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I think it's the superclass A of both G and M that defines the eigenvalue() function. Then when both G(A) and M(A) inherit from A, it captures the mathematical

by cft 4y ago

I think it's the superclass A of both G and M that defines the eigenvalue() function. Then when both G(A) and M(A) inherit from A, it captures the mathematical relationship. The subclasses indeed should implement the eigenvalues computations differently, like in real mathematics. Funcional programming is used in Coq because it captures logical chains, for theorem PROOFS, but not for specific COMPUTATIONS, such as eigenvalues.

abdullahkhalids 4y ago
I understand that this is possible. But this is not how mathematicians think. If you got together a bunch of mathematicians and asked to invent a programming language to do mathematics, they would never ever invent the concept of a class. Mathematics (outside of stuff like category theory etc) is simply sets and mappings between sets. Anything more complicated is forcing the user to think in a way that mathematics does not.
- klyrs 4y ago
  > But this is not how mathematicians think. If you got together a bunch of mathematicians and asked to invent a programming language to do mathematics, they would never ever invent the concept of a class. Hi, mathematician here. Please read the source of SageMath: written by mathematicians, for mathematicians. Therein, you will find thousands of classes. Almost all computer algebra systems, written by mathematicians for mathematicians, have a notion of classes. > Mathematics (outside of stuff like category theory etc) is simply sets and mappings between sets. This is an extremely narrow-minded view of mathematics. Mathematicians thrive on abstraction, (category theory is literally mathematics; that's a very strange exception for you to carve out), and if we were to boil everything down to "simply sets and mappings between sets" then we'd be bogged down in utter tedium and nothing would ever get done. Object-oriented programming, specifically class hierarchies and inheritance, are extremely valuable for doing all sorts of math at high levels of abstraction. Hell. If I were to be especially pedantic, I'd point out that category theory itself is "simply sets and mappings between sets" except that sets aren't quite large enough so it's actually "categories and mapping between categories".

by cft 4y ago

abdullahkhalids 4y ago

I understand that this is possible. But this is not how mathematicians think. If you got together a bunch of mathematicians and asked to invent a programming language to do mathematics, they would never ever invent the concept of a class. Mathematics (outside of stuff like category theory etc) is simply sets and mappings between sets. Anything more complicated is forcing the user to think in a way that mathematics does not.

klyrs 4y ago
> But this is not how mathematicians think. If you got together a bunch of mathematicians and asked to invent a programming language to do mathematics, they would never ever invent the concept of a class. Hi, mathematician here. Please read the source of SageMath: written by mathematicians, for mathematicians. Therein, you will find thousands of classes. Almost all computer algebra systems, written by mathematicians for mathematicians, have a notion of classes. > Mathematics (outside of stuff like category theory etc) is simply sets and mappings between sets. This is an extremely narrow-minded view of mathematics. Mathematicians thrive on abstraction, (category theory is literally mathematics; that's a very strange exception for you to carve out), and if we were to boil everything down to "simply sets and mappings between sets" then we'd be bogged down in utter tedium and nothing would ever get done. Object-oriented programming, specifically class hierarchies and inheritance, are extremely valuable for doing all sorts of math at high levels of abstraction. Hell. If I were to be especially pedantic, I'd point out that category theory itself is "simply sets and mappings between sets" except that sets aren't quite large enough so it's actually "categories and mapping between categories".