isWellDefined -- whether a map is well defined

Usage:

isWellDefined f
Inputs:
- f, a matrix or a ring map
Outputs:
- a Boolean value, whether f is a well-defined map

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

Ways to use isWellDefined:

isWellDefined(Matrix)
isWellDefined(RingMap)

For the programmer

The object isWellDefined is a method function.

The source of this document is in Macaulay2Doc/functions/isWellDefined-doc.m2:39:0.

isWellDefined -- whether a map is well defined

Description

See also

Ways to use isWellDefined:

For the programmer