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

• 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

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