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<div class="section" id="module-msinvar.iterators">
<span id="iterators"></span><h1>Iterators<a class="headerlink" href="#module-msinvar.iterators" title="Permalink to this headline">¶</a></h1>
<p>Collection of iterators.</p>
<p>EXAMPLES:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sage</span><span class="p">:</span> <span class="kn">from</span> <span class="nn">msinvar.iterators</span> <span class="kn">import</span> <span class="o">*</span>
<span class="n">sage</span><span class="p">:</span> <span class="nb">list</span><span class="p">(</span><span class="n">IntegerVectors_iterator</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">]))</span>
<span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</span>
</pre></div>
</div>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sage</span><span class="p">:</span> <span class="n">M</span><span class="o">=</span><span class="p">[[</span><span class="mi">1</span><span class="p">,</span><span class="mi">2</span><span class="p">,</span><span class="mi">1</span><span class="p">],[</span><span class="mi">3</span><span class="p">,</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">]]</span>
<span class="n">sage</span><span class="p">:</span> <span class="nb">list</span><span class="p">(</span><span class="n">Multiplicities_iterator</span><span class="p">(</span><span class="n">M</span><span class="p">,[</span><span class="mi">3</span><span class="p">,</span><span class="mi">4</span><span class="p">]))</span>
<span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span>
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span>
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span>
<span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">0</span><span class="p">,</span> <span class="mi">3</span><span class="p">]]</span>
</pre></div>
</div>
<dl class="py function">
<dt id="msinvar.iterators.IntegerVectors_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">IntegerVectors_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vect</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#IntegerVectors_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.IntegerVectors_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over integer vectors 0 < a <= vect</p>
<p>It is more efficient than
<code class="xref py py-meth docutils literal notranslate"><span class="pre">sage.combinat.vector_partition.IntegerVectorsIterator()</span></code>.</p>
<p><code class="docutils literal notranslate"><span class="pre">vect</span></code> – a list of integers.</p>
<p>EXAMPLES:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">sage</span><span class="p">:</span> <span class="kn">from</span> <span class="nn">msinvar.iterators</span> <span class="kn">import</span> <span class="o">*</span>
<span class="n">sage</span><span class="p">:</span> <span class="nb">list</span><span class="p">(</span><span class="n">IntegerVectors_iterator</span><span class="p">([</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">]))</span>
<span class="p">[[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">0</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">1</span><span class="p">],</span> <span class="p">[</span><span class="mi">0</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">1</span><span class="p">,</span> <span class="mi">2</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="p">,</span> <span class="mi">2</span><span class="p">]]</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.Multiplicities_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">Multiplicities_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">M</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">b</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#Multiplicities_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.Multiplicities_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over integer vectors a>0 such that M*a<=b,
where <code class="docutils literal notranslate"><span class="pre">M</span></code> is a matrix and <code class="docutils literal notranslate"><span class="pre">b</span></code> is a vector.</p>
<ul class="simple">
<li><p><code class="docutils literal notranslate"><span class="pre">M</span></code> – Matrix of size m x n</p></li>
<li><p><code class="docutils literal notranslate"><span class="pre">b</span></code> – Vector of size m</p></li>
</ul>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.OrderedMultiPartitionsLE_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">OrderedMultiPartitionsLE_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vect</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#OrderedMultiPartitionsLE_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.OrderedMultiPartitionsLE_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over collections of vectors
(a_1,..,a_k) such that a_1+..+a_k <= <code class="docutils literal notranslate"><span class="pre">vect</span></code> and a_i>0.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.OrderedMultiPartitions_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">OrderedMultiPartitions_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vect</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#OrderedMultiPartitions_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.OrderedMultiPartitions_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over collections of vectors
(a_1,…,a_k) such that a_1+…+a_k = <code class="docutils literal notranslate"><span class="pre">vect</span></code> and a_i>0.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.OrderedPartitionsLE_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">OrderedPartitionsLE_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#OrderedPartitionsLE_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.OrderedPartitionsLE_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over collections of positive numbers
(a_1,..,a_k) such that a_1+..+a_k <= <code class="docutils literal notranslate"><span class="pre">n</span></code>.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.OrderedPartitions_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">OrderedPartitions_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#OrderedPartitions_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.OrderedPartitions_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over collections of positive numbers
(a_1,…,a_k) such that a_1+…+a_k = <code class="docutils literal notranslate"><span class="pre">n</span></code>.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.MultiPartitionsLE_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">MultiPartitionsLE_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vect</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bound</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#MultiPartitionsLE_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.MultiPartitionsLE_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over collections of vectors
<code class="docutils literal notranslate"><span class="pre">bound</span></code>>=a_1 >=…>=a_k>0 such that a_1+…+a_k <= <code class="docutils literal notranslate"><span class="pre">vect</span></code>.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.MultiPartitions_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">MultiPartitions_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vect</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bound</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#MultiPartitions_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.MultiPartitions_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over collections of vectors
<code class="docutils literal notranslate"><span class="pre">bound</span></code>>=a_1>=…>=a_k>0 such that a_1+…+a_k = <code class="docutils literal notranslate"><span class="pre">vect</span></code>.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.Subsets_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">Subsets_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">n</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#Subsets_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.Subsets_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over non-empty subsets of the set {0,..,n-1}.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.ListPartitions_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">ListPartitions_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">l</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#ListPartitions_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.ListPartitions_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over collections of nonempty disjoint lists (l1,..,lk)
such that l1+…+lk= <code class="docutils literal notranslate"><span class="pre">l</span></code>.</p>
</dd></dl>
<dl class="py function">
<dt id="msinvar.iterators.UnorderedMultiPartitions_iterator">
<code class="sig-prename descclassname"><span class="pre">msinvar.iterators.</span></code><code class="sig-name descname"><span class="pre">UnorderedMultiPartitions_iterator</span></code><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">vect</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">bound</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">None</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/msinvar/iterators.html#UnorderedMultiPartitions_iterator"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#msinvar.iterators.UnorderedMultiPartitions_iterator" title="Permalink to this definition">¶</a></dt>
<dd><p>Iterator over sets of vectors
(a_1,…,a_k) such that a_1+…+a_k = <code class="docutils literal notranslate"><span class="pre">vect</span></code> and a_i>0.
We order vectors lexicographically.</p>
</dd></dl>
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