Re: [sage-support] Compute equalizer of maps between polynomial rings?

[John H Palmieri]

One issue is that f-id is not a ring homomorphism. So do I restrict to a 
range of degrees, convert to vector spaces, and compute the kernel? I'm not 
sure of the right approach.

On Thursday, August 25, 2022 at 3:11:12 AM UTC-7 pedrito...@gmail.com wrote:

> Dear John,
> Wouldn’t be of some help to consider the kernel of  f-Id (with Id the 
> identity map)?
> Best,
> Pedro
>
> El El jue, 25 ago 2022 a las 8:22, Dima Pasechnik  
> escribió:
>
>>
>>
>> On Thu, 25 Aug 2022, 00:38 John H Palmieri,  wrote:
>>
>>> I have a polynomial ring R = k[x1, x2, ..., xn] and a ring homomorphism 
>>> f: R -> R. In case it matters, k=GF(2). I would like to find the subring of 
>>> elements x satisfying f(x) = x: that is, I want to find the equalizer of 
>>> the pair of maps (f, 1). Is there anything in Sage that will compute this? 
>>> The more polynomial generators this can handle, the better.
>>>
>>
>> Is this subring finitely generated? Invariant theory in positive 
>> characteristic is full of surprises...
>>
>>
>>> -- 
>>> John
>>>
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>>>  
>>> 
>>> .
>>>
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>>  
>> 
>> .
>>
>

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Re: [sage-support] Compute equalizer of maps between polynomial rings?

[John H Palmieri]

Good question, and I don't whether the subring is finitely generated. I 
want to compute examples — what's the subring in a range of degrees — to 
see what's going on.

On Wednesday, August 24, 2022 at 11:22:31 PM UTC-7 dim...@gmail.com wrote:

>
>
> On Thu, 25 Aug 2022, 00:38 John H Palmieri,  wrote:
>
>> I have a polynomial ring R = k[x1, x2, ..., xn] and a ring homomorphism 
>> f: R -> R. In case it matters, k=GF(2). I would like to find the subring of 
>> elements x satisfying f(x) = x: that is, I want to find the equalizer of 
>> the pair of maps (f, 1). Is there anything in Sage that will compute this? 
>> The more polynomial generators this can handle, the better.
>>
>
> Is this subring finitely generated? Invariant theory in positive 
> characteristic is full of surprises...
>
>
>> -- 
>> John
>>
>> -- 
>> You received this message because you are subscribed to the Google Groups 
>> "sage-support" group.
>> To unsubscribe from this group and stop receiving emails from it, send an 
>> email to sage-support...@googlegroups.com.
>> To view this discussion on the web visit 
>> https://groups.google.com/d/msgid/sage-support/6b028ddf-d0b7-4156-adad-7315cc6220a1n%40googlegroups.com
>>  
>> 
>> .
>>
>

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Re: [sage-support] Compute equalizer of maps between polynomial rings?

[pedritomele...@gmail.com]

Dear John,
Wouldn’t be of some help to consider the kernel of  f-Id (with Id the
identity map)?
Best,
Pedro

El El jue, 25 ago 2022 a las 8:22, Dima Pasechnik 
escribió:

>
>
> On Thu, 25 Aug 2022, 00:38 John H Palmieri, 
> wrote:
>
>> I have a polynomial ring R = k[x1, x2, ..., xn] and a ring homomorphism
>> f: R -> R. In case it matters, k=GF(2). I would like to find the subring of
>> elements x satisfying f(x) = x: that is, I want to find the equalizer of
>> the pair of maps (f, 1). Is there anything in Sage that will compute this?
>> The more polynomial generators this can handle, the better.
>>
>
> Is this subring finitely generated? Invariant theory in positive
> characteristic is full of surprises...
>
>
>> --
>> John
>>
>> --
>> You received this message because you are subscribed to the Google Groups
>> "sage-support" group.
>> To unsubscribe from this group and stop receiving emails from it, send an
>> email to sage-support+unsubscr...@googlegroups.com.
>> To view this discussion on the web visit
>> https://groups.google.com/d/msgid/sage-support/6b028ddf-d0b7-4156-adad-7315cc6220a1n%40googlegroups.com
>> 
>> .
>>
> --
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> 
> .
>

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