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Clarify in docs that monoids are commutative and associative #469

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eriknw merged 3 commits into from
Jun 28, 2023
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Clarify in docs that monoids are commutative and associative #469

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Clarify in docs that monoids are commutative and associative
eriknw Jun 23, 2023
480e7a7
Refine language about commutative monoids.
eriknw Jun 28, 2023
1155676
Merge branch 'main' into monoids_commute_and_associate
eriknw Jun 28, 2023
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9 changes: 6 additions & 3 deletions docs/user_guide/operators.rst
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Expand Up @@ -89,9 +89,12 @@ registered from numpy are located in ``graphblas.binary.numpy``.
Monoids
-------

Monoids extend the concept of a binary operator to require a single domain for all inputs and
the output. Monoids are also associative, so the order of the inputs does not matter. And finally,
monoids have a default identity such that ``A op identity == A``.
Monoids extend the concept of a binary operator to require a single domain for all inputs and the output.
Monoids are also associative so the order of operations does not matter
(for example, ``(a + b) + c == a + (b + c)``).
GraphBLAS primarily uses *commutative monoids* (for example, ``a + b == b + a``),
and all standard monoids in python-graphblas commute.
And finally, monoids have a default identity such that ``A op identity == A``.

Monoids are commonly for reductions, collapsing all elements down to a single value.

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