Note that there are linear algebra and numerical analysis programs below. More linear algebra and numerical analysis programs will be added as soon as possible.

Discrete Mathematics and Number Theory

Long Division of Polynomials (Finds the quotient and the remainder when polyonmial a(x) is divided by polynomial b(x). Warning: Enter the variables the way you'll be asked to. Notice that the exponents must be nonnegative integers. Also, you have to combine like terms of each polynomial.) Improved Version of Long Division (but not tested carefully)

Finding gcd(a,b), the linear combination, and lcm(a,b) Or you can use this one. (Finds the greatest common divisor of a and b and writes it as a linear combination of a and b. It also finds$ least common multiple of a and b. Warning: Enter the variables the way you'll be asked to. Both a and b must be nonzero integers.)

Solving Congruence Systems (Solves the linear congruence system: a x + b y = u (mod n) c x + d y = v (mod n) Warning: Enter the variables the way you'll be asked to. Notice that n must be a natural number and a, b, c, d, u, and v must be integers.)

Solving Linear Congruence Equations (Solves the linear congruence equation: a x = b (mod n) Warning: Enter the variables the way you'll be asked to. Notice that n must be a natural number and both a and b must be integers.)

Solving Quadratic Congruence Equations (Solves the quadratic congruence equation: a x2 + b x + c = 0 (mod n) Warning: Enter the variables the way you'll be asked. Notice that n must be a natural number and a, b, and c must be integers.)

Finding the Quotient and the Remainder Or you can use this. (Finds the quotient and the remainder when a is divided by b. Warning: Enter the variables the way you'll be asked to. Notice that both and b must be nonzero integers.)

Is n prime? Or you can use this. (Finds whether a natural number n is prime or not. If not, then it returns the number of nontrivial positive divisors of n. Trivial positive divisors are 1 and n. Warning: Enter the variables the way you'll be asked to. Notice that n must be a natural number greater than 4.)

Are a and b relatively prime? (Finds whether two nonzero integers a and b are relatively prime. If yes, then it write 1 as a linear comination of them. Trivial positive divisors are 1 and n. Warning: Enter the variables the way you'll be asked to. Notice that both and b must be nonzero integers.)

Conversion from one number system to another Converts a decimal number to binary/octal/hexadecimal and a binary/octal/hexadecimal number to decimal.

This program finds the inverse of a in Zn

This program finds the canonical factorization of a positive integer.

Numerical Analysis

Lagrange Polynomial Interpolation This program finds the Lagrange polynomial interpolation of a set of points.

Newton Polynomial Interpolation This program finds the Newton polynomial interpolation of a set of points.

Natural Cubic Splines Interpolation This program finds the natural cubic splines interpolation of a set of points.

Clamped Cubic Splines Interpolation This program finds the clamped cubic splines interpolation of a set of points.

LU Factorization This program finds the LU factorization (LU decomposition) of a positive definite matrix.

Cholesky Factorization This program finds the Cholesky factorization of a positive definite matrix.

The Jacobi Method for Linear Systems This program solves a linear system of the form A x = b by the Jacobi method.

Gauss-Seidel Method for Linear Systems This program solves a linear system of the form A x = b by the Gauss-Seidel method.

A simple calculator and conversion from binary/octal/hexadecimal to any other system of these three.