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normalize -- normalize a ChainComplex over QQ or RR

Synopsis

• Usage:
B = normalize C
• Inputs:
• C, , over RR or QQ
• Outputs:
• B, , an isomorphic ChainComplex over QQ or RR

Description

We divide each matrix by its entry of maximal absolute value, to obtain a complex with entries of absolute size $\le 1$.

 i1 : setRandomSeed "nice example 2"; i2 : C=randomChainComplex({1,1,1},{2,2}) 3 5 3 o2 = ZZ <-- ZZ <-- ZZ 0 1 2 o2 : ChainComplex i3 : C.dd 3 5 o3 = 0 : ZZ <------------------------- ZZ : 1 | -14 -7 5 5 3 | | 8 13 1 -17 -21 | | -13 -15 1 18 21 | 5 3 1 : ZZ <------------------- ZZ : 2 | -11 5 -10 | | 26 -29 37 | | 19 -16 23 | | -41 -1 -22 | | 46 -16 38 | o3 : ChainComplexMap i4 : B=normalize C 3 5 3 o4 = QQ <-- QQ <-- QQ 0 1 2 o4 : ChainComplex i5 : B.dd 3 5 o5 = 0 : QQ <------------------------------------ QQ : 1 | -2/3 -1/3 5/21 5/21 1/7 | | 8/21 13/21 1/21 -17/21 -1 | | -13/21 -5/7 1/21 6/7 1 | 5 3 1 : QQ <---------------------------- QQ : 2 | -11/46 5/46 -5/23 | | 13/23 -29/46 37/46 | | 19/46 -8/23 1/2 | | -41/46 -1/46 -11/23 | | 1 -8/23 19/23 | o5 : ChainComplexMap

Ways to use normalize :

• normalize(ChainComplex)

For the programmer

The object normalize is .