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import sympy as sp
import diofant as df
from IPython.display import display


    

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sp.__version__


    

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x = sp.Symbol('x')
y = df.Symbol('y')


    

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A = sp.Matrix(4,4,[0,1,0,0,-1,0,1,0,0,0,0,1,1,0,-3, 0])
B = df.Matrix(4,4,[0,1,0,0,-1,0,1,0,0,0,0,1,1,0,-3, 0])


    

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A


    

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B


    

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ea = A.exp()
eb = B.exp()


    

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ea[0,0].n()


    

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eb[0,0].n()


    

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ebx = (y*B).exp()          # dauert mehrere Minuten
sebx = df.simplify(ebx)


    

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tmp = sebx[0,0].radsimp().expand()
tmp


    

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tmp.collect([df.exp(df.I*y*df.sqrt(2-df.sqrt(2))), df.exp(df.I*y*df.sqrt(2+df.sqrt(2)))])


    

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x, y, z = df.symbols('x y z', positive=True)


    

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f = df.sqrt(x**2+y**2+z**2)
f


    

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F=f.integrate(z)


    

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Fs = F.simplify()
Fs


    

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s = df.Symbol('s')
a = df.Symbol('a')
glg = df.Eq(s, (df.exp(a) - df.exp(-a))/2)
glg


    

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Lsg = df.solve(glg, a)
Lsg


    

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terme = Fs.args
terme


    

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x1 = df.Wild('x1')
x2 = df.Wild('x2')
x3 = df.Wild('x3')


    

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pattern = x1 * df.asinh(x2)
m = terme[0].match(pattern)
m


    

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ersatz = x1 * Lsg[1].subs(s, x2)
t0 = ersatz.subs(m).simplify()


    

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m = terme[1].match(pattern)
t1 = ersatz.subs(m).simplify()


    

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G = t0 + t1 + terme[2]
G


    

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G.diff(z).simplify()


    

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