Maxima Function
init_atensor (alg_type, opt_dims)
init_atensor(alg_type)
Initializes the atensor package with the specified algebra type. alg_type
can be one of the following:
universal: The universal algebra has no commutation rules.
grassmann: The Grassman algebra is defined by the commutation
relation u.v+v.u=0.
clifford: The Clifford algebra is defined by the commutation
relation u.v+v.u=-2*sf(u,v) where sf is a symmetric
scalar-valued function. For this algebra, opt_dims can be up
to three nonnegative integers, representing the number of positive,
degenerate, and negative dimensions of the algebra, respectively. If
any opt_dims values are supplied, atensor will configure the
values of adim and aform appropriately. Otherwise,
adim will default to 0 and aform will not be defined.
symmetric: The symmetric algebra is defined by the commutation
relation u.v-v.u=0.
symplectic: The symplectic algebra is defined by the commutation
relation u.v-v.u=2*af(u,v) where af is an antisymmetric
scalar-valued function. For the symplectic algebra, opt_dims can
be up to two nonnegative integers, representing the nondegenerate and
degenerate dimensions, respectively. If any opt_dims values are
supplied, atensor will configure the values of adim and aform
appropriately. Otherwise, adim will default to 0 and aform
will not be defined.
lie_envelop: The algebra of the Lie envelope is defined by the
commutation relation u.v-v.u=2*av(u,v) where av is
an antisymmetric function.
The init_atensor function also recognizes several predefined
algebra types:
complex implements the algebra of complex numbers as the
Clifford algebra Cl(0,1). The call init_atensor(complex) is
equivalent to init_atensor(clifford,0,0,1).
quaternion implements the algebra of quaternions. The call
init_atensor(quaternion) is equivalent to
init_atensor(clifford,0,0,2).
pauli implements the algebra of Pauli-spinors as the Clifford-algebra
Cl(3,0). A call to init_atensor(pauli) is equivalent to
init_atensor(clifford,3).
dirac implements the algebra of Dirac-spinors as the Clifford-algebra
Cl(3,1). A call to init_atensor(dirac) is equivalent to
init_atensor(clifford,3,0,1).