primaryDecompositionPseudomonomial -- primary decomposition of a square free pseudomonomial ideal

i1 : R=ZZ/2[x1,x2,x3,x4,x5];

i2 : I = ideal(x1*x2,x3*x4,x5);

o2 : Ideal of R

i3 : primaryDecompositionPseudomonomial(I) 

o3 = {ideal (x5, x1, x3), ideal (x5, x1, x4), ideal (x5, x2, x3), ideal (x5,
     ------------------------------------------------------------------------
     x2, x4)}

o3 : List

i4 : R=QQ[x1,x2,x3,x4,x5];

i5 : I = ideal(x1*(x2-1),(x3-1)*x4,x5);

o5 : Ideal of R

i6 : primaryDecompositionPseudomonomial(I) 

o6 = {ideal (x5, x1, x3 - 1), ideal (x5, x1, x4), ideal (x5, x2 - 1, x3 - 1),
     ------------------------------------------------------------------------
     ideal (x5, x2 - 1, x4)}

o6 : List

i7 : R=ZZ/2[x1,x2];

i8 : I = ideal(x1*(x2-1),(x1-1)*(x2-1),x1*x2,(x1-1)*x2);

o8 : Ideal of R

i9 : primaryDecompositionPseudomonomial(I) 

o9 = {}

o9 : List

i10 : R=QQ[x1,x2,x3,x4,x5];

i11 : I = ideal(x5,x1*(x3-1)*(x5-1));

o11 : Ideal of R

i12 : primaryDecompositionPseudomonomial(I) 

o12 = {ideal (x5, x1), ideal (x5, x3 - 1)}

o12 : List

i13 : R=ZZ/3[x1,x2];

i14 : I = ideal(x5,(x3-1));

o14 : Ideal of QQ[x1, x2, x3, x4, x5]

i15 : primaryDecompositionPseudomonomial(I) 

o15 = {ideal (x5, x3 - 1)}

o15 : List