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.
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&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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