Description
If A is not present, then it is understood to be the ultimate ambient polynomial ring of B. In general, A may be any ring of which B is a quotient.
In the examples below, A is the ultimate ambient polynomial ring of A, B and C.
i1 : A = QQ[a..d];
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i2 : B = A/(a^2,b^3);
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i3 : C = B/(a*b*c,b*c*d, b^2);
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i4 : presentation A
o4 = 0
1
o4 : Matrix A <-- 0
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i5 : presentation B
o5 = | a2 b3 |
1 2
o5 : Matrix A <-- A
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i6 : presentation C
o6 = | abc bcd b2 a2 b3 |
1 5
o6 : Matrix A <-- A
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i7 : presentation(B,C)
o7 = | abc bcd b2 |
1 3
o7 : Matrix B <-- B
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i8 : presentation(A,C)
o8 = | abc bcd b2 a2 b3 |
1 5
o8 : Matrix A <-- A
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i9 : minimalPresentation C
QQ[a..d]
o9 = --------------------------
2 3 2
(a , b , a*b*c, b*c*d, b )
o9 : QuotientRing
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