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pbillet
Posts:
31
From:
paris
Registered:
9/23/09


Annoucement : smib0.32 release
Posted:
May 21, 2013 3:04 PM


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, probalility and stochastic calculus) and also some physics (e.g. electromagnetism and quantum mechanic). 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)).
Download page : http://sourceforge.net/projects/smib/
In this version :  What can we do with euclidean division of polynomial : * GCD * polynomial equations * modular inversion * chinese remainder theorem  Factorization, field of rational function.
V 0.31 :  stochastic differential equation in higher dimension  partial differential equation simulation using stochastic differential equation  some improvement in documentation.
V 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
V 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
V 0.28 :  some optimizations in generalized stochastic differential equation  Mertens fonction  new documentation
V 0.27 :  quantum mechanic using smib
V 0.26 :  quaternions  bug corrections
V 0.25 :  antiderivative v2 : new version of defint too  perfect number & harmonic mean of divisors  bug corrections
V 0.24 :  rational fonction & decomposition  antiderivative  bug corrections
V 0.23 :  Some polynomial algebra : * Bezout identity (extended greater divisor) * squarefree factorization * resultant * discriminant
V 0.22 :  law of large numbers & central limit theorem  some simplifications in hyperbolic trigonometry  almost all warnings suppressed (using Wnowritestrings option)
V 0.21 :  generalized stochastic differential equation (not only with brownian motion): mean and variance computation  Stratonovitch stochastic integral with brownian motion  bug correction.
V 0.20 :  stochastic differential equation : mean and variance computation  nonlinear least squares approximation.
V 0.19 :  Lagrange interpolation using Newton polynomials  sample applied to quantile and median.
V 0.18 :  complex analysis : complex path, complex path integral, complex path index, number of singularities  bug fix: simplification of expressions, numerical evaluation.
V 0.17 :  derivation of samples (integer & fractional)  bug correction.
V 0.16 :  Numerical application to special functions : Bessel functions, Hankel functions & Airy functions  Some new example applied to differential geometry, probability & statistic.
V 0.15 :  tensor calculus finally documented V 0.14 :  numerical analysis :  fractionnal derivative  new version of Euler scheme : ODE and coupled ODEs are treated by one program  probability & statistic :  gaussian random nuber  new version of brownian motion  bugs correction.
V 0.13 :  numerical analysis :  first order differential equation  system of two first order differential equations (using Euler scheme).
 probability & statistic :  quantile & median  stochastic differential equation (EulerMurayama & Milstein schemes)
 new documentation.
V 0.12 :  probality & statistic :  expected value  variance  standard deviation  skewness  kurtosis  least square line
 differential geometry :  planar curves  3D curves  theory of surfaces using Gauss approach
 improvement :  simplify (if A=(x1)*(x+1)/(x1), simplify(A) returns : 1 + x)  numint (if simpsonint = 1, Simpson scheme is used, else Gauss scheme is used), for probability, it is a good idea to set simsonint to 1.



