divideByVariable -- divide all columns by a (power of a) variable

Description

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   |, 2)
      | b2 a2d |

o3 : Sequence

i4 : divideByVariable(m,a,1)

o4 = (| b  ac  |, 1)
      | b2 a3d |

o4 : Sequence

We may eliminate this routine.

Caveat

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.

Ways to use divideByVariable:

divideByVariable(Matrix,RingElement)
divideByVariable(Matrix,RingElement,ZZ)

For the programmer

The object divideByVariable is a method function.