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Lt spinor inv is not involutive #464

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eric-wieser opened this issue Sep 24, 2020 · 0 comments
Open

Lt spinor inv is not involutive #464

eric-wieser opened this issue Sep 24, 2020 · 0 comments

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@eric-wieser
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Likely related to #462

>>> base = Ga('a b', g=[1, 1], coords=symbols('x, y', real=True))
>>> a, b = base.mv()
>>> R = base.mv('R', 'spinor')

# inverse of the inverse should be the original, right?
>>> f = base.lt(R)
>>> g = f.inv().inv()
>>> h = f.inv().inv().inv().inv()

# wrong
>>> f(a)
(R**4 - R__xy**4)*a - 2*R*R__xy*(R**2 + R__xy**2)*b
>>> g(a)
(R**10 + 3*R**8*R__xy**2 + 2*R**6*R__xy**4 - 2*R**4*R__xy**6 - 3*R**2*R__xy**8 - R__xy**10)*a - 2*R*R__xy*(R**8 + 4*R**6*R__xy**2 + 6*R**4*R__xy**4 + 4*R**2*R__xy**6 + R__xy**8)*b
>>> h(a)
(R**34 + 15*R**32*R__xy**2 + 104*R**30*R__xy**4 + 440*R**28*R__xy**6 + 1260*R**26*R__xy**8 + 2548*R**24*R__xy**10 + 3640*R**22*R__xy**12 + 3432*R**20*R__xy**14 + 1430*R**18*R__xy**16 - 1430*R**16*R__xy**18 - 3432*R**14*R__xy**20 - 3640*R**12*R__xy**22 - 2548*R**10*R__xy**24 - 1260*R**8*R__xy**26 - 440*R**6*R__xy**28 - 104*R**4*R__xy**30 - 15*R**2*R__xy**32 - R__xy**34)*a - 2*R*R__xy*(R**32 + 16*R**30*R__xy**2 + 120*R**28*R__xy**4 + 560*R**26*R__xy**6 + 1820*R**24*R__xy**8 + 4368*R**22*R__xy**10 + 8008*R**20*R__xy**12 + 11440*R**18*R__xy**14 + 12870*R**16*R__xy**16 + 11440*R**14*R__xy**18 + 8008*R**12*R__xy**20 + 4368*R**10*R__xy**22 + 1820*R**8*R__xy**24 + 560*R**6*R__xy**26 + 120*R**4*R__xy**28 + 16*R**2*R__xy**30 + R__xy**32)*b
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