sm1.ahg
-------

sm1.ahg(A)
     : It idential with sm1.gkz(A).

sm1.bfunction
-------------

sm1.bfunction(F)
     : It computes the global b-function of F.

It no longer calls sm1's original bfunction. Instead, it calls asir "bfct".

Algorithm: M.Noro, Mathematical Software, icms 2002, pp.147--157.

Example:

      sm1.bfunction(x^2-y^3);

sm1.generalized_bfunction
-------------------------

sm1.generalized_bfunction(I,V,VD,W)
     : It computes the generalized b-function (indicial equation) of I with respect to the weight W.

It no longer calls sm1's original function. Instead, it calls asir "generic_bfct".

Example:

      sm1.generalized_bfunction([x^2*dx^2-1/2,dy^2],[x,y],[dx,dy],[-1,0,1,0]);

sm1.restriction
---------------

sm1.restriction(I,V,R)
     : It computes the restriction of I as a D-module to the set defined by R. V is the list of variables. When the optional variable DEGREE=d is given, only the restrictions from 0 to d are computed. Note that, in case of vector input,  RESTRICTION VARIABLES MUST APPEAR FIRST in the list of variable V. We are using wbfRoots to get the roots of b-functions, so we can use only generic weight vector for now.

sm1.restriction(I,V,R | DEGREE=key0)
     : This function allows optional variables DEGREE

Algorithm: T.Oaku and N.Takayama, math.AG/9805006, http://xxx.langl.gov

Example:

      sm1.restriction([dx^2-x,dy^2-1],[x,y],[y]);

sm1.saturation
--------------

sm1.saturation(T)
     : T = [I,J,V]. It returns saturation of I with respect to J^infty. V is a list of variables.

Example:

      sm1.saturation([[x2^2,x2*x4, x2, x4^2], [x2,x4], [x2,x4]]);