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

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..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

Ways to use this method:

The source of this document is in /__w/M2/M2/macaulay2-1.26.05+ds/M2/Macaulay2/packages/Macaulay2Doc/functions/presentation-doc.m2:52:0.