add functionality for counting, generating, and manipulating non-negative integer matrices

[saliola]

Counting, generating, and manipulating non-negative integer matrices with
prescribed row sums and column sums.

    An *integer matrix* `m` with column sums `c := (c_1,...,c_k)` and row
    sums `l := (l_1,...,l_n)` where `c_1+...+c_k` is equal to `l_1+...+l_n`,
    is a `n \times k` matrix `m = (m_{i,j})` such that
    `m_{1,j}+\dots+m_{n,j} = c_j`, for all `j` and
    `m_{i,1}+\dots+m_{i,k} = l_i`, for all `i`.

    EXAMPLES:

    There are `6` integer matrices with row sums `[3,2,2]` and column sums
    `[2,5]`::

        sage: from sage.combinat.integer_matrices import IntegerMatrices
        sage: IM = IntegerMatrices([3,2,2], [2,5]); IM
        Non-negative integer matrices with row sums [3, 2, 2] and column sums [2, 5]
        sage: IM.list()
        [
        [2 1]  [1 2]  [1 2]  [0 3]  [0 3]  [0 3]
        [0 2]  [1 1]  [0 2]  [2 0]  [1 1]  [0 2]
        [0 2], [0 2], [1 1], [0 2], [1 1], [2 0]
        ]
        sage: IM.cardinality()
        6

CC: @sagetrac-chrisjamesberg

Component: combinatorics

Keywords: sd40, ncsf

Author: Franco Saliola

Reviewer: Chris Berg

Merged: sage-5.3.beta0

Issue created by migration from https://trac.sagemath.org/ticket/13238

[sagetrac-chrisjamesberg]

comment:3

Attachment: trac_13238-integer_matrices-fs.patch.gz

[jdemeyer]

Merged: sage-5.3.beta0