smib (SMall Is Beautiful) is an open source and free command-line software implemented in C and designed from the offset as one of the simplest and smallest computer algebra systems in the whole world. Keep in mind that simple does not mean simplistic!
Supports number theory, numerical analysis and differential geometry
With smib you will be able to explore numerous branches of mathematics, as well as various physics branches. It supports number theory, algebra, analysis, numerical analysis, differential geometry, calculus on samples, probability and statistic.
The software can work with arithmetic functions, infinite size integers, Fourier transform, Fourier analysis, primality, integral calculus, differential calculus, numerical integration, derivation, antiderivative, vectors, polynomials, matrices, tensors, integration, Taylor series, and ODE.
In addition, the program supports Riemann-like and Gauss-like differential geometry, integral and differential calculus, kurtosis, stochastic calculus, variance, skewness, quantile, expected value, as well as median. It also comes with some comprehensive documentation about how to use various functions.
Interactive mode vs Script mode
The program can only be used from the command-line via any terminal emulator. It provides two modes, interactive and script. While the interactive mode is the most easy to use one, as all you have to do is to run the ‘smib’ command to access the shell prompt and use the program, the script mode requires a valid file, then run ‘./smib ./documentation/tutorial’.
Various examples for the script mode can be found in the /smib/documentation folder or the /smib/documentation/application directory inside the source package. Also, you should check the /smib/documentation/tutorial folder for various basics examples.
What is new in this release:
- Variational calculus : Euler-Lagrange operator
- Functions of matrix : exponential, logarithm
- System of ordinary linear differential equations
- antider : some new integrals handled (if versionint=5 it may give interesting result or infinite loop)
What is new in version 0.37:
- PDE simulation using SDE and Feynman-Kac formula : 1D & 2D
- Graph : number of connected components
- Weyl sum : some plottings
- Bugs correction
What is new in version 0.36:
- PDE simulation using SDE and Feynman-Kac formula : 1D & 2D
- Graph : number of connected components
- Weyl sum : some plottings
- Bugs correction
What is new in version 0.35:
- Partial differential equation simulation using stochastic differential equation and Feynman-Kac formula.
What is new in version 0.34:
- Differential operators in orthogonal system of coordinates
- Gosper algorithm : antidifference
- antiderivative : new version
- Bugs correction
What is new in version 0.33:
- propositional logic : operators, truth table, tautology, antilogy
- 60 seconds in a minute, why ?
- on nonassociativity and Jacobi identity
What is new in version 0.32:
- What can we do with euclidean division of polynomial:
- GCD
- polynomial equations
- modular inversion
- chinese remainder theorem
- Factorization, field of rational function.
What is new in version 0.31:
- Stochastic differential equation in higher dimension;
- Partial differential equation simulation using stochastic differential equation;
- Some improvement in documentation.
What is new in version 0.30:
- spectral theory of undirected graphs:
- adjacency matrix
- degree matrix
- laplacian matrix
- number of triangles
- number of connected components
- electromagnetic tensor and its properties
- odesolve : second order if a particular solution is known
What is new in version 0.29:
- odesolve : ordinary differential equation solver (for first order - using dsolve-, and second order if coefficients are constant)
- dsolve uses antider instead of integral (calling a smib program in the smib kernel (in C language))
- Syracuze conjecture (dynamic allocation of arrays)
- Mertens function & Redheffer matrix
What is new in version 0.28:
- some optimizations in generalized stochastic differential equation
- Mertens fonction
- new documentation
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