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

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

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

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.

We may eliminate this routine.

Ways to use divideByVariable :

divideByVariable(Matrix,RingElement)

divideByVariable(Matrix,RingElement,ZZ)