Thanks, Dima. That works for me, too, and it's much faster than Sage was.
Now I'm trying some bigger examples...
On Monday, October 30, 2023 at 3:56:00 PM UTC-7 Dima Pasechnik wrote:
> Hi John,
> I tried running msolve on your input (more precisely, converting it
> into the problem of
>
Hi John,
I tried running msolve on your input (more precisely, converting it
into the problem of
finding the Grobner basis w.r.t. to the elimination order, as I
explained), and I see that
it's an injective map.
Computation takes about 3 minutes on an old laptop.
Specifically, I merely run msolve
On Mon, 30 Oct 2023, 20:50 Dima Pasechnik, wrote:
>
>
> On Mon, 30 Oct 2023, 20:25 John H Palmieri,
> wrote:
>
>>
>>
>> On Monday, October 30, 2023 at 12:28:18 PM UTC-7 Dima Pasechnik wrote:
>>
>> On Mon, Oct 30, 2023 at 5:04 PM John H Palmieri
>> wrote:
>> >
>> > Are endomorphisms better to
On Mon, 30 Oct 2023, 20:25 John H Palmieri, wrote:
>
>
> On Monday, October 30, 2023 at 12:28:18 PM UTC-7 Dima Pasechnik wrote:
>
> On Mon, Oct 30, 2023 at 5:04 PM John H Palmieri
> wrote:
> >
> > Are endomorphisms better to work with? I might be able to extend my map
> to an endomorphism of
On Monday, October 30, 2023 at 12:28:18 PM UTC-7 Dima Pasechnik wrote:
On Mon, Oct 30, 2023 at 5:04 PM John H Palmieri
wrote:
>
> Are endomorphisms better to work with? I might be able to extend my map
to an endomorphism of the larger ring, if that would make the computation
easier.
On Mon, Oct 30, 2023 at 5:04 PM John H Palmieri wrote:
>
> Are endomorphisms better to work with? I might be able to extend my map to an
> endomorphism of the larger ring, if that would make the computation easier.
> Probably just send xi1 -> xi1, xi2 -> xi2, etc.
these are "already there",
On Mon, Oct 30, 2023 at 5:02 PM John H Palmieri wrote:
>
> So Sage doesn't already use Gröbner bases when computing kernels of such
> maps? Okay, I'll try that.
yes, it certainly does. I just thought that using a non-default
Gröbner basis backend would help.
(and you can only do this if you
Are endomorphisms better to work with? I might be able to extend my map to
an endomorphism of the larger ring, if that would make the computation
easier. Probably just send xi1 -> xi1, xi2 -> xi2, etc.
On Monday, October 30, 2023 at 7:14:16 AM UTC-7 Dima Pasechnik wrote:
> On Mon, Oct 30, 2023
So Sage doesn't already use Gröbner bases when computing kernels of such
maps? Okay, I'll try that.
Now that I've looked at the code a little bit, I see that
`phi.is_injective()` just calls `phi.kernel()` and checks whether it's
zero. I was hoping that there was something more clever: if I
On Mon, Oct 30, 2023 at 12:54 PM Kwankyu wrote:
>
> Isn't this what you want?
>
> sage: R. = QQ[]
> sage: phi = R.hom([x,x])
> sage: phi
> Ring endomorphism of Multivariate Polynomial Ring in x, y over Rational Field
> Defn: x |--> x
> y |--> x
> sage: phi.kernel()
> Ideal (x - y) of
Isn't this what you want?
sage: R. = QQ[]
sage: phi = R.hom([x,x])
sage: phi
Ring endomorphism of Multivariate Polynomial Ring in x, y over Rational
Field
Defn: x |--> x
y |--> x
sage: phi.kernel()
Ideal (x - y) of Multivariate Polynomial Ring in x, y over Rational Field
On Monday,
On Mon, 30 Oct 2023, 05:57 John H Palmieri, wrote:
> Does anyone have any tips for how to compute the kernel of a map between
> polynomial algebras, or for checking whether the map is injective? I have
> families of such maps involving algebras with many generators. I'm working
> over GF(2), if
Does anyone have any tips for how to compute the kernel of a map between
polynomial algebras, or for checking whether the map is injective? I have
families of such maps involving algebras with many generators. I'm working
over GF(2), if that matters. In one example I defined the map phi: R -> S
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