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# id -- identity map

## Synopsis

• Usage:
id_F
• Inputs:
• Outputs:
• , , or the identity map on F

## Description

 i1 : R = QQ[a..d]; i2 : id_R o2 = map (R, R, {a, b, c, d}) o2 : RingMap R <-- R i3 : id_(R^3) o3 = | 1 0 0 | | 0 1 0 | | 0 0 1 | 3 3 o3 : Matrix R <-- R i4 : C = res coker vars R 1 4 6 4 1 o4 = R <-- R <-- R <-- R <-- R <-- 0 0 1 2 3 4 5 o4 : ChainComplex i5 : id_C 1 1 o5 = 0 : R <--------- R : 0 | 1 | 4 4 1 : R <------------------- R : 1 {1} | 1 0 0 0 | {1} | 0 1 0 0 | {1} | 0 0 1 0 | {1} | 0 0 0 1 | 6 6 2 : R <----------------------- R : 2 {2} | 1 0 0 0 0 0 | {2} | 0 1 0 0 0 0 | {2} | 0 0 1 0 0 0 | {2} | 0 0 0 1 0 0 | {2} | 0 0 0 0 1 0 | {2} | 0 0 0 0 0 1 | 4 4 3 : R <------------------- R : 3 {3} | 1 0 0 0 | {3} | 0 1 0 0 | {3} | 0 0 1 0 | {3} | 0 0 0 1 | 1 1 4 : R <------------- R : 4 {4} | 1 | 5 : 0 <----- 0 : 5 0 o5 : ChainComplexMap

## Ways to use id :

• id _ ChainComplex
• id _ Module
• id _ Ring
• id _ CoherentSheaf (missing documentation)

## For the programmer

The object id is .