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5.1.24 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
Syntax:
diff ( number_expression, ring_parameter )
Type:
- number
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.
respectively if the coefficient ring is a transcendental field extension, differentiates a
number (that is, a rational function) by a transcendental variable (ring parameter).
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
// differentiation of rational functions:
ring R=(0,t),(x),dp;
number f = t^2/(1-t)^2;
diff(f,t);
==> (-2t)/(t3-3t2+3t-1)
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See
contract;
ideal;
jacob;
matrix;
module;
poly;
var;
vector.
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