divideByVariable

divideByVariable(m,v) -- divide each column of the matrix 'm' by as high a power of the variable 'v' as possible.
divideByVariable(m,v,d) -- divide each column of the matrix 'm' by as high a power of the variable 'v' as possible, but divide by no more than v^d.

     i1 = R = ZZ/101[a..d]
     
     o1 = R
     
     o1 : PolynomialRing

     i2 = m = matrix{{a*b, a^2*c}, {a*b^2, a^4*d}}
     
     o2 = | ab  a2c |
          | ab2 a4d |
     
                  2       2
     o2 : Matrix R  <--- R

     i3 = divideByVariable(m,a)
     
     o3 = | b  c   |
          | b2 a2d |
     
                  2       2
     o3 : Matrix R  <--- R

     i4 = divideByVariable(m,a,1)
     
     o4 = | b  ac  |
          | b2 a3d |
     
                  2       2
     o4 : Matrix R  <--- R

Caveats and limitations: you can only divide by a variable, not a monomial, and you have little control on what power will be divided. This routine is mostly used by the saturation commands as a fast internal way of dividing.

We may eliminate this routine.

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