Singular Manual: difformIsSmaller

| #### D.15.2.22 difformIsSmaller Procedure from library `difform.lib` (see difform_lib). Usage: df < dg OR difformIsSmaller(df,dg,#); df,dg difform, # list Return: - 1, if df is smaller than dg with respect to the monomial ordering in the differential algebra - 0, otherwise - 1, if df is smaller 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),lp;
    diffAlgebra();
    ==> // The differential algebra Omega_R was constructed and the differential \
       forms dDx, dDy, dDz, dx, dy, dz are available.
    ////////////////////////////
    // With standard ordering //
    ////////////////////////////
    dz < dy;
    ==> 1
    x*dz < y*dz;
    ==> 0
    y2*z2*dy < x;
    ==> 0
    dx*dz < dy;
    ==> 0
    ///////////////////////////
    // With changed ordering //
    ///////////////////////////
    difformIsSmaller(dz,dy,"gen","ls");
    ==> 0
    difformIsSmaller(x*dz,y*dz,"ringvar","ls");
    ==> 1
    difformIsSmaller(y2*z2*dy,x,"gen","wp",intvec(1,-1,1));
    ==> 1
    difformIsSmaller(dx*dz,dy,"gen","ws",intvec(1,-1,-1));
    ==> 1
    kill Omega_R,dx,dy,dz;
See also: diffAlgebraChangeOrd; difformIsBigger.

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