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5.1.68 jet
Syntax:
jet ( poly_expression, int_expression )
jet ( vector_expression, int_expression )
jet ( ideal_expression, int_expression )
jet ( module_expression, int_expression )
jet ( poly_expression, int_expression, intvec_expression )
jet ( vector_expression, int_expression, intvec_expression )
jet ( ideal_expression, int_expression, intvec_expression )
jet ( module_expression, int_expression, intvec_expression )
jet ( poly_expression, poly_expression, int_expression )
jet ( vector_expression, poly_expression, int_expression )
jet ( ideal_expression, matrix_expression, int_expression )
jet ( module_expression, matrix_expression, int_expression )
Type:
- the same as the type of the first argument
Purpose:
- deletes from the first argument all terms of degree bigger than the second argument.
If a third argument w of type intvec is given, the degree is replaced by the weighted degree defined by w .
If a second argument u of type poly or matrix is given, the first argument p is replaced by p/u . In this case, the coeffcient must be from a field.
Example:
| ring r=32003,(x,y,z),(c,dp);
jet(1+x+x2+x3+x4,3);
==> x3+x2+x+1
poly f=1+x+x2+xz+y2+x3+y3+x2y2+z4;
jet(f,3);
==> x3+y3+x2+y2+xz+x+1
intvec iv=2,1,1;
jet(f,3,iv);
==> y3+y2+xz+x+1
// the part of f with (total) degree >3:
f-jet(f,3);
==> x2y2+z4
// the homogeneous part of f of degree 2:
jet(f,2)-jet(f,1);
==> x2+y2+xz
// the part of maximal degree:
jet(f,deg(f))-jet(f,deg(f)-1);
==> x2y2+z4
// the absolute term of f:
jet(f,0);
==> 1
// now for other types:
ideal i=f,x,f*f;
jet(i,2);
==> _[1]=x2+y2+xz+x+1
==> _[2]=x
==> _[3]=3x2+2y2+2xz+2x+1
vector v=[f,1,x];
jet(v,1);
==> [x+1,1,x]
jet(v,0);
==> [1,1]
v=[f,1,0];
module m=v,v,[1,x2,z3,0,1];
jet(m,2);
==> _[1]=[x2+y2+xz+x+1,1]
==> _[2]=[x2+y2+xz+x+1,1]
==> _[3]=[1,x2,0,0,1]
ring rs=0,x,ds;
// 1/(1+x) till degree 5
jet(1,1+x,5);
==> 1-x+x2-x3+x4-x5
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See
deg;
ideal;
int;
intvec;
module;
poly;
vector.
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