5.1.18 diff

Syntax:

diff ( poly_expression, ring_variable )
diff ( vector_expression, ring_variable )
diff ( ideal_expression, ring_variable )
diff ( module_expression, ring_variable )
diff ( matrix_expression, ring_variable )

Type:

the same as the type of the first argument

Syntax:

diff ( ideal_expression, ideal_expression )

Type:

matrix

Purpose:

computes the partial derivative of a polynomial object by a ring variable (first forms)
respectively differentiates each polynomial (1..n) of the second ideal by the differential operator corresponding to each polynomial (1..m) in the first ideal, producing an m x n matrix.

Example:

ring r=0,(x,y,z),dp; poly f=2x3y+3z5; diff(f,x); → 6x2y vector v=[f,y2+z]; diff(v,z); → 15z4*gen(1)+gen(2) ideal j=x2-yz,xyz; ideal i=x2,x2+yz,xyz; // corresponds to differential operators // d2/dx2, d2/dx2+d2/dydz, d3/dxdydz: print(diff(i,j)); → 2,0, → 1,x, → 0,1

See contract; ideal; jacob; matrix; module; poly; var; vector.