source(DGAlgebraMap) -- The source of a DG algebra map

Function: source
Usage:

A = source phi
Inputs:
- phi, an instance of the type DGAlgebraMap,
Outputs:
- A, an instance of the type DGAlgebra, the source DG algebra of phi

Description

Returns the DGAlgebra from which phi is defined.

i1 : R = ZZ/101[a,b,c]/ideal{a^3, b^3, c^3}

o1 = R

o1 : QuotientRing

i2 : S = R / ideal{a^2*b^2*c^2}

o2 = S

o2 : QuotientRing

i3 : A = acyclicClosure(R, EndDegree => 2)

o3 = {Ring => R                                        }
      Underlying algebra => R[T   ..T   ]
                               1,1   2,3
                                 2       2       2
      Differential => {a, b, c, a T   , b T   , c T   }
                                   1,1     1,2     1,3

o3 : DGAlgebra

i4 : B = acyclicClosure(S, EndDegree => 2)

o4 = {Ring => S                                                                                    }
      Underlying algebra => S[T   ..T   , T   ..T   , T   ..T   ]
                               1,1   1,3   2,1   2,4   3,1   3,3
                                 2       2       2         2 2       2 2        2 2        2 2
      Differential => {a, b, c, a T   , b T   , c T   , a*b c T   , b c T   , -a b T   , -a c T   }
                                   1,1     1,2     1,3         1,1       2,1        2,3        2,2

o4 : DGAlgebra

i5 : phi = liftToDGMap(B, A, map(S, R))

o5 = map (S[T   ..T   , T   ..T   , T   ..T   ], R[T   ..T   ], {T   , T   , T   , T   , T   , T   , a, b, c})
             1,1   1,3   2,1   2,4   3,1   3,3      1,1   2,3     1,1   1,2   1,3   2,1   2,2   2,3

o5 : DGAlgebraMap

i6 : source phi === A

o6 = true

Ways to use this method:

source(DGAlgebraMap) -- The source of a DG algebra map

The source of this document is in DGAlgebras/doc.m2:9255:0.

source(DGAlgebraMap) -- The source of a DG algebra map

Description

See also

Ways to use this method: