ideal(Module) -- converts a module to an ideal

Synopsis

• Function: ideal

• Usage:

  ideal M

• Inputs:
  • M, a module, which is a submodule of a free module of rank 1
• Outputs:
  • an ideal, given by the generators of M

Description

i1 : R = QQ[w,x,y,z];

i2 : f = map(R^1,R^3, matrix{{x^2-w*y, x*y-w*z, x*z-y^2}})

o2 = | x2-wy xy-wz -y2+xz |

             1      3
o2 : Matrix R  <-- R

i3 : image f

o3 = image | x2-wy xy-wz -y2+xz |

                             1
o3 : R-module, submodule of R

i4 : ideal image f

             2                      2
o4 = ideal (x  - w*y, x*y - w*z, - y  + x*z)

o4 : Ideal of R

See also

• generators(Module) -- the generator matrix of a module
• ambient -- ambient free module of a subquotient, or ambient ring
• isSubmodule -- whether a module is evidently a submodule of a free module
• isIdeal -- whether something is an ideal