diff(Matrix,Matrix) -- differentiate a matrix by a matrix

• Function: diff

• Usage:

  diff(m,n)

• Inputs:
  • m, a matrix, a map m : F <--- P between free modules of ranks f and p.
  • n, a matrix, a map n : G <--- Q between free modules of ranks g and q.
• Outputs:
  • a matrix, with the shape h : dual F ** G <--- dual P ** Q, whose entry in the slot h_g*i+j,q*k+l is the result of differentiating n_j,l by the differential operator corresponding to m_i,k.

i1 : R = QQ[a,b,c][x,y,z]

o1 = R

o1 : PolynomialRing

i2 : m = transpose vars R

o2 = {-1, 0} | x |
     {-1, 0} | y |
     {-1, 0} | z |

             3      1
o2 : Matrix R  <-- R

i3 : n = matrix{{x^2-a*y^3, x^3-z^2*y, x*y-b, x*z-c}}

o3 = | -ay3+x2 x3-yz2 xy-b xz-c |

             1      4
o3 : Matrix R  <-- R

i4 : diff(m,n)

o4 = {1, 0} | 2x    3x2  y z |
     {1, 0} | -3ay2 -z2  x 0 |
     {1, 0} | 0     -2yz 0 x |

             3      4
o4 : Matrix R  <-- R