Singular

D.15.12.21 difformIsBigger

Usage:

df > dg OR difformIsBigger(df,dg,#); df,dg difform, # list

Return:

- 1, if df is bigger than dg with respect to the monomial ordering in the differential algebra - 0, otherwise - 1, if df is bigger than dg with respect to a given monomial ordering on the generators/ringvariables - 0, otherwise

Note:

the procedure uses diffAlgebraChangeOrd to change the order on the differential algebra, therefore an ordering is defined via the following pattern:
- #[i] = 'gen' defines the ordering on the generators dx_i - #[i+1] must then be a valid monomial ordering as string - #[i+2] an optional weight vector
- #[i] = 'ringvar' defines the ordering on the ringvariables - #[i+1] must then be a valid monomial ordering as string - #[i+2] an optional weight vector

LIB "difform.lib";
ring R = 0,(x,y,z),dp;
diffAlgebra();
==> // The differential algebra Omega_R was constructed and the differential \
   forms dDx, dDy, dDz, dx, dy, dz are available.
////////////////////////////
// With standard ordering //
////////////////////////////
dx > dy;
==> 1
x37*dy > dz;
==> 1
x*dz > y*x*dy;
==> 0
x3*dx - y*dx*dz > dx*dy*dz;
==> 0
///////////////////////////
// With changed ordering //
///////////////////////////
difformIsBigger(dx,dy,"gen","ls");
==> 0
difformIsBigger(x37*dy,dz,"gen","wp",intvec(1,-1,1));
==> 0
difformIsBigger(x*dz,y*x*dy,"gen","wp",intvec(1,-1,1),"ringvar","wp",intvec(1,-1,1));
==> 1
difformIsBigger(x3*dx - y*dx*dz,dx*dy*dz,"gen","wp",intvec(-1,-1,1));
==> 1
kill Omega_R,dx,dy,dz;