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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
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For a problem of combinatorial commutative algebra I wanted to compute the Hilbert series of an algebra. I ran into
` ? int overflow in hilb 1`
As far as I can see, there is no `bigintvec`. I…
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Should check that the valid monoid within a semiring is in fact commutative. Monoid validity should check for algebraic properties of monoid structures, such as having an associative binary operator a…
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The names of algebraic structures can sometimes be quite intimidating. The fundamental operations and their possible properties are less so. Perhaps one way of achieving this could be:
``` rust
// Ma…
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Reported by email by Rene Marczinzik. This calculation reports that `U` is commutative, while it is not:
```
gap> G:=QuaternionGroup(8);
gap> R:=GroupRing(Rationals,G);
gap> W:=WedderburnDec…
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The `NumberWrapper` class opens up some interesting possibilities as to what one might be able to interpret the result of symbol operations as. Without looking under the hood, it would seem to me that…
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it seem to assume that the matrix constructor is expecting to receive components of basis vectors as:
`X.x`, `Y.x`, `Z.x`, `W.x`, `X.y`, `Y.y`, `Z.y`, `W.y`, `X.z`, `Y.z`, `Z.z`, `W.z`, `X.w`, `Y.w`,…
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Assume Pappus’s condition is satisfied. Recent developments in commutative Lie theory (Watanabe 2008; Wiener 2018) have raised the question of whether is ordered, simply separable, -dimensional and c…
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Right now, `spire` has a finer grained distinction of commutative rings, namely:
- the availability of `gcd` and `lcm` operations,
- the availability of Euclidean division (`emod`, `equot`),
in…
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Here is our definition of "field".
```
Definition invpair (X:monoid) (x:X) := Σ x':X, ( x' * x = 1 ) × ( x * x' = 1 ).
Definition multinvpair ( X : rig ) ( x : X ) := invpair ( rigmultmonoid X ) x .
…