image(DifferentialModule) -- computes the image of the differential of a differential module

Synopsis

• Function: image

• Usage:

  image D

• Inputs:
  • D, a differential module,
• Outputs:
  • a module,

Description

i1 : R = QQ[x,y]

o1 = R

o1 : PolynomialRing

i2 : M = R^1/ideal(x^2,y^2)

o2 = cokernel | x2 y2 |

                            1
o2 : R-module, quotient of R

i3 : phi = map(M,M,x*y, Degree => 2)

o3 = | xy |

o3 : Matrix M <-- M

i4 : D = differentialModule phi

o4 = M  <-- M <-- M
                   
     -1     0     1

o4 : DifferentialModule

i5 : D' = image D

o5 = subquotient (| xy |, | x2 y2 |)

                               1
o5 : R-module, subquotient of R

See also

• differential(DifferentialModule) -- returns the differential of a differential module
• image(DifferentialModule) -- computes the image of the differential of a differential module
• kernel(DifferentialModule) -- computes the kernel of the differential in a differential module.