i1 = R = ZZ/32003[a..d]
o1 = R
o1 : PolynomialRing
i2 = I = monomialCurve(R,{1,3,4})
o2 = ideal | bc-ad c3-bd2 ac2-b2d b3-a2c |
o2 : Ideal
i3 = J = ideal(a^3,b^3,c^3-d^3)
o3 = ideal | a3 b3 c3-d3 |
o3 : Ideal
i4 = I = intersect(I,J)
o4 = ideal | b4-a3d ab3-a3c bc4-ac3d-bcd3+ad4 c6-bc3d2-c3d3+bd5 ac5-b2c3d-ac2d3+b2d4 a2c4-a3d3+b3d3-a2cd3 b3c3-a3d3 ab2c3-a3cd2+b3cd2-ab2d3 a2bc3-a3c2d+b3c2d-a2bd3 a3c3-a3bd2 a4c2-a3b2d |
o4 : Ideal
i5 = removeLowestDimension I
o5 = ideal | bc-ad c3-bd2 ac2-b2d b3-a2c |
o5 : Ideal
i6 = top I
o6 = ideal | bc-ad c3-bd2 ac2-b2d b3-a2c |
o6 : Ideal
i7 = radical I
o7 = ideal | bc-ad ac2-b2d b3-a2c c6-c3d3-b2d4+bd5 |
o7 : Ideal
i8 = decompose I
o8 = {ideal | -c+d b a |,ideal | c2+cd+d2 b a |,ideal | bc-ad c3-bd2 ac2-b2d b3-a2c |}
o8 : List
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