One of the tasks that Matlab is very good at, is in solving systems of linear equations.
In this problem we shall tackle a system of linear Diophantine Equations in which the roots are limited to certain range.
Given the number of variables n, positive integers, a, b and a root limit, L, create the function, numRoots(n,a,b,L), that outputs the number of posible integer root sets of the following system of equations:
with:
.For example, if 
, the system of equations: 
and 
, where 
, has only one root set, namely: 
. Therefore, numRoots(2,10,4,1) = 1.
, the system of equations: and , where , has only one root set, namely: . Therefore, numRoots(2,10,4,1) = 1.If 
, two of the possible roots of:
, two of the possible roots of:
; and
where: 
are 
and 
. In fact, there are 
possible root sets. Therefore, numRoots(4,20,6,3) = 16.
and . In fact, there are possible root sets. Therefore, numRoots(4,20,6,3) = 16.There are no possible roots for 
and 
, therefore in these cases the function should return: numRoots = 0.
and , therefore in these cases the function should return: numRoots = 0.-------------------------
NOTE: As an added challenge, only those solutions with Cody program size of less than or equal to 200 will be accepted.
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Update: Programs of cody size <= 200 is now accepted.