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In the algebra hierarchy, we naturally have this diamond.
```
CommutativeRing (CR)
/ \
Ring (R) CommutativeSemiring (CSR)
\ …
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From @mikesol in Discord:
> Would it make sense to revamp `Semiring` so that it had only the operators `add` and `mul` and then use `Dioid` for `zero` and `one`? There is some precedent for that: htt…
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Trying to resolve our concepts of `Arithmetic` prime fields, `Symbolic` fields, our existing numerical hierarchy, Haskell's numerical hierachy, and the mathematics of semirings leads me to this numeri…
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Suppose we form a simple tropical polynomial in the following way:
```
using Oscar
Qt, t = rational_function_field(QQ, "t")
nu = tropical_semiring_map(Qt, t)
Qtx, (x,) = polynomial_ring(Qt, […
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A common use case for the ANY monoid (see #21) is in the ANY_PAIR semiring that is currently in SuiteSparse:GraphBLAS. The PAIR operator is called ONEB in the C spec, and, mathematically, ~FIRST_ONEB~…
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We should prove the fundamental theorem of arithmetic for `nat` and `IsPrime`. The basic statement says that any given `nat` has a factorisation and any two factorisations are unique up to a permutati…
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In `GAP` according to the documentation and the code `IsSemiring` is defined as an additive magma that is also a magma, and multiplication distributes over addition. In particular neither addition, no…
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A Semiring requires commutative addition, but the addition operation for Free is list concatenation, which is not commutative.
It looks like Free is an encoding of the idea described in the [wikipe…
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Find suitable algorithms to test the (in)equivalence of two elements of the counting-SR (depends on the representation, of course).
It would also be fine to have an incomplete test (since the theoret…
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For a project I’m working on, I needed something like a commutative semiring of decidable types. I defined the following existential wrapper to get the homogeneity required by the algebraic structures…
conal updated
3 years ago