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**MatricesForHomalg
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Chapter 1.
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Chapter 2.

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Chapter 3.

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Chapter 4.
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Chapter 5.
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[46] [47] [48] [49] [50] [51]
Chapter 6.
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Appendix A.
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Appendix B.
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t/m/n/10.95 GetRowIndependentUnitPositions \T1/ptm/m/n/10.95 is bound then the 
stan-dard method
 []


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\T1/ptm/m/n/10.95 of the op-er-a-tion \T1/cmtt/m/n/10.95 GetRowIndependentUnitP
ositions \T1/ptm/m/n/10.95 ([][]5.5.19[][]) shown be-low re-turns
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[67] [68]
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[]\T1/ptm/m/n/10.95 Let $\OML/ztmcm/m/it/10.95 R \OT1/ztmcm/m/n/10.95 :=$ \T1/c
mtt/m/n/10.95 HomalgRing$\OT1/ztmcm/m/n/10.95 ([])$ \T1/ptm/m/n/10.95 and $\OML
/ztmcm/m/it/10.95 RP \OT1/ztmcm/m/n/10.95 :=$ \T1/cmtt/m/n/10.95 homalgTable$\O
T1/ztmcm/m/n/10.95 (\OML/ztmcm/m/it/10.95 R\OT1/ztmcm/m/n/10.95 )$\T1/ptm/m/n/1
0.95 . If the \T1/cmtt/m/n/10.95 homalgTable \T1/ptm/m/n/10.95 com-
 []


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\T1/ptm/m/n/10.95 po-nent $\OML/ztmcm/m/it/10.95 RP$\T1/ptm/m/n/10.95 !.\T1/cmt
t/m/n/10.95 PositionOfFirstNonZeroEntryPerRow \T1/ptm/m/n/10.95 is bound then t
he stan-dard method
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\T1/ptm/m/n/10.95 of the at-tribute \T1/cmtt/m/n/10.95 PositionOfFirstNonZeroEn
tryPerRow \T1/ptm/m/n/10.95 ([][]5.4.8[][]) shown be-low re-turns
 []

[69]
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[]\T1/ptm/m/n/10.95 Let $\OML/ztmcm/m/it/10.95 R \OT1/ztmcm/m/n/10.95 :=$ \T1/c
mtt/m/n/10.95 HomalgRing$\OT1/ztmcm/m/n/10.95 ([])$ \T1/ptm/m/n/10.95 and $\OML
/ztmcm/m/it/10.95 RP \OT1/ztmcm/m/n/10.95 :=$ \T1/cmtt/m/n/10.95 homalgTable$\O
T1/ztmcm/m/n/10.95 (\OML/ztmcm/m/it/10.95 R\OT1/ztmcm/m/n/10.95 )$\T1/ptm/m/n/1
0.95 . If the \T1/cmtt/m/n/10.95 homalgTable \T1/ptm/m/n/10.95 com-
 []


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\T1/ptm/m/n/10.95 po-nent $\OML/ztmcm/m/it/10.95 RP$\T1/ptm/m/n/10.95 !.\T1/cmt
t/m/n/10.95 PositionOfFirstNonZeroEntryPerColumn \T1/ptm/m/n/10.95 is bound the
n the stan-dard method
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\T1/ptm/m/n/10.95 of the at-tribute \T1/cmtt/m/n/10.95 PositionOfFirstNonZeroEn
tryPerColumn \T1/ptm/m/n/10.95 ([][]5.4.9[][]) shown be-low re-turns
 []

[70] [71]
Appendix C.

