Introduce is_known according to #4394.
#4507
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| @@ -240,3 +240,10 @@ function groebner_basis(I::MPolyIdeal; ordering::MonomialOrdering = default_orde | |||
| is_global(ordering) || error("Ordering must be global") | |||
| return standard_basis(I, ordering=ordering, complete_reduction=complete_reduction, algorithm=algorithm) | |||
| end | |||
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| function is_known(I::MPolyIdeal, ::typeof(groebner_basis); | |||
| ordering::Union{MonomialOrdering, Nothing}=nothing) | |||
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Could/should this also accept the complete_reduction kwarg?
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That depends on the user's need. In principle, I think, it could be added (if we agree on supporting forwarding of kwargs for is_known). But as this is just a demonstration right now, I restricted to this signature for the time being.
| return ideal(base_ring(I), unique!(newgens)) | ||
| result = ideal(base_ring(I), unique!(newgens)) | ||
| # carry over eventual information about the dimension | ||
| is_known(I, dim) && is_known(J, dim) && (result.dim = maximum([dim(I), dim(J)])) |
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Matter of taste, but I personally think assignments in a chain of && takes it a step to far in terms of how it affects code clarity. But feel free to ignore this suggestion shrug
| is_known(I, dim) && is_known(J, dim) && (result.dim = maximum([dim(I), dim(J)])) | |
| if is_known(I, dim) && is_known(J, dim) | |
| result.dim = maximum([dim(I), dim(J)])) | |
| end |
| get_attribute(I, :is_prime, false) && return true | ||
| return false | ||
| function is_known(I::MPolyIdeal, ::typeof(is_radical)) | ||
| is_known(I, is_prime) && is_prime(I) && return true |
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This is starting to look like a reinvention of GAP's property implications (albeit manually and much less powerful -- no offense intended). See also issue #982 by @HereAround
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Maybe, but I don't know too much about the GAP internals, to be honest. @HereAround 's request seems related indeed. Again, for the moment this is thought of as a demonstration of potential use cases for is_known. I think it can well be integrated in any other (more powerful) logical deduction system, can it not? It's the programmer's liberty how to make use of it. This is just to say: Look, this is what you can do for example.
| D = minimal_primes(I) | ||
| return length(D) == 1 && issubset(D[1], I) | ||
| end | ||
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| function is_known(I::MPolyIdeal, ::typeof(is_prime)) | ||
| has_attribute(I, :is_prime) && return true | ||
| is_known(I, primary_decomposition) && return true |
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Shouldn't this be
| is_known(I, primary_decomposition) && return true | |
| is_known(I, primary_decomposition) && is_one(length(primary_decomposition(I))) && return true |
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No, I don't think so. The point of is_known is whether or not the result can be computed in constant time. Once the primary decomposition is there, I think it takes (almost) constant time to check whether its length is one and whether the single component P is a subset of I.
Well, now that I think of it again, this should probably also involve an is_known(I, groebner_basis). But I think your particular suggestion is not correct.
| has_attribute(I, :is_prime) && return true | ||
| is_known(I, primary_decomposition) && return true | ||
| is_known(I, minimal_primes) && return true | ||
| if coefficient_ring(base_ring(I)) isa Field |
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Wouldn't it suffice if the base_ring is a domain, as echeck via is_domain_type ? I.e.
| if coefficient_ring(base_ring(I)) isa Field | |
| if is_domain_type(base_ring_type(I)) |
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You are probably right. This might be a reasonable extension. Just didn't occur to me when I wrote it up.
| return true | ||
| end | ||
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| is_known(I, is_prime) && is_prime(I) && return true | ||
| D = primary_decomposition(I) | ||
| return length(D) == 1 | ||
| end |
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Should there also be a is_known(I::MPolyIdeal, ::typeof(is_primary)) method?
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If we have that function, then yes: Extending the is_known functionality for that seems reasonable. But again: This PR is just to demonstrate some applications of is_known so that we can all contemplate where the journey goes. I do not make any claim about coverage of the subject on mpoly-ideals or elsewhere. So far, one of our decisions is that we do not guarantee support for is_known just by introduction of a method of a unary function for an object. So in cases like this, functionality can be extended at need and request.
Still waiting for a PR in AA to first be discussed.