Fast symbolics for interpolatory quadrature rules

Quadrature rules are usually classified in terms of their degree of exactness. We show that the vector of weights of a rule, as the least-squares or minimax solution of a fundamental linear system, leads to a new parameter which we call the angle of the rule. Numerical evidence for some standard quadrature rules shows that the angle of a rule can be more interesting than its degree of exactness, providing an explanation why low degree rules can be almost performant as rules of much higher degree.