smib is probably one of the smallest and simpliest computer algebra system in the world, but simple does not mean simplistic.
Using smib you can explore many branches of mathematics (e.g. number theory, algebra, calculus, numerical analysis, differential geometry, probability and stochastic calculus) and also some physics (e.g. electromagnetism and quantum mechanics)..
By simple you can understand easy to program (smib is a weakly typed language, with strong affinity to recursivity, programs are often short and powerful and maybe useful for teaching), and also easy to modify (source code is free, written in C language, and based on notions of stacks (like FORTH language), and lists (like LISP language)).
In this version : partial differential equation solver using stochastic process and Feynman-Kac formula.
- Number theory : infinite size integers, arithmetic functions, primality
- Algebra : polynomials, vectors, matrices, tensors
- Analysis : derivation, integration, antiderivative, Taylor series, Fourier analysis
- Numerical analysis : numerical integration, Fourier transform, and ODE
- Differential geometry : Gauss-like or Riemann-like
- Calculus on samples : differential and integral calculus, Fourier transform
- Probability & Statistic : expected value, variance, skewness, kurtosis
- Probability & Statistic : median, quantile, stochastic calculus
Thank you for your work.