Introduce a scalar product function (and operator)?

[eric-wieser]

Today, all of the following are ways to compute scalar products

1. (a * b)[()]
2. (a | b)[()]
3. (a << b)[()]
4. (a * b)[0]
5. (a | b)[0]
6. (a << b)[0]

The problems with these approaches are:

• 1 and 4 compute a lot of unwanted terms
• 2 and 5 compute some unwanted terms
• 3 and 6 compute fewer unwanted terms
• 4, 5, and 6 fail if a.layout._basis_blade_order.bitmap_to_index[0] != 0.

It would be straightforward to compile a smt_func in the same way we compile the other functions. The question is, what should the API look like?

Some options:

• a @ b - treads on the toes of #267
• a % b
• a // b - weird, because // suggests division
• clifford.operator.sp(a, b)
• a.sp(b)
• a.scalar_product(b)
• ...

Other libraries:

• Ganja: no scalar product operator
• tpga: no scalar product operator
• garamon: a.scalarProduct(b)
• Galgebra:
  • docs suggest & was once the scalar product operator, but not implemented
  • a.Ga.scalar_product(a, b)
• Galgebra.jl: A ⊛ B