Singular

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