. _ _ _ HE-DOT _ _ _ _ _ _ _ _ _ _ _ _ operator
The . operator is used to denote the scalar product of two Lorentz four-vectors.
<vector> . <vector>
<vector> must be an identifier declared to be of type vector to h ave the scalar product definition. When applied to arguments that are not vectors, the cons operator is used, whose symbol is also ``dot.''
vector aa,bb,cc; let aa.bb = 0; aa.bb; 0 aa.cc; AA.CC q := aa.cc; Q := AA.CC q; AA.CC
Since vectors are special high-energy physics entities that do not contain values, the . product will not return a true scalar product. You can assign a scalar identifier to the result of a . operation, or assign a . operation to have the value of the scalar you supply, as shown above. Note that the result of a . operation is a scalar, not a vector.
The metric tensor g(u,v) can be represented by u.v. If contraction over the indices is required, u and v should be declared to be of type index.
The dot operator has the highest precedence of the infix operators, so expressions involving . and other operators have the scalar product evaluated first before other operations are done.