<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AlmostSplitSequence</code>( <var class="Arg">M</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<div class="func"><table class="func" width="100%"><tr><td class="tdleft"><code class="func">‣ AlmostSplitSequence</code>( <var class="Arg">M</var>, <var class="Arg">e</var> )</td><td class="tdright">( attribute )</td></tr></table></div>
<p>Arguments: <var class="Arg">M</var> - an indecomposable non-projective module, <var class="Arg">e</var> - either l = left or r = right<br /></p>
<p>Returns: the almost split sequence ending in the module <var class="Arg">M</var> if it is indecomposable and not projective, for the first variant. The second variant finds the almost split sequence starting or ending in the module <var class="Arg">M</var> depending on whether the second argument <var class="Arg">e</var> is l or r (l = almost split sequence starting with <var class="Arg">M</var>, or r = almost split sequence ending in <var class="Arg">M</var>), if the module is indecomposable and not injective or not projective, respectively. It returns fail if the module is injective (l) or projective (r).</p>
<p>The almost split sequence is returned as a pair of maps, the monomorphism and the epimorphism. The function assumes that the module <var class="Arg">M</var> is indecomposable, and the source of the monomorphism (l) or the range of the epimorphism (r) is a module that is isomorphic to <var class="Arg">M</var>, not necessarily identical.</p>
<p>Returns: the almost split sequence in <span class="Math">^\perp T</span> ending in the module <var class="Arg">M</var>, if the module is indecomposable and not projective (that is, not projective object in <span class="Math">^\perp T</span>). It returns fail if the module <var class="Arg">M</var> is in <span class="Math">\add T</span> projective. The almost split sequence is returned as a pair of maps, the monomorphism and the epimorphism, and the range of the epimorphism is a module that is isomorphic to the input, not necessarily identical.</p>
<p>The function assumes that the module <var class="Arg">M</var> is indecomposable and in <span class="Math">^\perp T</span>, and the range of the epimorphism is a module that is isomorphic to the input, not necessarily identical.</p>
<p>Returns: the collection of irreducible morphisms ending and starting in the module <var class="Arg">M</var>, respectively. The argument is assumed to be an indecomposable module.</p>
<p>The irreducible morphisms are returned as a list of maps. Even in the case of only one irreducible morphism, it is returned as a list. The function assumes that the module <var class="Arg">M</var> is indecomposable over a quiver algebra with a finite field as the ground ring.</p>
<p>Returns: <code class="code">i</code>, where <code class="code">i</code> is the smallest positive integer less or equal <code class="code">n</code> such that the representation <var class="Arg">M</var> is isomorphic to the <span class="SimpleMath">τ^i(M)</span>, and false otherwise.</p>
<p>Returns: the predecessors of the module <var class="Arg">M</var> in the AR-quiver of the algebra <var class="Arg">M</var> is given over of distance less or equal to <var class="Arg">n</var>.</p>
<p>It returns two lists, the first is the indecomposable modules in the different layers and the second is the valuations for the arrows in the AR-quiver. The different entries in the first list are the modules at distance zero, one, two, three, and so on, until layer <var class="Arg">n</var>. The <code class="code">m</code>-th entry in the second list is the valuations of the irreducible morphism from indecomposable module number <code class="code">i</code> in layer <code class="code">m+1</code> to indecomposable module number <code class="code">j</code> in layer <code class="code">m</code> for the values of <code class="code">i</code> and <code class="code">j</code> there is an irreducible morphism. Whenever <code class="code">false</code> occur in the output, it means that this valuation has not been computed. The function assumes that the module <var class="Arg">M</var> is indecomposable and that the quotient of the path algebra is given over a finite field.</p>
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