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products/Sources/formale Sprachen/GAP/pkg/homalg/doc/ (GAP Algebra Version 4.15.1^©) Datei vom 10.0.2024 mit Größe 35 kB

Quelle chap6_mj.html

Sprache: HTML

products/Sources/formale Sprachen/GAP/pkg/homalg/doc/chap6_mj.html

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<p>The fourth syntax creates

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<span
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&A3 4 anring;
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&of right&;
<span class="GAPprompt">gap></span> <span class="GAPinput">IsMorphism( phi );</span>
true
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java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 0
< <

<p>Check

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<h5>6.3-8 IsShortExactSequence</h5

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<p>Check

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<h5>6.3-9 IsSplitShortExactSequence

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<p>In [ 0 .. 1 ]&

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Z
< =java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
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<
----------
at
2java.lang.StringIndexOutOfBoundsException: Index 9 out of bounds for length 9
-----
[
  [  0,  0class=""java.lang.StringIndexOutOfBoundsException: Range [5, 4) out of bounds for length 25

the map is currently java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 0
----v------java.lang.StringIndexOutOfBoundsException: Index 25 out of bounds for length 25
at homology java.lang.StringIndexOutOfBoundsException: Range [0, 18) out of bounds for length 7
Z^(1 x 2)
------
[ java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
  [0 0 ]]

the map is <  java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 80
------------v----->/
java.lang.StringIndexOutOfBoundsException: Index 2 out of bounds for length 0
Z( 2
-------------------------
<java.lang.StringIndexOutOfBoundsException: Index 1 out of bounds for length 0
p><a id="div f"<java.lang.StringIndexOutOfBoundsException: Range [25, 24) out of bounds for length 227
<span java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0

<span class="GAPprompt">gap></span> java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
false
<span class="GAPprompt  java.lang.StringIndexOutOfBoundsException: Range [28, 25) out of bounds for length 28
morphismsleftjava.lang.StringIndexOutOfBoundsException: Range [73, 69) out of bounds for length 80
2];
pre/

<p>java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<h5>6.5-2 java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<div class="func"
<p>Returns>.3 IsSplitShortExactSequence

<p>java.lang.StringIndexOutOfBoundsException: Index 4 out of bounds for length 0

<div class="example"><pre>
java.lang.StringIndexOutOfBoundsException: Index 6 out of bounds for length 0
        "for homalg complexesjava.lang.StringIndexOutOfBoundsException: Range [12, 11) out of bounds for length 99
        [ IsHomalgComplex

  (  )

    List( ( C   ;

    if Lengthp>:< class="odetrue<code<code class="code"span=>&t;/>=> =java.lang.StringIndexOutOfBoundsException: Range [84, 83) out of bounds for length 96
         );
    fi;

    IsZero( ;2x matrix

    return C;

end );
<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0

<p>This method performs side effects on its

<java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<G"gt/>< java.lang.StringIndexOutOfBoundsException: Range [51, 50) out of bounds for length 99
Z
<span class="GAPprompt">gap&&;A java.lang.StringIndexOutOfBoundsException: Range [23, 18) out of bounds for length 44
ringg;
<=">>/span>< ="APinput=( M>
<A non-torsion left module presented by 2 relations <>: <<p>Returns: <code>&t/anjava.lang.StringIndexOutOfBoundsException: Range [45, 44) out of bounds for length 87
<span class="GAPprompt">
&; 2x 4 matrix   g;
<span class="GAPpromptclass=Gjava.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 95
<A non leftmodule presented<A non-zero acyclic complex containing  java.lang.StringIndexOutOfBoundsException: Range [23, 22) out of bounds for length 82
<span "">gap&;/span> <pan =GAPinput">matjava.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<span class="GAPprompt">></span> <span class=  0  2 ,  ]
<span ="">gt<
<span =GAPprompt>;</> span=GAPinput0 3,6   <span>
<span classdiv class="func"><table class="func" width="100%"><tr><td class="tdleft"><code java.lang.StringIndexOutOfBoundsException: Index 81 out of bounds for length 21
&;A3x  matrix over  internalring;
<span class="GAPprompt">gap></span> <span class
<A "java.lang.StringIndexOutOfBoundsException: Index 11 out of bounds for length 0
<span class="GAPprompt">gap></span>
java.lang.StringIndexOutOfBoundsException: Index 13 out of bounds for length 4
<span class="java.lang.StringIndexOutOfBoundsException: Index 21 out of bounds for length 0
&; homomorphismofleft modules;
<="GAPprompt">gap></pan><span class="APinput> : ( phi);</span
<A -zeroacyclic  complex  a singleof left atde\
grees [ 0 .. 1 p>the syntax themorphism var class="></ is tothe ()chain  var ="java.lang.StringIndexOutOfBoundsException: Range [116, 115) out of bounds for length 691
<java.lang.StringIndexOutOfBoundsException: Range [6, 5) out of bounds for length 82
------------------
at homology degree: 1
[ [  2,  3,  Z
  [  5,  6,  7 ] ]

Cokernel of the map

Z^(1x2) --> Z^(1x3),

currently represented by the <A  of left modules&t
----------
[ [  0,  3,  6,  &tAnon-zero  complex containing a single morphism of left modules at  [0. 1 &;
  [  0,  2,  4,  6 ],
  [0  3 6,9 ]

the map is homology degree 1
----------------
at homology degree< class=""gap>----------
[ [[ 0, 0  0]java.lang.StringIndexOutOfBoundsException: Index 17 out of bounds for length 17
  [  6,java.lang.StringIndexOutOfBoundsException: Index 8 out of bounds for length 0

Cokernel of the map

Z^(1x2) --> Z^(1x4),

currentlyrepresented by the above matrix
----------    0,0] ]
</pre><divjava.lang.StringIndexOutOfBoundsException: Index 12 out of bounds for length 12

<p>And now:</p>

<div class=example"<pre>
<span class="GAPprompt">gap></span> <span class="java.lang.StringIndexOutOfBoundsException: Index 54 out of bounds for length 9
<  [  0,   ]]
grees [ 0 java.lang.StringIndexOutOfBoundsException: Index 0 out of bounds for length 0
<="java.lang.StringIndexOutOfBoundsException: Index 55 out of bounds for length 25
-------------------------
at homologydegree:1
Z/< 3 > + Z^(1 x 1)
------------------
[,java.lang.StringIndexOutOfBoundsException: Range [3, 2) out of bounds for length 21
  [  2<pan lass=chlinkprevnextbot>nbsp;<a href="chap0_mj.html">[Top of Book]</a>   <a href="chap0_mj.

the map is currently represented by the above 2 x 3 matrix
-------v---------
atfalse
Z/&span class="GAPprompt">gap></span> <span class="GAPinput">C;</span>
---------------------
</pre></div>

<div iv class="chlinkprevnextbot">div class=chlinkbot"span ="chlink1> Chapter: /span>a java.lang.StringIndexOutOfBoundsException: Index 69 out of bounds for length 12

<div <divclass"func">tableclass="func"="%>java.lang.StringIndexOutOfBoundsException: Range [0, 54) out of bounds for length 7

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