In analogy with something like

type(<1,2>,'Vector'(2,posint));

it would have been nice if something like

type({1,2},'set'(2,posint));
type([1,2],'list'(2,posint));

was possible. How can one, using type, check for a certain number of elements in sets and lists?

Using the procedure permsPosNeg as given in the blog entry Positive and negative permutations, including the improvement obtained in the blog entry Refactoring Maple code, consider the following procedure:

In connection with tensors, I would like to be able to treat arbitrary symmetries (positive permutations) and antisymmetries (negative permutations) of the entries of an Array.

An example is the Riemannian curvature tensor which has the following positive and negative permutations:

The recent thread A crossprod problem, although not directly related, inspired me to write this blog entry about bilinear cross products and their noticable property [see for instance P. Lounesto, Clifford Algebras and Spinors, 2nd ed. (Cambridge University Press, Cambridge, 2001)]:

Theorem: A bilinear cross product obeying the orthogonality property and the Pythagorean property, see below, exists only in 3 or 7 (real or complex) dimensions.

In working out the procedure isDeeplyAlgebraic in the post Deeply algebraic, I was trying to use something like `and` and `or`, analogously to `+`, `*`, `.`, etc.