def __init__(self, ring, algebra1, algebra2, side1, side2):
"""Specifies the algebras and sides of the type DD action."""
FreeModule.__init__(self, ring)
assert isinstance(algebra1, DGAlgebra)
assert isinstance(algebra2, DGAlgebra)
self.algebra1 = algebra1
self.side1 = side1
self.algebra2 = algebra2
self.side2 = side2
# Construct A tensor A tensor M. Add diff and the left action on this
# tensor product.
self.AAtensorM = Tensor((algebra1, algebra2, self))
def _mul_AA_AAtensorM((AGen1, AGen2, MGen), (ACoeff1, ACoeff2)):
"""To be used as rmultiply() in AAtensorM. Multiply ACoeff1 with
AGen1 and ACoeff2 with AGen2.
"""
return expandTensor((ACoeff1*AGen1, ACoeff2*AGen2, MGen),
self.AAtensorM)
def _diff_AAtensorM((AGen1, AGen2, MGen)):
"""To be used as diff() in AAtensorM."""
return expandTensor((AGen1.diff(), AGen2, MGen), self.AAtensorM) \
+ expandTensor((AGen1, AGen2.diff(), MGen), self.AAtensorM) \
+ (AGen1, AGen2) * (MGen.delta())