[R] Specify model with polynomial interaction terms up to degree n

[YTP]

I would like to specify a model with all polynomial interaction terms between
two variables, say, up to degree 6. For example, terms like a^6 + (a^5 *
b^1)  +  (a^4 * b^2) + ... and so on.  The documentation states

The ^ operator indicates crossing to the specified degree.

so I would expect a model specified as y ~ (a+b)^6 to produce these terms.
However doing this only returns four slope coefficients, for Intercept, a,
b, and a:b.  Does anyone know how to produce the desired result? Thanks in
advance.

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