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 : - 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 - rational fonction & decomposition - antiderivative - bug corrections
V 0.22 : - law of large numbers & central limit theorem - some simplifications in hyperbolic trigonometry - almost all warnings suppressed (using -Wno-write-strings 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 - 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.