Singular

D.15.12.23 difformIsBigger

Procedure from library `difform.lib` (see difform_lib).

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

Example:
 ```LIB "difform.lib"; ring R = 0,(x,y,z),dp; diffAlgebra(); ==> // The differential algebra Omega_R was constructed and the differential \ forms 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; ```