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5.1.66 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
See deg; ideal; int; intvec; module; poly; vector.