image(SimplicialMap) -- construct the image of a simplicial map

Synopsis

• Function: image

• Usage:

  image f

• Inputs:
  • f, a map of abstract simplicial complexes,
• Outputs:
  • an abstract simplicial complex, the image of the source of $f$ in the target of $f$

Description

i1 : R = ZZ/229[a,b,c];

i2 : D = simplicialComplex{a*b*c}

o2 = simplicialComplex | abc |

o2 : SimplicialComplex

i3 : E = simplicialComplex{a*b,b*c}

o3 = simplicialComplex | bc ab |

o3 : SimplicialComplex

i4 : f = map(E,D,{a,b,a})

o4 = | a b a |

o4 : SimplicialMap simplicialComplex | bc ab | <--- simplicialComplex | abc |

i5 : isWellDefined f

o5 = true

i6 : image f

o6 = simplicialComplex | ab |

o6 : SimplicialComplex

See also

• Working with simplicial maps -- information about simplicial maps and the induced operations
• source(SimplicialMap) -- get the source of the map
• target(SimplicialMap) -- get the target of the map
• isInjective(SimplicialMap) -- checks if a simplicial map is injective
• isSurjective(SimplicialMap) -- checks if a simplicial map is surjective