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Summary
At the moment polynomials are employed via IntegrationRule1D, Basis1D, and Basis2D types. These exist mainly to cache results of computing integration and evaluation of basis at nodes. This could be much nicer accomplished in the way that GLL nodes and weights are cached at the moment.
Proposed Changes
Remove the three types mentioned above or change their implementation. These can be handled via caches, which would then mean that you could have different integration rules or polynomials, then just store the type and order in order. When you finally need the values, just request them from the cache.
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