#14507: Implement the tropical semiring
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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:
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Comment (by vdelecroix):
If you have a semi-ring `R`, you can always consider `R^n` and linear
applications on it (here `ax+by` means `max(a+x,b+y)` or `min(a+x,b+y)`).
But, be careful, matrix multiplication does not become matrix addition: it
is composition of the corresponding linear applications. Right now, Sage
is not happy with matrices with entries in a semi-ring
{{{
sage: matrix(ZZ,[[0,1],[2,3]]) # no problem
[0 1]
[2 3]
sage: matrix(NN,[[0,1],[2,3]]) # BOOM!
Traceback (most recent call last):
...
ValueError: Invalid matrix constructor. Type matrix? for help
}}}
If you know how to fix it easily it would be '''wonderful'''. Otherwise, I
will have to work to play with my max-plus matrices.
Vincent
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/14507#comment:4>
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