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Find all non-negative integer solutions of $a+b+c+d+e = 8$ in Sagemath

asked 2017-02-11 04:26:08 -0500

davis gravatar image

Find all non-negative integer a, b, c,d, e such that

$$a+b+c+d+e = 8$$

Is there any method for this? I have no idea. I can just fix the limit.

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See also http://math.stackexchange.com/questio... where this has several answers.

kcrisman gravatar imagekcrisman ( 2017-02-11 07:28:41 -0500 )edit

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answered 2017-02-12 17:05:59 -0500

If the order of a, b, etc. matters:

sage: IntegerVectors(8, 5)
Integer vectors of length 5 that sum to 8
sage: list(IntegerVectors(8, 5))
[[8, 0, 0, 0, 0],
 [7, 1, 0, 0, 0],
 [7, 0, 1, 0, 0],
 [7, 0, 0, 1, 0],
 [7, 0, 0, 0, 1],
 [6, 2, 0, 0, 0],
 [6, 1, 1, 0, 0],
 [6, 1, 0, 1, 0],
 [6, 1, 0, 0, 1],
 ...

If you don't care about the order:

sage: Partitions(8, max_length=5)
Partitions of the integer 8 satisfying constraints max_length=5
sage: list(Partitions(8, max_length=5))
[[8],
 [7, 1],
 [6, 2],
 [6, 1, 1],
 [5, 3],
 [5, 2, 1],
 [5, 1, 1, 1],
 [4, 4],
 [4, 3, 1],
 [4, 2, 2],
 [4, 2, 1, 1],
 [4, 1, 1, 1, 1],
 [3, 3, 2],
 [3, 3, 1, 1],
 [3, 2, 2, 1],
 [3, 2, 1, 1, 1],
 [2, 2, 2, 2],
 [2, 2, 2, 1, 1]]
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answered 2017-02-11 07:06:05 -0500

tmonteil gravatar image

updated 2017-02-11 07:07:00 -0500

While this particular example could be easily done without Sage, you can have a look at Mixed Integer Linear Programming as a general method, see http://doc.sagemath.org/html/en/refer... and http://doc.sagemath.org/html/en/thema...

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Asked: 2017-02-11 03:30:54 -0500

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Last updated: Feb 12