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  <div class="section" id="manifolds">
<h1>Manifolds<a class="headerlink" href="#manifolds" title="Permalink to this headline">¶</a></h1>
<p>This is the Sage implementation of manifolds resulting from the
<a class="reference external" href="http://sagemanifolds.obspm.fr/">SageManifolds project</a>.
This section describes only the &#8220;manifold&#8221; part of SageManifolds;
the pure algebraic part is described in the section
<a class="reference external" href="../tensor_free_modules/index.html#tensors-on-free-modules" title="(in Sage Reference Manual: Tensors on free modules of finite rank v6.8)"><em>Tensors on free modules of finite rank</em></a>.</p>
<p>More documentation (in particular example worksheets) can be found
<a class="reference external" href="http://sagemanifolds.obspm.fr/documentation.html">here</a>.</p>
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<li class="toctree-l1"><a class="reference internal" href="manifold.html">Topological manifolds</a><ul>
<li class="toctree-l2"><a class="reference internal" href="sage/manifolds/manifold.html">Topological manifolds</a></li>
<li class="toctree-l2"><a class="reference internal" href="sage/manifolds/point.html">Points of topological manifolds</a></li>
<li class="toctree-l2"><a class="reference internal" href="sage/manifolds/subset.html">Subsets of topological manifolds</a></li>
<li class="toctree-l2"><a class="reference internal" href="chart.html">Coordinate charts</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/chart.html">Coordinate charts</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/coord_func.html">Coordinate functions</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/coord_func_symb.html">Symbolic coordinate functions</a></li>
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<li class="toctree-l2"><a class="reference internal" href="scalarfield.html">Scalar fields</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/scalarfield_algebra.html">Scalar field algebra</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/scalarfield.html">Scalar fields</a></li>
</ul>
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<li class="toctree-l2"><a class="reference internal" href="continuous_map.html">Continuous maps</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/manifold_homset.html">Sets of morphisms between topologial manifolds</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/continuous_map.html">Continuous maps between topological manifolds</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="diff_manifold.html">Differentiable manifolds</a><ul>
<li class="toctree-l2"><a class="reference internal" href="sage/manifolds/differentiable/manifold.html">Differentiable manifolds</a></li>
<li class="toctree-l2"><a class="reference internal" href="sage/manifolds/differentiable/chart.html">Coordinate charts on differentiable manifolds</a></li>
<li class="toctree-l2"><a class="reference internal" href="sage/manifolds/differentiable/real_line.html">The real line and open intervals</a></li>
<li class="toctree-l2"><a class="reference internal" href="diff_scalarfield.html">Scalar fields</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/scalarfield_algebra.html">Algebra of differentiable scalar fields</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/scalarfield.html">Differentiable scalar fields</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="diff_map.html">Differentiable maps and curves</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/manifold_homset.html">Sets of morphisms between differentiable manifolds</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/diff_map.html">Differentiable maps between differentiable manifolds</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/curve.html">Curves in manifolds</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="tangent_space.html">Tangent spaces</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/tangent_space.html">Tangent spaces</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/tangent_vector.html">Tangent vectors</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="vectorfield.html">Vector fields</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/vectorfield_module.html">Vector field modules</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/vectorfield.html">Vector fields</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/vectorframe.html">Vector frames</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/automorphismfield_group.html">Group of tangent-space automorphism fields</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/automorphismfield.html">Tangent-space automorphism fields</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="tensorfield.html">Tensor fields</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/tensorfield_module.html">Tensor field modules</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/tensorfield.html">Tensor fields</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/tensorfield_paral.html">Tensor fields with values on a parallelizable manifold</a></li>
</ul>
</li>
<li class="toctree-l2"><a class="reference internal" href="diff_form.html">Differential forms</a><ul>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/diff_form_module.html">Differential form modules</a></li>
<li class="toctree-l3"><a class="reference internal" href="sage/manifolds/differentiable/diff_form.html">Differential forms</a></li>
</ul>
</li>
</ul>
</li>
<li class="toctree-l1"><a class="reference internal" href="sage/manifolds/utilities.html">Utilities for calculus</a></li>
</ul>
</div>
</div>
<div class="section" id="indices-and-tables">
<h1>Indices and Tables<a class="headerlink" href="#indices-and-tables" title="Permalink to this headline">¶</a></h1>
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