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Macaulay2Doc :: Ideal / Ideal

Ideal / Ideal -- quotient module

Synopsis

Description

i1 : R = QQ[a,b,c]

o1 = R

o1 : PolynomialRing
i2 : I = ideal vars R

o2 = ideal (a, b, c)

o2 : Ideal of R
i3 : M = I / I^2

o3 = subquotient (| a b c |, | a2 ab ac b2 bc c2 |)

                               1
o3 : R-module, subquotient of R
There is a diffference between typing I/J and (I+J)/J in Macaulay2, although conceptually they are the same module. The former has as its generating set the generators of I, while the latter has as its (redundant) generators the generators of I and J. Generally, the former method is preferable.
i4 : gens M

o4 = | a b c |

             1       3
o4 : Matrix R  <--- R
i5 : N = (I + I^2)/I^2

o5 = subquotient (| a b c a2 ab ac b2 bc c2 |, | a2 ab ac b2 bc c2 |)

                               1
o5 : R-module, subquotient of R
i6 : gens N

o6 = | a b c a2 ab ac b2 bc c2 |

             1       9
o6 : Matrix R  <--- R

See also