1.2.19 `sm1.slope'
------------------

sm1.slope(II,V,F_FILTRATION,V_FILTRATION|proc=P)
     ::  Returns the slopes of differential equations II.

RETURN
     List

P
     Number

II
     List  (equations)

V
     List  (variables)

F_FILTRATION
     List  (weight vector)

V_FILTRATION
     List (weight vector)

   * `sm1.slope' returns the (geometric) slopes of the system of
     differential equations II along the hyperplane specified by the V
     filtration V_FILTRATION.

   * V is a list of variables.

   * The return value is a list of lists.  The first entry of each list
     is the slope and the second entry is the weight vector for which
     the microcharacteristic variety is not bihomogeneous.

Algorithm: see "A.Assi, F.J.Castro-Jimenez and J.M.Granger, How to
calculate the slopes of a D-module, Compositio Math, 104, 1-17, 1996"
Note that the signs of the slopes are negative, but the absolute values
of the slopes are returned.


     [284] A= sm1.gkz([  [[1,2,3]],  [-3] ]);


     [285] sm1.slope(A[0],A[1],[0,0,0,1,1,1],[0,0,-1,0,0,1]);

     [286] A2 = sm1.gkz([ [[1,1,1,0],[2,-3,1,-3]], [1,0]]);
          (* This is an interesting example given by Laura Matusevich,
             June 9, 2001 *)

     [287] sm1.slope(A2[0],A2[1],[0,0,0,0,1,1,1,1],[0,0,0,-1,0,0,0,1]);

Reference
     `sm.gb'

* Menu:

* sm1.ahg::
* sm1.bfunction::
* sm1.call_sm1::
* sm1.ecart_homogenize01Ideal::
* sm1.ecartd_gb::
* sm1.ecartd_gb_oxRingStructure::
* sm1.ecartd_isSameIdeal_h::
* sm1.ecartd_reduction::
* sm1.ecartd_reduction_noh::
* sm1.ecartd_syz::
* sm1.gb_oxRingStructure::
* sm1.gb_reduction::
* sm1.gb_reduction_noh::
* sm1.generalized_bfunction::
* sm1.isSameIdeal_in_Dalg::
* sm1.restriction::
* sm1.saturation::

