isIdeal Module -- whether something is an ideal

isIdeal Module -- whether something is an ideal

Synopsis:

Usage: b = isIdeal(M)

Function: isIdeal -- whether something is an ideal

Input:

M, an instance of class Module.

Output:

b, an instance of class Boolean: whether M is evidently an ideal.

No computation is done. This routine checks the given description of M to see if it is an ideal.

i1 : R = QQ[a..d]/(a*b*c*d);

i2 : I = ideal(a^2,b^2) * R^1



o2 = image | a2 b2 |



                             1

o2 : R-module, submodule of R

i3 : isIdeal I



o3 = true

i4 : J = a^2 * R^2 + a*b * R^2



o4 = image | a2 0  ab 0  |

           | 0  a2 0  ab |



                             2

o4 : R-module, submodule of R

i5 : isIdeal J



o5 = false

Code:

     -- ../../../Macaulay2/m2/modules.m2:45
     isIdeal Module := M -> isSubmodule M and rank ambient M === 1