John,
On Sunday, July 19, 2020 at 9:04:26 PM UTC+2 John H Palmieri wrote:
> Let me go back to a question I asked Sverre: what happens in your code if
you allow nonhomogeneous elements? It may not be something you would ever
want to do, but maybe it would just work without breaking anything,
John,
On Sunday, July 19, 2020 at 1:00:21 AM UTC+2 John H Palmieri wrote:
> Can you give a specific example of a computation in which you care about
> the degree where your zero element lives? Or where you can't just recover
> it from its component elements (if ab=0, then you have an element
Hi John,
Your question is a good one, to look at the places where the notion that 0 has
no degree
causes extra effort.I have strong memories of having to go through minor but
annoying contortions to deal with this, both in sage and in MAGMA, for decades
now,
but don't have examples fresh in
Hi Bob,
Mathematically, a classical example of a graded object is a polynomial
ring, and non-topologists often consider nonhomogeneous polynomials, for
reasons that are beyond me. But once you do that, it seems that you're
forced to live in a direct sum. Sage could have two different
On 19.07.20 00:34, rrbold wrote:
Hi Christian and John,
Christian, your first sentence puts the finger on the correct spot:
I take the position that a graded abelian group is not an abelian
group. It is a sequence of abelian groups.
For any category C, one can consider Gr(C), the
On Jul 18, rrbold wrote:
Hi Christian and John,
Christian, your first sentence puts the finger on the correct spot: I take
the position that a graded abelian group is not an abelian group. It is a
sequence of abelian groups.
For any category C, one can consider Gr(C), the category of
Hi Christian and John,
Christian, your first sentence puts the finger on the correct spot: I
take the position that a graded abelian group is not an abelian group. It
is a sequence of abelian groups.
For any category C, one can consider Gr(C), the category of graded objects
in C, which
On 19.07.20 01:01, John H Palmieri wrote:
On Saturday, July 18, 2020 at 2:57:21 PM UTC-7, Christian Nassau wrote:
Hi Sverre,
I don't think it's a good idea to have different zeroes in an
algebraic structure that is also categorized as an abelian group,
unless you take the
On Saturday, July 18, 2020 at 2:57:21 PM UTC-7, Christian Nassau wrote:
>
> Hi Sverre,
>
> I don't think it's a good idea to have different zeroes in an algebraic
> structure that is also categorized as an abelian group, unless you take the
> point that a "graded abelian group" should not be
Can you give a specific example of a computation in which you care about
the degree where your zero element lives? Or where you can't just recover
it from its component elements (if ab=0, then you have an element in degree
= deg(a) + deg(b)). I'm struggling to understand this.
If you are doing
On Saturday, July 18, 2020 at 11:31:43 PM UTC+2, John H Palmieri wrote:
>
> In any case where the degree matters, you should first test whether an
> element is zero (in which case it won't have a degree) and then perhaps
> whether it is homogeneous. If not, you can raise an error (to keep
Hi Sverre,
I don't think it's a good idea to have different zeroes in an algebraic
structure that is also categorized as an abelian group, unless you take
the point that a "graded abelian group" should not be an "abelian group".
But let me also point out that something similar to what you
Hi,
Thank you for your comments so far. I feel I need to expand some more on
the issue of zero elements which is the central thing for the problem we
are adressing.
It is mathematically equivalent to think of a graded k-algebra A as either
1) a direct sum A = \bigosum_i A_i, together with a
On Saturday, July 18, 2020 at 2:31:01 AM UTC-7, Sverre Lunøe-Nielsen wrote:
>
> Dear list,
>
> I have been involved in preparing a package by M. Catanzaro and R. Bruner
> lately, which implements finitely presented modules over the mod `p`
> Steenrod algebra.
>
> We have encountered a conflict
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