Clifford algebras are represented in Magma as structure constant algebras and so many of the functions described in Chapter ALGEBRAS apply to Clifford algebras. The Magma type of a Clifford algebra is AlgClff and all Clifford algebras have the attributes
Thus the elements of C can be represented by a sequence of pairs < S, a > where S is a subset of {1, 2, ..., n} and a is a field element. Multiplication is determined by the fact that for all u, v∈V we have
v2 = Q(v).1quadand uv + vu = β(u, v).1,
where βis the polar form of Q.
This function returns a triple C, V, f, where C is the Clifford algebra of the quadratic form Q, V is the quadratic space of Q, and f is the standard embedding of V into C.
If V is a quadratic space with quadratic form Q, this function returns the pair C, f, where C is the Clifford algebra of Q and f is the standard embedding of V into C.
Given a Clifford algebra C of dimension m = 2n over a field F, and field elements r1, r2, ..., rm ∈F construct the element r1 * C.1 + r2 * C.2 + ... + rm * C.m of C.
Given a Clifford algebra C of dimension m = 2n and a sequence L = [r1, r2, ..., rm] of elements of the base ring R of C, construct the element r1 * C.1 + r2 * C.2 + ... + rm * C.m of C.
Return the product of the i-th and j-th basis element of the Clifford algebra C.
The basis element C.j of the Clifford algebra C corresponding to the subset L of {1, 2, ..., n} where j = 1 + ∑k∈L2k - 1. If e1, e2, ..., en is the standard basis for the vector space on which C is based, this corresponds to the product ei1 * ei2 * ... * eih, where L = {i1, i2, ..., ih} and i1 < i2 < ... < ih.[Next][Prev] [Right] [Left] [Up] [Index] [Root]