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Macaulay2Doc :: isWellDefined

isWellDefined -- whether a map is well defined

Synopsis

Description

In order to check whether a matrix, whose source module is not free, is well defined, then a Gröbner basis computation will probably be required.
i1 : R = QQ[a..d];
i2 : f = map(R^1,coker vars R,{{1_R}})

o2 = | 1 |

o2 : Matrix
i3 : isWellDefined f

o3 = false
i4 : isWellDefined map(coker vars R, R^1, {{1_R}})

o4 = true
In order to check whether a ring map is well defined, it is often necessary to check that the image of an ideal under a related ring map is zero. This often requires a Gröbner basis as well.
i5 : A = ZZ/5[a]

o5 = A

o5 : PolynomialRing
i6 : factor(a^3-a-2)

       3
o6 = (a  - a - 2)

o6 : Expression of class Product
i7 : B = A/(a^3-a-2);
i8 : isWellDefined map(A,B)

o8 = false
i9 : isWellDefined map(B,A)

o9 = true

See also

Ways to use isWellDefined :