Hi, all,
I'm new here and new-ish to sage and I was hoping you could help me
with a rather complicated problem. My professor gave me this
inequality:
0 < (2*n*(i+j+k))/(-k*n+j*(n-s)+i*s) < 1
and he wants me to see if I can find solutions within the following
constraints: 0 < s < n, i,j,k integers, and i <= j+k, j <= i+k, k<=i
+j.
It seemed like it would be possible to get Sage to do this for me, and
sure enough, when i input:
sage: n = var('n')
sage: sage: s = var('s')
sage: sage: assume(s>0)
sage: sage: assume(n>s)
sage: sage: i = var('i')
sage: sage: j = var('j')
sage: sage: k = var('k')
sage: sage: assume(i,'integer')
sage: sage: assume(j,'integer')
sage: sage: assume(k,'integer')
sage: assume(i<=j+k)
sage: assume(j<=i+k)
sage: assume(k<=i+j)
sage: solve((0 < (2*n*(i+j+k))/(-k*n+j*(n-s)+i*s) < 1),n)
I got a result, namely:
[[k < -i - j, 0 < n, -i*s - j*n + j*s + k*n > 0], [-i - j < k, n < 0, -
i*s - j*n + j*s + k*n > 0], [-i - j < k, 0 < n, i*s + j*n - j*s - k*n
> 0], [k < -i - j, n < 0, i*s + j*n - j*s - k*n > 0]]
My problem is, first, that I'm not sure the solutions are correct--
note that some of them have n < 0, when I'm assuming the contrary (and
when I try to have it assume explicitly that n > 0, Sage will tell me
that my assumption is redundant); and second, that I'm not sure how to
get specific numbers out of this. I've tried assigning specific values
to the variables, one by one, but I keep getting equations that don't
work, or simply []
Does anyone know what's going on, and if this problem is solvable in
sage?
Thank you!
Cal
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