Implementation of mutations for matrices

[stumpc5]

This patch implements a method to mutate matrices. This method is needed for the cluster algebra and quiver package, see Ticket #10298.

Depends on #10347

CC: @hughrthomas

Component: combinatorics

Keywords: matrix mutation

Author: Christian Stump

Reviewer: Hugh Thomas

Merged: sage-5.0.beta6

Issue created by migration from https://trac.sagemath.org/ticket/10349

[stumpc5]

Description changed:

--- 
+++ 
@@ -1 +1,3 @@
 This patch implements a method to mutate matrices. This method is needed for the cluster algebra and quiver package, see Ticket #10298.
+
+Depends on #10347.

[stumpc5]

comment:3

For the buildbot:

Depends on #10347.

[stumpc5]

Dependencies: 10347

[stumpc5]

Description changed:

--- 
+++ 
@@ -1,3 +1 @@
 This patch implements a method to mutate matrices. This method is needed for the cluster algebra and quiver package, see Ticket #10298.
-
-Depends on #10347.

[stumpc5]

Changed dependencies from 10347 to #10347

[hughrthomas]

Reviewer: Hugh Thomas

[hughrthomas]

comment:6

Hi Christian--

What do you think about the idea of checking that 0 <= k < min(ncols,nrows)? Your code is very nicely written to be safe even if someone tries to mutate a 2x2 matrix at row 15, but they shouldn't be doing that. More importantly, they shouldn't be trying to mutate a 2n x n matrix at row j for n<= j < 2n -- for such a parameter, mutation is undefined. Returning what looks like meaningful output in such a case is potentially deceptive. (That's my view, at any rate, though if you disagree, I could be convinced otherwise.)

It's also true that the principal part of B should be skew-symmetrizable, but I don't think it's necessary to check that -- though maybe it would be good to mention this in the documentation? (The legit range of k values should also go in the documentation, I guess.)

And, Zelevinsky :)

Otherwise, though, it looks good.

cheers,

Hugh

[hughrthomas]

comment:7

Oh, one more comment, in the doc-string, you have "b-matrix"; I'd prefer "B-matrix".

cheers

Hugh