In this paper we present a space-time calculus for symmetric spinors,
including a product with a number of index contractions followed by
symmetrization. As all operations stay within the class of symmetric spinors,
no involved index manipulations are needed. In fact spinor indices are not
needed in the formalism. It is also general because any covariant tensor
expression in a 4-dimensional Lorentzian spacetime can be translated to this
formalism. The computer algebra implementation SymSpin as part of xAct for
Mathematica is also presented.