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Compute Wronskian for [] of functions

               | f1    f2     ...   fn  |
               | f1'   f2'    ...   fn' |
               |  .     .     .      .  |
W(f1,...,fn) = |  .     .      .     .  |
               |  .     .       .    .  |
               |  n     n           n   |
               | D(f1) D(f2)  ...  D(fn)|
(more...)

        def wronskian(functions, var, method='bareis'):
    """Compute Wronskian for [] of functions

                   | f1    f2     ...   fn  |
                   | f1'   f2'    ...   fn' |
                   |  .     .     .      .  |
    W(f1,...,fn) = |  .     .      .     .  |
                   |  .     .       .    .  |
                   |  n     n           n   |
                   | D(f1) D(f2)  ...  D(fn)|

    see: http://en.wikipedia.org/wiki/Wronskian
    """

    for index in xrange(0, len(functions)):
        functions[index] = sympify(functions[index])
    n = len(functions)
    if n == 0:
        return 1
    W = Matrix(n, n, lambda i,j: functions[i].diff(var, j) )
    return W.det(method)
        


src/s/y/sympy-HEAD/sympy/solvers/ode.py   sympy(Download)
 
from sympy.functions import cos, exp, im, log, re, sin, tan, sqrt, sign, Piecewise
from sympy.matrices import wronskian
from sympy.polys import Poly, RootOf, terms_gcd, PolynomialError
from sympy.polys.polytools import cancel, degree, div
    gensols = r['list']
    gsol = r['sol']
    wr = wronskian(gensols, x)
 
    if r.get('simplify', True):
    negoneterm = (-1)**(order)
    for i in gensols:
        psol += negoneterm*C.Integral(wronskian([sol for sol in gensols if sol != i], x)*r[-1]/wr, x)*i/r[order]
        negoneterm *= -1
 

src/s/y/sympy-polys-HEAD/sympy/solvers/ode.py   sympy-polys(Download)
 
from sympy.functions import cos, exp, im, log, re, sin, sign
from sympy.matrices import wronskian
from sympy.polys import RootsOf, discriminant, RootOf
from sympy.series import Order
    gensols = r['list']
    gsol = r['sol']
    wr = wronskian(gensols, x)
 
    if r.get('simplify', True):
    negoneterm = (-1)**(order)
    for i in gensols:
        psol += negoneterm*C.Integral(wronskian(filter(lambda x: x != i, \
        gensols), x)*r[-1]/wr, x)*i/r[order]
        negoneterm *= -1

src/s/y/sympy-HEAD/sympy/matrices/tests/test_matrices.py   sympy(Download)
from sympy.matrices.matrices import (ShapeError, MatrixError,
    NonSquareMatrixError, DeferredVector)
from sympy.matrices import (
    GramSchmidt, ImmutableMatrix, ImmutableSparseMatrix, Matrix,
    SparseMatrix, casoratian, diag, eye, hessian,
def test_wronskian():
    assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
    assert wronskian([exp(x), exp(2*x)], x) == exp(3*x)
    assert wronskian([exp(x), x], x) == exp(x) - x*exp(x)
    assert wronskian([1, x, x**2], x) == 2

src/s/y/sympy-0.7.5/sympy/matrices/tests/test_matrices.py   sympy(Download)
from sympy.matrices.matrices import (ShapeError, MatrixError,
    NonSquareMatrixError, DeferredVector)
from sympy.matrices import (
    GramSchmidt, ImmutableMatrix, ImmutableSparseMatrix, Matrix,
    SparseMatrix, casoratian, diag, eye, hessian,
def test_wronskian():
    assert wronskian([cos(x), sin(x)], x) == cos(x)**2 + sin(x)**2
    assert wronskian([exp(x), exp(2*x)], x) == exp(3*x)
    assert wronskian([exp(x), x], x) == exp(x) - x*exp(x)
    assert wronskian([1, x, x**2], x) == 2