> where it’s obvious what the operation is (inherently mathematical types like vectors and matrices)
Considering there are like 3 different types of matrix multiplication operations, I don't think it's obvious at all. Feels like you should either use a language with complete support for implementing custom DSLs (that can express the whole domain naturally) or eschew ambiguous operator overloading altogether (gaining consistency and quality at the expense of a few keystrokes).
I think we all know what someone means when they say “matrix multiplication”. Asserting that * could mean, say, the Hadamard product or the tensor product is a reach. In practice I have never seen it mean anything else for matrices.
DSLs just push the complexity away from the language into someone else’s problem in a way that has much higher sum complexity. You’re making authors of numerical libraries second-class citizens by doing so. For some languages that’s probably not a bad choice (Go is one example where I don’t feel the language is targeted at such use cases).
Also, the lack of a standard interface for things like addition, multiplication, etc. means that mathematical code becomes less composable between different libraries. Unless everyone standardizes on the same DSL, but I find this an unlikely proposition, given that DSLs are far more opinionated than mere operator overloads.
Considering there are like 3 different types of matrix multiplication operations, I don't think it's obvious at all. Feels like you should either use a language with complete support for implementing custom DSLs (that can express the whole domain naturally) or eschew ambiguous operator overloading altogether (gaining consistency and quality at the expense of a few keystrokes).