i1 : k = toField (QQ[x]/(x^2+x+1));
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i2 : R = k[y]/(x-y+2);
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i3 : flattenRing(R, Result => 1)
o3 = R
o3 : QuotientRing
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i4 : flattenRing(R, Result => 2)
o4 = (R, map (R, R, {x + 2, x}))
o4 : Sequence
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i5 : flattenRing(R, Result => 3)
o5 = (R, map (R, R, {x + 2, x}), map (R, R, {x + 2, x}))
o5 : Sequence
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i6 : flattenRing(R, Result => (Nothing, RingMap))
o6 = (, map (k[y], R, {x + 2, x}))
o6 : Sequence
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i7 : flattenRing(R, Result => (Ring, Nothing, RingMap))
o7 = (R, , map (R, R, {x + 2, x}))
o7 : Sequence
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i8 : flattenRing(R, Result => (Nothing, ))
o8 = (, map (k[y], R, {x + 2, x}))
o8 : Sequence
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i9 : flattenRing(R, Result => ( , Nothing, ) )
o9 = (R, , map (R, R, {x + 2, x}))
o9 : Sequence
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i10 : I = ideal(x*y+y^2-5);
o10 : Ideal of R
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i11 : flattenRing(I, Result => 1)
o11 = ideal (- y + x + 2, 4x - 3)
o11 : Ideal of k[y]
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i12 : flattenRing(I, Result => 3)
o12 = (ideal (- y + x + 2, 4x - 3), map (k[y], R, {x + 2, x}), map (R, k[y],
-----------------------------------------------------------------------
{x + 2, x}))
o12 : Sequence
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i13 : flattenRing(I, Result => (Ring, Nothing, RingMap))
k[y] k[y]
o13 = (---------------------, , map (R, ---------------------, {x + 2, x}))
(- y + x + 2, 4x - 3) (- y + x + 2, 4x - 3)
o13 : Sequence
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i14 : flattenRing(I, Result => (Ideal, Nothing, RingMap))
o14 = (ideal (- y + x + 2, 4x - 3), , map (R, k[y], {x + 2, x}))
o14 : Sequence
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i15 : flattenRing(I, Result => (Ring, RingMap))
k[y] k[y]
o15 = (---------------------, map (---------------------, R, {0, 0}))
(- y + x + 2, 4x - 3) (- y + x + 2, 4x - 3)
o15 : Sequence
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i16 : flattenRing(I, Result => Ideal)
o16 = ideal (- y + x + 2, 4x - 3)
o16 : Ideal of k[y]
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