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Commutativity is important for e.g. parallel programming. See e.g. <https://youtu.be/dPK6t7echuA https://youtu.be/dPK6t7echuA>. In the context of linear algebr

• MereInterest 3y ago
  Isn’t it more often associativity that is required for parallel programming? Being able to parallelize “a+b+c+d” only requires associativity to order the operations as “(a+b) + (c+d)”. Sure, there’s additional benefits for memory locality if you can rearrange the term to “(a+c) + (b+d)”, assuming that the four terms are stored in contiguous memory and each sum is computed with vector operations, but that’s not strictly required for parallelization.
  • phlakaton 3y ago
    In parallel programming, subcomputations may complete out of order. The ability to combine those subcomputations in any order can be pretty useful!
    • BeetleB 3y ago
      That, though, is associativity, not commutativity. In FP arithmetic, operations are commutative, not associative.
      • phlakaton 3y ago
        If you receive b before a and combine them as b*a, that's commutative. Both properties are useful in parallel programming, but you may only need one in a specific case, depending on your application.
  • GrumpySloth 3y ago
    Both are important. I replied to a comment about commutativity, so I focused on that.