map(SimplicialMap) -- the underlying ring map associated to a simplicial map

Synopsis

• Function: map

• Usage:

  phi = map f

• Inputs:
  • f, a map of abstract simplicial complexes,
• Optional inputs:
  • Degree => ..., default value null, ignored
  • DegreeLift => ..., default value null, ignored
  • DegreeMap => ..., default value null, ignored
• Outputs:
  • phi, a ring map, a map from the ring of the source of $f$ to the ring of the target of $f$.

Description

i1 : S = ZZ/101[a,b,c,d];

i2 : Δ = simplexComplex(3,S)

o2 = simplicialComplex | abcd |

o2 : SimplicialComplex

i3 : f = map(Δ,Δ,matrix{{a,b,c,d}})

o3 = | a b c d |

o3 : SimplicialMap simplicialComplex | abcd | <--- simplicialComplex | abcd |

i4 : map f

o4 = map (S, S, {a, b, c, d})

o4 : RingMap S <-- S

See also

• Working with simplicial maps -- information about simplicial maps and the induced operations
• map(SimplicialComplex,SimplicialComplex,RingMap) -- create a simplicial map between simplicial complexes
• source(SimplicialMap) -- get the source of the map
• target(SimplicialMap) -- get the target of the map
• matrix(SimplicialMap) -- get the underlying map of rings
• isWellDefined(SimplicialMap) -- whether underlying data is uncontradictory