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)
.