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presentation(PolynomialRing,QuotientRing) -- presentation of a quotient ring

Synopsis

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];
i2 : B = A/(a^2,b^3);
i3 : C = B/(a*b*c,b*c*d, b^2);
i4 : presentation A

o4 = 0

             1
o4 : Matrix A  <--- 0
i5 : presentation B

o5 = | a2 b3 |

             1       2
o5 : Matrix A  <--- A
i6 : presentation C

o6 = | abc bcd b2 a2 b3 |

             1       5
o6 : Matrix A  <--- A
i7 : presentation(B,C)

o7 = | abc bcd b2 |

             1       3
o7 : Matrix B  <--- B
i8 : presentation(A,C)

o8 = | abc bcd b2 a2 b3 |

             1       5
o8 : Matrix A  <--- A
i9 : minimalPresentation C

           QQ[a, b, c, d]
o9 = --------------------------
       2   3                 2
     (a , b , a*b*c, b*c*d, b )

o9 : QuotientRing

Caveat

The given presentation is often not minimal

See also