Abakus

A numerical, graphical and symbolic calculator
Abakus is a computer algebra program which performs not only
arithmetic but even symbolic calculations of mathematical formulas.
The current version contains the following functions:
Exact arithmetic calculations:
- Exact calculation of integer numbers of "arbitrary" size
- Calculation of real numbers with "arbitrary" precision
- Exact calculation of fractions
- Least common multiple, greatest common divisor
- Factorial, binomial coefficient
- Prime numbers, prime factor separation, divisor set
Transforming mathematical formulas:
- Simplify, multiply, and factorize formulas; building the common denominator
- Normalize, divide, and factorize polynomials; separate into partial fractions
Discussing mathematical functions:
- Calculate function values
- Zeros, singularities, extremal points, turn points
- Differentiation, integration (even with solution steps)
- Calculation of limits
- Graphical representation (2D and 3D)
Solving mathematical equations:
- Exact and numerical solution of linear and non-linear equations
- Exact solution of systems of linear equations
Vector and matrix calculations:
- Simplify and invert matrices
- Calculate determinants, Eigenvalues, and Eigenvectors
For example, the function "integrate + trace" applied to the formula
"x*sin(x)" with variable "x" yields the following output:
int(x*sin(x),x)
# Partial integration:
int(u(x)*v'(x),x) = u(x)*v(x)-int(u'(x)*v(x),x)
# u = x, v' = sin(x) => u' = 1, v = -cos(x)
-x*cos(x)-int(-cos(x),x)
# int(c*f(x),x) = c*int(f(x),x)
-x*cos(x)-(-1)*int(cos(x),x)
# Table
-x*cos(x)-(-1)*sin(x)
# Simplify
-x*cos(x)+sin(x).
At the moment, the following functions are supported:
sin,cos,tan,cot (trigonometric functions),
arcsin,arccos,arctan,arccot (inverse trigonometric functions),
sinh,cosh,tanh,coth (hyperbolic functions),
arsinh,arcosh,artanh,arcoth (inverse hyperbolic functions),
sqrt (square root),
crt (cubic root),
exp (exponential function),
ln (natural logarithm),
abs (Betrags function),
sgn (signum function).
Feasible operators are '+' (addition), '-' (subtraction), '*' (multiplication), '/' (division), and '^' or '**' (power).
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Copyright © 2016 K.-H. Erhard. All rights reserved.