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identityDGAlgebraMap -- The identity DGAlgebraMap on a DG algebra

Description

Returns the identity self-map of A as a DGAlgebraMap. Under the hood the underlying RingMap A.natural -> A.natural is the identity map on every generator (including the base-ring generators).

i1 : R = QQ[x,y]/ideal(x^2,y^2)

o1 = R

o1 : QuotientRing
 
i2 : A = koszulComplexDGA R

o2 = {Ring => R                          }
      Underlying algebra => R[T   ..T   ]
                               1,1   1,2
      Differential => {x, y}

o2 : DGAlgebra
 
i3 : idA = identityDGAlgebraMap A

o3 = map (R[T   ..T   ], R[T   ..T   ], {T   , T   , x, y})
             1,1   1,2      1,1   1,2     1,1   1,2

o3 : DGAlgebraMap
 
i4 : (idA * idA) == idA

o4 = true

See also

Ways to use identityDGAlgebraMap:

  • identityDGAlgebraMap(DGAlgebra)

For the programmer

The object identityDGAlgebraMap is a method function.

The source of this document is in /build/reproducible-path/macaulay2-1.26.05+ds/M2/Macaulay2/packages/DGAlgebras/doc.m2:580:0.