diff -- differentiate or take difference

Synopsis

• Usage:

  diff(f,g) or diff(P) or diff(P,i)

Description

The second use, less common but sometimes useful, is to compute the difference polynomial of a Hilbert polynomial.

The arguments can also be ring elements or vectors.

i1 : R = ZZ[x,y,z]

o1 = R

o1 : PolynomialRing

i2 : f = vars R ** vars R

o2 = | x2 xy xz xy y2 yz xz yz z2 |

             1       9
o2 : Matrix R  <--- R

i3 : diff(transpose vars R, f)

o3 = {1} | 2x y z y 0  0 z 0 0  |
     {1} | 0  x 0 x 2y z 0 z 0  |
     {1} | 0  0 x 0 0  y x y 2z |

             3       9
o3 : Matrix R  <--- R

i4 : diff(x, f)

o4 = | 2x y z y 0 0 z 0 0 |

             1       9
o4 : Matrix R  <--- R

i5 : diff(y, f)

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

             1       9
o5 : Matrix R  <--- R

i6 : diff(z, f)

o6 = | 0 0 x 0 0 y x y 2z |

             1       9
o6 : Matrix R  <--- R

See also

• diff and contract
• diff' -- differentiate a matrix by a matrix, the dual notion
• contract -- contract one matrix by another
• jacobian -- the Jacobian matrix of partial derivatives
• hilbertPolynomial -- compute the Hilbert polynomial

Menu

differentiation

• diff(RingElement,RingElement) -- differentiation
• diff(RingElement,Matrix) -- differentiate each entry of a matrix
• diff(Matrix,RingElement) -- differentiation
• diff(Matrix,Matrix) -- differentiate a matrix by a matrix

difference operator for Hilbert polynomials

• diff(ProjectiveHilbertPolynomial)
• diff(ProjectiveHilbertPolynomial,ZZ)