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[]\T1/ptm/m/n/10.95 In case the ma-trix [] was cre-ated us-ing \T1/cmtt/m/n/10.
95 HomalgInitialMatrix \T1/ptm/m/n/10.95 ([][]5.2.1[][]) then the fil-ter
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[72

]
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\T1/ptm/m/n/10.95 fil-ter \T1/cmtt/m/n/10.95 IsInitialIdentityMatrix \T1/ptm/m/
n/10.95 for [] is set to true and the \T1/cmtt/m/n/10.95 homalgTable \T1/ptm/m/
n/10.95 func-tion ($\OMS/ztmcm/m/n/10.95 !$
 []

[73] [74] [75]
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[]\T1/ptm/m/n/10.95 In case the ma-trix [] was cre-ated us-ing \T1/cmtt/m/n/10.
95 LeftInverseLazy \T1/ptm/m/n/10.95 ([][]5.5.4[][]) then the fil-ter
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[76]
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[]\T1/ptm/m/n/10.95 In case the ma-trix [] was cre-ated us-ing \T1/cmtt/m/n/10.
95 RightInverseLazy \T1/ptm/m/n/10.95 ([][]5.5.5[][]) then the fil-ter
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[77] [78]
Underfull \hbox (badness 10000) in paragraph at lines 6119--6120
[]\T1/ptm/m/n/10.95 In case the ma-trix was cre-ated us-ing \T1/cmtt/m/n/10.95 
CertainColumns \T1/ptm/m/n/10.95 ([][]5.5.8[][]) then the fil-ter
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[79]
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[]\T1/ptm/m/n/10.95 In case the ma-trix was cre-ated us-ing \T1/cmtt/m/n/10.95 
UnionOfColumns \T1/ptm/m/n/10.95 ([][]5.5.10[][]) then the fil-ter
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[80] [81]
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[]\T1/ptm/m/n/10.95 In case the ma-trix was cre-ated us-ing \T1/cmtt/m/n/10.95 
KroneckerMat \T1/ptm/m/n/10.95 ([][]5.5.12[][]) then the fil-ter
 []


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\T1/cmtt/m/n/10.95 HasEvalKroneckerMat \T1/ptm/m/n/10.95 for [] is set to true 
and the \T1/cmtt/m/n/10.95 homalgTable \T1/ptm/m/n/10.95 func-tion \T1/cmtt/m/n
/10.95 KroneckerMat
 []

[82] [83] [84] [85] [86]
Appendix D.
[87

] [88] [89] [90] [91] [92] [93] [94] [95] [96] [97] [98] [99] [100]
Appendix E.

Underfull \hbox (badness 10000) in paragraph at lines 7656--7661

 []


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 []


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[101

] [102]
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[103] [104]
Appendix F.
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[105

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[]\T1/cmtt/m/n/10.95 Basis\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Algorithm\T1/pt
m/m/n/10.95 -\T1/cmtt/m/n/10.95 Respects\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 P
rincipal\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Ideals\T1/ptm/m/n/10.95 ,
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[]\T1/cmtt/m/n/10.95 Coefficients\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Of\T1/pt
m/m/n/10.95 -\T1/cmtt/m/n/10.95 Numerator\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 
Of\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Hilbert\T1/ptm/m/n/10.95 -
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m/m/n/10.95 -\T1/cmtt/m/n/10.95 Unreduced\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 
Numerator\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Of\T1/ptm/m/n/10.95 -
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] [110]
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95 Variables\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Of\T1/ptm/m/n/10.95 -
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[]\T1/cmtt/m/n/10.95 IsHomalg\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Ring\T1/ptm/
m/n/10.95 -\T1/cmtt/m/n/10.95 Relations\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 As
\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Generators\T1/ptm/m/n/10.95 -\T1/cmtt/m/n
/10.95 Of\T1/ptm/m/n/10.95 -
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[]\T1/cmtt/m/n/10.95 IsHomalg\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Ring\T1/ptm/
m/n/10.95 -\T1/cmtt/m/n/10.95 Relations\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 As
\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Generators\T1/ptm/m/n/10.95 -\T1/cmtt/m/n
/10.95 Of\T1/ptm/m/n/10.95 -
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[111]
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n/10.95 -\T1/cmtt/m/n/10.95 First\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Non\T1/p
tm/m/n/10.95 -\T1/cmtt/m/n/10.95 Zero\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Entr
y\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95 Per\T1/ptm/m/n/10.95 -\T1/cmtt/m/n/10.95
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