I'm not sure if the title fits.
I'm basically just looking for a way to define a value and constrain it to $[a,b]$ when I use Solve later.
More specifically, I have a set of three equations where both sides are normalized to be in $[0, 1]$.
The right hand side is just a Ratio $\dfrac{b_i}{\sum{b_i}}$.
The left hand side is similar because it is also normalized to be in $[0, 1]$. I have an index which is based on a multiplicative function where I have a product of some variables which are all to the power of some exponent and then divided by the sum of the indices, therefore $[0, 1]$.
Since Solve is not able to solve this and for context reasons, I would like to restrict the exponents to values from $[-1, 1]$. Can I do this?
n = 3;
ebau[1] = Ebau - Sum[ebau[i], {i, 2, n}];
a[1] = A - Sum[a[i], {i, 2, n}];
b[1] = B - Sum[b[i], {i, 2, n}];
Fair = Table[a[i]^(\[Alpha])*ebau[i]^(-\[Beta])*b[i]^(\[Gamma]), {i, 1, n}];
Weight = Simplify[Fair/Sum[Fair[[i]], {i, n}]];
phiSO = {b[1]/B, b[2]/B, b[3]/B};
Solve[Table[ phiSO[[i]] == Weight[[i]], {i, 1, n}],
{\[Alpha], \[Beta], \[Gamma]}, Reals]
Solve[]andReduce[]do support constraining the variables (via inequalities), but unless you give a more concrete example, we can't be very helpful... – 0x4A4D♦ Aug 24 '12 at 10:28Solvein your code withJoin[Table[phiSO[[i]] == Weight[[i]], {i, 1, n}], (-1 <= # <= 1) & /@ {\[Alpha], \[Beta], \[Gamma]}]to include the constraints on\[Alpha], \[Beta], \[Gamma]. – kguler Aug 24 '12 at 11:25watch outmeans. But if you writeD=1then you'll get an error. And if you writeZ=1and in Mathematica version 11 they add Z to the list of protected symbols (WRI can do that, since they told you not to use UpperrCase), then your program will not work any more. – Nasser Aug 24 '12 at 13:06