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Add methods to check whether a number is nilpotent, abelian, or cyclic. A number `n` is called nilpotent (abelian/cyclic) if every group of order `n` is nilpotent (abelian/cyclic). More details abou…
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1) from Smoktunowicz, ["Makar-Limanov's conjecture on free subalgebras"](https://arxiv.org/pdf/0903.1626):
- [ ] Th1.3: over every countable field $K$ there is a nil algebra $N$ such that the polynom…
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We add a few constructions of difference matrices whose lambda parameter is not 1.
We then modify the orthogonal arrays and transversal designs constructions
to take advantage of these additions. F…
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(Warning, this is a doozy.)
It would be really nice if we had a [type checker plugin](https://downloads.haskell.org/~ghc/latest/docs/html/users_guide/compiler-plugins.html#typechecker-plugins) capabl…
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Given that we've chosen addition as the monoid for money, we can define an instance for Group too.
But where should we get group from? The [groups](http://hackage.haskell.org/package/groups) package …
gwils updated
7 years ago
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This will greatly facilitate writing generic code.
```
sage: from sage.groups.multiplicative_wrapper import MultiplicativeWrapper
sage: R. = ZZ[]
sage: G = MultiplicativeW…
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Schemes are ticking along nicely, as is commutative algebra. Currently we still don't have schemes in mathlib, or etale maps of rings, but it is not hard to imagine them being there at some point in t…
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My definition of well ordered set is this:
```
Definition hasSmallest {X : UU} (R : hrel X) : hProp
:= ∀ S : hsubtype X, (∃ x, S x) ⇒ ∃ x:X, S x ∧ ∀ y:X, S y ⇒ R x y.
Definition isWellOrder {X…
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I've now written up the new approach to the sign homomorphism in Sec. 4.5 (after commit c20b570).
Please have a look! There's a little puzzle left: I give a pointed map, Bsgn, from n-element sets t…
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The `__init__` method of GroupAlgebra did not check for commutativity of the group so that this would happen:
```
sage: G = AbelianGroup(2)
sage: A = GroupAlgebra(G)
sage: A.is_commutative()
True
s…