diff(Matrix,RingElement) -- differentiation

• Function: diff

• Usage:

  diff(f,g)

• Inputs:
  • f, a matrix, a matrix
  • g, a ring element, a polynomial with the same ring as f
• Outputs:
  • the result of differentiating g by the differential operator corresponding to each entry of f.

i1 : R = QQ[x,y,z,q];

i2 : f = vars R

o2 = | x y z q |

             1      4
o2 : Matrix R  <-- R

i3 : diff(f, (x+y-z)^2)

o3 = | 2x+2y-2z 2x+2y-2z -2x-2y+2z 0 |

             1      4
o3 : Matrix R  <-- R

i4 : f2 = genericMatrix(R,2,2)

o4 = | x z |
     | y q |

             2      2
o4 : Matrix R  <-- R

i5 : diff(f2, (x+y-z)^2)

o5 = | 2x+2y-2z -2x-2y+2z |
     | 2x+2y-2z 0         |

             2      2
o5 : Matrix R  <-- R