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Features

Core capabilities

Polynomen

Documentatie

  • Rekenen: delen, grootste gemene deler, ...
  • Factoren ontbinden
  • Kwadraatvrije decompositie
  • Gröbner bases
  • Breuksplitsingen
  • Resultanten

Analyse

Integration Documentation

  • Limieten limit(x*log(x), x, 0) -> 0
  • Afgeleiden nemen
  • Integratie: Maakt gebruikt van Risch-Norman heuristiek
  • Taylor (Laurent) reeksen

Vergelijkingen oplossen

Documentatie

Combinatoriek

Documentatie

  • Permutaties
  • Combinaties
  • Partities
  • Deelverzamelingen
  • Permutatiegroepen: Polyhedral, Rubik, Symmetric, ...
  • Prufer and Gray Codes

Discrete wiskunde

  • Binomiaalcoëfficiënten
  • Sommaties
  • Producten
  • Getaltheorie: generating prime numbers, primality testing, integer factorization, Diophantine equation solving...
  • Logische uitdrukkingen

Matrices

Documentatie

  • Rekenoperaties
  • Eigenwaarden/eigenvectoren
  • Determinanten
  • Inversie
  • Oplossen
  • Abstracte uitdrukkingen

Meetkunde

Documentatie

  • points, lines, rays, segments, ellipses, circles, polygons, ...
  • Doorsnede
  • Raking
  • Gelijkvormigheid

Plotten

Documentatie

  • Coordinate modes
  • Het plotten van meetkundige entiteiten
  • 2D en 3D
  • Interactieve interface
  • Kleuren
  • Matplotlib support
SymPy plot of sin(2 sin(2 sin(x))) with matplotlib
plot(sin(2*sin(2*sin(x))))
SymPy plot of x, x^2, and x^3, from x = -5 to 5
plot(x, x**2, x**3, (x, -5, 5))
SymPy parametric plot of x=cos(u), y=sin(u), from u = -5 to 5
plot_parametric(cos(u), sin(u), (u, -5, 5))
SymPy 3D surface plot of xy, from x = -5 to 5, from y = -5 to 5
plot3d(x*y, (x, -5, 5), (y, -5, 5))
SymPy 3D parametric line plot of x=cos(u), y=sin(u), z=u, from u = -5 to 5
plot3d_parametric_line(cos(u), sin(u), u, (u, -5, 5))
SymPy 3D parametric surface plot of x=cos(u+v), y=sin(u-v), z=u-v, u and v from -5 to 5
plot3d_parametric_surface(cos(u + v), sin(u - v), u - v, (u, -5, 5), (v, -5, 5))
SymPy implicit plot of x^2 + y^2 = 5
plot_implicit(Eq(x**2 + y**2, 5))
SymPy implicit plot of y > x^2
plot_implicit(y > x**2)
SymPy implicit plot of y > x (logical and) y > -x
plot_implicit(And(y > x, y > -x))
Matplotlib interactive interface of SymPy 3D parametric surface plot of x=cos(u+v), y=sin(u-v), z=u-v, u and v from -5 to 5
plot3d_parametric_surface(cos(u + v), sin(u - v), u - v, (u, -5, 5), (v, -5, 5))
SymPy Gamma plot of x=cos(t), y=sin(t)
SymPy Gamma plot

Natuurkunde

Documentatie

  • Eenheden
  • Mechanica
  • Quantum
  • Gaussische Optica
  • Pauli Algebra

IPython Notebook Examples

Statistiek

Documentatie

  • Random variable types:
    • Normale distributies
    • Uniforme distributies
    • Bernoulli distributions
    • Binomial distributions
    • Hypergeometric distributions
    • More…
  • Waarschijnlijkheid
  • Expected value and variance
  • Probability density

Cryptography

Documentatie

  • Shift cipher
  • Affine cipher
  • Bifid ciphers
  • Vigenere’s cipher
  • Substitution ciphers
  • Hill’s cipher
  • RSA
  • Kid RSA
  • Linear feedback shift registers
  • ElGamal encryption

Parsing

Documentatie

  • Conversion from Python objects to SymPy objects
  • Optional implicit multiplication and function application parsing
  • Limited Mathematica and Maxima parsing: example on SymPy Live
  • Custom parsing transformations

Printen

Documentatie

  • Netjes printen: ASCII/Unicode pretty printing, LaTeX
  • Genereren van code: C, Fortran, Python
  • Theano interaction
Unicode printing in a Python shell
Unicode printing
LaTeX printing in an IPython notebook
LaTeX printing