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<li class="toctree-l2 current"><a class="current reference internal" href="#">Symbolic computation</a><ul>
<li class="toctree-l3"><a class="reference internal" href="#spatialmath.base.symbolic.cos"><code class="docutils literal notranslate"><span class="pre">cos()</span></code></a></li>
<li class="toctree-l3"><a class="reference internal" href="#spatialmath.base.symbolic.det"><code class="docutils literal notranslate"><span class="pre">det()</span></code></a></li>
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<section id="module-spatialmath.base.symbolic">
<span id="symbolic-computation"></span><h1>Symbolic computation<a class="headerlink" href="#module-spatialmath.base.symbolic" title="Permalink to this heading"></a></h1>
<p>This package provides a light-weight wrapper to support use of SymPy. It
generalizes some common functions so that they can accept numerical or
Symbolic arguments.</p>
<p>If SymPy is not installed then only the standard numeric operations are
supported.</p>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.cos">
<span class="sig-name descname"><span class="pre">cos</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#cos"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.cos" title="Permalink to this definition"></a></dt>
<dd><p>Generalized cosine function</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>θ</strong> (<em>float</em><em> or </em><em>symbolic</em>) – argument</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>cos(θ)</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float or symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">theta</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'theta'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">cos</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
<span class="go">cos(theta)</span>
<span class="gp">>>> </span><span class="n">cos</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="go">0.8775825618903728</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.cos()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.det">
<span class="sig-name descname"><span class="pre">det</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#det"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.det" title="Permalink to this definition"></a></dt>
<dd><p>Symbolic determinant</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>m</strong> – matrix</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>determinant</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>ndarray with symbolic elements</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span> File <span class="nb">"/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/sympy/simplify/simplify.py"</span>, line <span class="m">603</span>, in <span class="n">simplify</span>
<span class="w"> </span><span class="n">original_expr</span> <span class="o">=</span> <span class="n">expr</span> <span class="o">=</span> <span class="n">collect_abs</span><span class="p">(</span><span class="n">signsimp</span><span class="p">(</span><span class="n">expr</span><span class="p">))</span>
File <span class="nb">"/opt/hostedtoolcache/Python/3.8.18/x64/lib/python3.8/site-packages/sympy/simplify/radsimp.py"</span>, line <span class="m">625</span>, in <span class="n">collect_abs</span>
<span class="w"> </span><span class="k">return</span> <span class="n">expr</span><span class="o">.</span><span class="n">replace</span><span class="p">(</span>
<span class="gr">AttributeError</span>: <span class="n">'NoneType' object has no attribute 'replace'</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>Converts to a SymPy <code class="docutils literal notranslate"><span class="pre">Matrix</span></code> and then back again.</p>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.issymbol">
<span class="sig-name descname"><span class="pre">issymbol</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">var</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#issymbol"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.issymbol" title="Permalink to this definition"></a></dt>
<dd><p>Test if variable is symbolic</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>var</strong> (<span class="sphinx_autodoc_typehints-type"><code class="xref py py-data docutils literal notranslate"><span class="pre">Any</span></code></span>) – variable to test</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>whether variable is symbolic</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>bool</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">theta</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'theta'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">issymbol</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
<span class="go">True</span>
<span class="gp">>>> </span><span class="n">issymbol</span><span class="p">(</span><span class="mf">3.4</span><span class="p">)</span>
<span class="go">False</span>
</pre></div>
</div>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.negative_one">
<span class="sig-name descname"><span class="pre">negative_one</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#negative_one"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.negative_one" title="Permalink to this definition"></a></dt>
<dd><p>Symbolic constant: negative one</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>-1</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">negative_one</span><span class="p">()</span>
<span class="go">-1</span>
<span class="gp">>>> </span><span class="n">negative_one</span><span class="p">()</span> <span class="o">*</span> <span class="n">x</span>
<span class="go">-x</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.S.NegativeOne()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.one">
<span class="sig-name descname"><span class="pre">one</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#one"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.one" title="Permalink to this definition"></a></dt>
<dd><p>Symbolic constant: one</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>1</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">one</span><span class="p">()</span>
<span class="go">1</span>
<span class="gp">>>> </span><span class="n">one</span><span class="p">()</span> <span class="o">*</span> <span class="n">x</span>
<span class="go">x</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.S.One()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.pi">
<span class="sig-name descname"><span class="pre">pi</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#pi"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.pi" title="Permalink to this definition"></a></dt>
<dd><p>Symbolic constant: pi</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>π</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="kn">import</span><span class="w"> </span><span class="nn">math</span>
<span class="gp">>>> </span><span class="n">sin</span><span class="p">(</span><span class="n">pi</span><span class="p">())</span>
<span class="go">0</span>
<span class="gp">>>> </span><span class="n">sin</span><span class="p">(</span><span class="n">math</span><span class="o">.</span><span class="n">pi</span><span class="p">)</span>
<span class="go">1.2246467991473532e-16</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.S.Pi()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.simplify">
