Contraction

$\mathbf{i}_{\alpha^{\sharp}}\beta=\star(\alpha\wedge\star\beta)$



In [1]:

    
from dec.symbolic import *



In [2]:

    
c = Chart(x, )
u = Function('u')(x)
v = Function('v')(x)



In [3]:

    
α = form(1, c, (u,))
β = form(1, c, (v,))
α.C(β) == (α ^ β.H).H









    Out[3]:





True



In [4]:

    
c = Chart(x, y)
u = Function('u')(x, y)
v = Function('v')(x, y)
w = Function('w')(x, y)
q = Function('q')(x, y)



In [5]:

    
α = form(1, c, (u,v))
β = form(1, c, (w,q))
α.C(β) == (α ^ β.H).H









    Out[5]:





True



In [6]:

    
α = form(1, c, (u,v))
β = form(2, c, (w,))
α.C(β) == (α ^ β.H).H









    Out[6]:





True



In [7]:

    
# Not implemented yet