Extraneous cases in simplified piecewise function

I'm trying to get Mathematica to simplify a piecewise function, but as you can see below it's making some strange errors: • I'm telling it i and g are integers, so it ought to know that 2g>4+i is extraneous;
• In the cases where equality is assigned, it doesn't make the obvious substitutions: if 2g=5+i can I make it output an expression involving g instead?
• Also, can I get it to output the cases "solved for i?" That is, instead of saying 2g>5+i say i<2g-5?

Thanks for any insight!

Edit: Here's a minimal working example:

c = 1;
cPlane = 1;
f[i_] := Piecewise[{{1 + i, 0 <= i < 2*g - 4}, {1 - i, i >= 2*g - 4}}]
w[i_, j_] := Piecewise[{{f[i + 1] - f[j], 0 <= j <= i}, {0, j > i}}]
sigma[i_] := f[i] - c*Sum[w[i, j], {j, 0, i}]

fPlane[i_] := Sum[w[i, j], {j, 0, 2 g - 5}]
sigmaPlane[i_] := fPlane[i] - cPlane*Sum[w[i, j], {j, 0, i}]

Refine[FullSimplify[-sigmaPlane[i]/sigma[i], 0 < i && i <= n - 2 && Element[i | g, Integers] && g >= 3]]
• Please enter your code in copy-and-pastable Mathematica code, properly formatted in code blocks. (Use either four-spaces or back-tick marks: see the help for how to do this.) It helps potential answerers here if they can just copy and paste into their own copies of Mathematica. (So: also include your definitions of sigmaPlane and sigma.) – march Oct 13 '16 at 15:57

Perhaps PiecewiseExpand can help:

pwf = FullSimplify[-sigmaPlane[i]/sigma[i],
0 < i && i <= n - 2 && Element[i | g, Integers] && g >= 3];

Assuming[0 < i && i <= n - 2 && Element[i | g, Integers] && g >= 3,
FullSimplify@PiecewiseExpand[-sigmaPlane[i]/sigma[i],
Method -> {"ConditionSimplifier" -> Simplify, "OrderlessConditions" -> True}]
] • @MattGrimes You're welcome! – Michael E2 Oct 13 '16 at 18:47