Math Pac

The Math Pac provides fourteen modules that calculate different functions in algebra, analytical geometry, number theory, trigonometry and special functions. The algebraic functions include complex number operations, factors, prime factors, polynomial solutions, greatest common divisor, least common denominator, decimal-to-fractions conversions and matrix operations. For analytical geometry, coordinate transformations and intersections of lines and circles routines are provided. In number theory, prime numbers generation and interpolation methods are available. The special functions include the gamma function, Bessel functions, error function, hyperbolic functions and base conversions.

The user interface provides an intuitive input view with validation of range values and necessary input parameters. The output is presented in an easily comprehendible format.

Complex Number Operations module performs basic arithmetic operations and several other functions for complex numbers, z = a + b i. The arithmetic operations are addition, subtraction, multiplication and division. The other functions include magnitude, reciprocal, complex number raised to the Nth power, complex number raised to the 1/Nth power and e raised to the zth power. The program allows for chained calculations where the complex number result is provided as an input to the next calculation to be performed.

Factors and Primes module provides three functions - list all the prime numbers between lower and upper bounds or find all factors or prime factors of a positive integer number.

Polynomial Solutions module solves polynomial equations with real coefficients of degree 9 and below. The program presents the real or complex roots for the polynomial solution.

Matrix Operations module provides basic, arithmetic and solution functions for NxN matrices, where 2 ≤ n ≤ 50. The basic matrix functions include determinate, inverse matrix and transpose matrix functions. The arithmetic functions provide addition, subtraction and multiplication calculations. The program also calculates solutions for simultaneous linear equations where there are an equal number of equations and unknowns.

Base Conversions module converts a positive number in one base into its equivalent in another base. The bases can be any integer value from 2 to 36.

Hyperbolics program calculates hyperbolics and their inverses.

Greatest Common Divisor, Least Common Denominator and Decimal-to-Fractions module will find the greatest common divisor or least common multiple for two integer numbers. The program will also convert a decimal number into a fractional number.

Gamma Function program approximates the value of the gamma function.

Bessel Functions and Error Function module calculates the Bessel functions Jn(x) and In(x). The program also calculates the error function and complementary error function.

Coordinate Transformations module provides 2-dimensional and 3-dimensional coordinate translation. The transformations include origin translocations and/or rotation.

Intersections module calculates the point of intersection of two coplanar lines, a coplanar line and a circle, or two coplanar circles.

Circle Calculations module calculates the center point and radius of a circle based on three non-collinear points. The program also calculates the coordinates of points on a circle given the center and radius of a circle, starting angle and number of points on the circle or a delta angle.

Spherical Triangles module calculates the solution to all six cases of spherical triangles plus two ambiguous cases. Based on a combination of three sides or angles, the program calculates the remaining sides and/or angles of the spherical triangle.

Interpolation module calculates a point on a line or curve between given points. The program provides selection of one of three different interpolation routines – linear, Lagrangian and finite difference.