latex_check.py 文件源码

def reciprocal_frame_test():
    Print_Function()
    metric = '1 # #,' + \
             '# 1 #,' + \
             '# # 1,'

    (e1, e2, e3) = MV.setup('e1 e2 e3', metric)

    print('g_{ij} =', MV.metric)

    E = e1 ^ e2 ^ e3
    Esq = (E*E).scalar()
    print('E =', E)
    print('%E^{2} =', Esq)
    Esq_inv = 1/Esq

    E1 = (e2 ^ e3)*E
    E2 = (-1)*(e1 ^ e3)*E
    E3 = (e1 ^ e2)*E

    print('E1 = (e2^e3)*E =', E1)
    print('E2 =-(e1^e3)*E =', E2)
    print('E3 = (e1^e2)*E =', E3)

    w = (E1 | e2)
    w = w.expand()
    print('E1|e2 =', w)

    w = (E1 | e3)
    w = w.expand()
    print('E1|e3 =', w)

    w = (E2 | e1)
    w = w.expand()
    print('E2|e1 =', w)

    w = (E2 | e3)
    w = w.expand()
    print('E2|e3 =', w)

    w = (E3 | e1)
    w = w.expand()
    print('E3|e1 =', w)

    w = (E3 | e2)
    w = w.expand()
    print('E3|e2 =', w)

    w = (E1 | e1)
    w = (w.expand()).scalar()
    Esq = expand(Esq)
    print('%(E1\\cdot e1)/E^{2} =', simplify(w/Esq))

    w = (E2 | e2)
    w = (w.expand()).scalar()
    print('%(E2\\cdot e2)/E^{2} =', simplify(w/Esq))

    w = (E3 | e3)
    w = (w.expand()).scalar()
    print('%(E3\\cdot e3)/E^{2} =', simplify(w/Esq))
    return