of analytical calculation and can be applied to research and education of
mathematics, physics and various other science and engineering disciplines.
Other advantages include minimization of human errors and improvement of
accuracy during calculation by using computer software that incorporates known
algorithms and mathematical identities.
Symbolic Computing package is an add-on package that facilitates symbolic
computation in Mathematica. It enables display and interpretation of
derivatives, integrals, sums, products, vector operators, brakets, and various
forms of subscripts and superscripts using the traditional mathematical notation
based on the low-level box language and contains over 700 functions for
notation, algebraic manipulation and evaluation of various mathematical
expressions. The package function categories include: basic algebra, complex
variables, differential calculus, elementary functions, equation solving,
equations, formula manipulation, Fourier analysis, function analysis, integral
calculus, operator analysis, polynomials and series, products, sums,
trigonometric functions, vectors and matrices.
These features of the package allow the users to focus on the principles instead
of time-consuming and error-prone calculations and provide good readability and
minimization of human errors during calculations. Expressions that closely
resemble the traditional mathematical style, e.g., subscripts, superscripts and
vector notations, can be used and this will replace a lot of hand calculations.
Using this approach, materials and references including derivation of the
mathematical formulas can be contained in a single document.
The package has its own interpreter language, complete on-line documentation and
two palettes for entering mathematical expressions and execution control of
functions. This provides a powerful platform for streamlined manipulation of all
or parts of an expression and will significantly enhance the capabilities of the
kernel and user-defined functions. Development of the package and its
applications to various topics of mathematics and related disciplines will be
presented.