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-- -*- M2-comint -*- hash: -1215191058
i1 : R=CC[x11,x22,x21,x12,x23,x13,x14,x24];
i2 : system={x11*x22-x21*x12,x12*x23-x22*x13,x13*x24-x23*x14};
i3 : V=numericalIrreducibleDecomposition(system)
found 6 irreducible factors
o3 = V
o3 : NumericalVariety
i4 : WitSets=V#5; --witness sets are accessed by dimension
i5 : w=first WitSets;
i6 : w.cache.IsIrreducible
o6 = true
i7 : R=QQ[x11,x22,x21,x12,x23,x13,x14,x24];
i8 : system={x11*x22-x21*x12,x12*x23-x22*x13,x13*x24-x23*x14};
i9 : PD=primaryDecomposition(ideal(system))
o9 = {ideal (x13, x23, x11*x22 - x21*x12), ideal (x12, x22, x23*x14 -
------------------------------------------------------------------------
x13*x24), ideal (x23*x14 - x13*x24, x21*x14 - x11*x24, x22*x14 -
------------------------------------------------------------------------
x12*x24, x12*x23 - x22*x13, x11*x23 - x21*x13, x11*x22 - x21*x12)}
o9 : List
i10 : for i from 0 to 2 do print ("dim =" | dim PD_i | " " | "degree=" | degree PD_i)
dim =5 degree=2
dim =5 degree=2
dim =5 degree=4
i11 :
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