I wrote that code into the Sage library and it is supposed to be doing 
exactly what you proposed (clear denominators and do the computation in the 
polynomial ring). It is possible the regression was triggered by an update 
to Singular; it would indeed be helpful to identify a minimal example of 
the problem and then post it to a ticket.

I believe there are also some upstream bugs with minimal associated primes, 
e.g., https://github.com/sagemath/sage/issues/29671.

Kiran

On Monday, May 29, 2023 at 8:53:59 PM UTC-7 Travis Scrimshaw wrote:

> Dear Enrique,
>    I am having a bit of trouble understanding exactly what computations 
> are slow and fast from your description. As Nils said, can you give us some 
> explicit code (with some comments about which parts are slow)?
>
> Best,
> Travis
>
> On Tuesday, May 30, 2023 at 3:28:39 AM UTC+9 Nils Bruin wrote:
>
>> Dear Enrique,
>>
>> From what you write I get the impression you may be talking about a 
>> regression in performance relative to earlier versions of sage. If you want 
>> to make an actionable item out of this, you'll probably have to file a 
>> ticket with explicit code on it that can be profiled; preferably with an 
>> indication why you think the performance could be significantly improved. 
>> That doesn't guarantee someone will work on it but it at least gives them a 
>> place to start if they want to, including you yourself! You could file it 
>> as an "enhancement" or even as a "bug" if you can convincingly show it's a 
>> regression. In the latter case you would probably end up identifying a 
>> version in which performance was significantly better. A git diff on some 
>> of the relevant files could then perhaps very quickly show what's happening.
>>
>>
>>
>> On Monday, 29 May 2023 at 09:07:07 UTC-7 enriqu...@gmail.com wrote:
>>
>>> Some time ago I had some computations on ideals in Laurent polynomial 
>>> rings, namely looking for minimal associated primes. Basically, I converted 
>>> any generator into a polynomial, study the ideal in the polynomial ring, 
>>> and forget the prime ideals containing monomials. From some time ago, it is 
>>> much easier since it can be done directly in the ring of Laurent 
>>> polynomials. 
>>> Yesterday these computations on an ideal with 80 generators were really 
>>> slow, but for some reason I checked that if the generators were converted 
>>> to elements in the associated polynomial ring, and then the ideal in the 
>>> Laurent polynomial ring is constructed, then those computations were solved 
>>> really fast. 
>>> I checked the code but I was not able to isolate the reason. Best, 
>>> Enrique.
>>>
>>

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