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.