Question: Finding the shortest coefficient in a polynomial

I have a polynomial in the variables ya[i] and yd[i] where i are integers. I want to divide each of the coefficients by the 'shortest' coeficient. What i mean by that is the coefficient that is going to cause me the least trouble when i later do things with groebner bases of on the coefficients - I expect a good proxy for that is the one that has the smallest number of terms.

For example, for the polynomial:

2*yd[0]*k[a1]*k[d1]*ya[1]+(alpha*C[T]*k[a1]*k[m]-alpha*R[b]*k[a1]*k[d1]-alpha*R[m]*k[a1]*k[d1]-alpha*k[d1]*k[m])*ya[1]-2*k[a1]*k[d1]*yd[1]*yd[0]+(-alpha*C[T]*k[a1]*k[m]+alpha*R[b]*k[a1]*k[d1]+alpha*R[m]*k[a1]*k[d1]+alpha*k[d1]*k[m])*yd[1]

2*k[a1]*k[d1] is the shortest monomial coefficient

 

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