#14507: Implement the tropical semiring
----------------------------------------------+-----------------------------
Reporter: tscrim | Owner: tscrim
Type: enhancement | Status: needs_work
Priority: major | Milestone: sage-5.10
Component: algebra | Resolution:
Keywords: tropical geometry semiring | Work issues: documentation,
design
Report Upstream: N/A | Reviewers: Vincent
Delecroix
Authors: Travis Scrimshaw | Merged in:
Dependencies: | Stopgaps:
----------------------------------------------+-----------------------------
Comment (by tscrim):
So just to make sure, you want tropical operations being performed with
regular matrix multiplication, i.e.
{{{
[a b] * [c] = min(a+c, b+d)
[d]
}}}
Which makes more sense, I was thinking of the set of all `n x m` matrices
over a [totally ordered] ring R where the `min` would be the minimum of
all the entries.
In general, creating a matrix space requires something in the category of
`Rings`:
{{{
sage: MatrixSpace(NN, 3)
Traceback (most recent call last):
...
TypeError: base_ring (=Non negative integer semiring) must be a ring
}}}
(which is the same reason why the `matrix()` constructor fails). We could
probably loosen the restriction to the `Semirings` category since we still
have a `+` and `*`.
Best,[[BR]]
Travis
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14507#comment:5>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac?hl=en.
For more options, visit https://groups.google.com/groups/opt_out.
