Better pbw ideals arith #1591
Better pbw ideals arith #1591
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| @doc Markdown.doc""" | ||
| pbw_algebra(R::MPolyRing{T}, rel, ord::MonomialOrdering) where T | ||
| pbw_algebra(R::MPolyRing{T}, rel, ord::MonomialOrdering; check = true) where T | ||
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Why is this now checked by default? Isn't this horribly expensive?
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Perhaps we should discuss this in general and set a standard: speed over correctness or correctness over speed? Both have clear pros and cons...
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Personally I prefer correct, slow results over wrong, fast results... but of course we all prefer correct & fast results... The question is whether to expect people to explicitly say "trust me, I am an expert" (so it's their own fault for running against a wall; but it our fault if things are "slow" if one does not know about check=false). On the other hand, will people who are more cautious expect our functions to not validate inputs by default? Hmmm...
So yeah, my preference actually is to have check=true the default everywhere and then expect everyone to explicitly say check=false if they are sure about it. But I also realize I may be a minority here :-)
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I think that if the default is check = false, it makes the check argument useless. Then the only reason one would want to call a function with check = true is if one expects that the input is not valid. But then one should call the function which validates the input and not wait for an error in the constructor.
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I am not suggesting to start with check = false as default. Here is another example from the section on modules:
Warning
The functions do not check whether the resulting homomorphism is well-defined, that is, whether it sends the relations of M into the relations of N.
If you are uncertain with regard to well-definedness, use the function below. Note, however, that the check performed by the function requires a Gröbner basis computation. This may take some time.
is_welldefined(a::ModuleFPHom)
Return true if a is well-defined, and false otherwise.
I agree that we should agree on discussing this in general.
In the current example, we could do some time checks first.
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Isn't this horribly expensive?
No, it is just O(nvars^3) multiplications and additions in the algebra.
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By the way, I have no idea how to multiply two left ideals. |
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@tthsqe12 Please replace error("non-degeneracy condition is non-zero") by error("PBW-basis condition not satisfied") |
@wdecker