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Topic: Annoucement : smib-0.21 release
Replies: 0

 pbillet Posts: 31 From: paris Registered: 9/23/09
Annoucement : smib-0.21 release
Posted: Aug 27, 2011 1:48 AM

smib is a mosaic of FORTH and LISP, C Sauce and an experimental programming language in mathematics.
Some experimental fields :
- Arithmetic & number theory
- Differential geometry
- Numerical analysis
- Probability & statistics.

In this version :
- 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
- non-linear 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 (Euler-Murayama & 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=(x-1)*(x+1)/(x-1), 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.