<span class="sig-name descname"><span class="pre">simplify</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">x</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#simplify"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.simplify" title="Permalink to this definition"></a></dt>
<dd><p>Symbolic simplification</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>x</strong> (<em>symbolic</em>) – expression to simplify</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>-1</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">y</span> <span class="o">=</span> <span class="p">(</span><span class="n">x</span> <span class="o">-</span> <span class="mi">1</span><span class="p">)</span> <span class="o">*</span> <span class="p">(</span><span class="n">x</span> <span class="o">+</span> <span class="mi">1</span><span class="p">)</span> <span class="o">-</span> <span class="n">x</span> <span class="o">**</span> <span class="mi">2</span>
<span class="gp">>>> </span><span class="n">y</span>
<span class="go">-x**2 + (x - 1)*(x + 1)</span>
<span class="gp">>>> </span><span class="n">simplify</span><span class="p">(</span><span class="n">y</span><span class="p">)</span>
<span class="go">-1</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.simplify()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.sin">
<span class="sig-name descname"><span class="pre">sin</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#sin"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.sin" title="Permalink to this definition"></a></dt>
<dd><p>Generalized sine function</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>θ</strong> (<em>float</em><em> or </em><em>symbolic</em>) – argument</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>sin(θ)</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float or symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">theta</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'theta'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sin</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
<span class="go">sin(theta)</span>
<span class="gp">>>> </span><span class="n">sin</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="go">0.479425538604203</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.sin()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.sqrt">
<span class="sig-name descname"><span class="pre">sqrt</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">v</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#sqrt"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.sqrt" title="Permalink to this definition"></a></dt>
<dd><p>Generalized sqrt function</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>v</strong> (<em>float</em><em> or </em><em>symbolic</em>) – argument</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>√ v</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float or symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">sqrt</span><span class="p">(</span><span class="n">x</span> <span class="o">**</span> <span class="mi">2</span><span class="p">)</span>
<span class="go">Abs(x)</span>
<span class="gp">>>> </span><span class="n">sqrt</span><span class="p">(</span><span class="mi">4</span><span class="p">)</span>
<span class="go">2.0</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.sqrt()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.symbol">
<span class="sig-name descname"><span class="pre">symbol</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">name</span></span></em>, <em class="sig-param"><span class="n"><span class="pre">real</span></span><span class="o"><span class="pre">=</span></span><span class="default_value"><span class="pre">True</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#symbol"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.symbol" title="Permalink to this definition"></a></dt>
<dd><p>Create symbolic variables</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><ul class="simple">
<li><p><strong>name</strong> (<em>str</em>) – symbol names</p></li>
<li><p><strong>real</strong> (<em>bool</em><em>, </em><em>optional</em>) – assume variable is real, defaults to True</p></li>
</ul>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>SymPy symbols</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>sympy</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">theta</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'theta'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">theta</span>
<span class="go">theta</span>
<span class="gp">>>> </span><span class="n">theta</span><span class="p">,</span> <span class="n">psi</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'theta psi'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">theta</span>
<span class="go">theta</span>
<span class="gp">>>> </span><span class="n">psi</span>
<span class="go">psi</span>
<span class="gp">>>> </span><span class="n">q</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'q_:6'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">q</span>
<span class="go">(q_0, q_1, q_2, q_3, q_4, q_5)</span>
</pre></div>
</div>
<div class="admonition note">
<p class="admonition-title">Note</p>
<p>In Jupyter symbols are pretty printed.</p>
<ul class="simple">
<li><p>symbols named after greek letters will appear as greek letters</p></li>
<li><p>underscore means subscript as it does in LaTex, so the symbols <code class="docutils literal notranslate"><span class="pre">q</span></code></p></li>
</ul>
<p>above will be subscripted.</p>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.symbols()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.tan">
<span class="sig-name descname"><span class="pre">tan</span></span><span class="sig-paren">(</span><em class="sig-param"><span class="n"><span class="pre">theta</span></span></em><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#tan"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.tan" title="Permalink to this definition"></a></dt>
<dd><p>Generalized tangent function</p>
<dl class="field-list simple">
<dt class="field-odd">Parameters<span class="colon">:</span></dt>
<dd class="field-odd"><p><strong>θ</strong> (<em>float</em><em> or </em><em>symbolic</em>) – argument</p>
</dd>
<dt class="field-even">Returns<span class="colon">:</span></dt>
<dd class="field-even"><p>tan(θ)</p>
</dd>
<dt class="field-odd">Return type<span class="colon">:</span></dt>
<dd class="field-odd"><p>float or symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">theta</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'theta'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">tan</span><span class="p">(</span><span class="n">theta</span><span class="p">)</span>
<span class="go">tan(theta)</span>
<span class="gp">>>> </span><span class="n">tan</span><span class="p">(</span><span class="mf">0.5</span><span class="p">)</span>
<span class="go">0.5463024898437905</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.cos()</span></code></p>
</dd>
</dl>
</dd></dl>
<dl class="py function">
<dt class="sig sig-object py" id="spatialmath.base.symbolic.zero">
<span class="sig-name descname"><span class="pre">zero</span></span><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="reference internal" href="_modules/spatialmath/base/symbolic.html#zero"><span class="viewcode-link"><span class="pre">[source]</span></span></a><a class="headerlink" href="#spatialmath.base.symbolic.zero" title="Permalink to this definition"></a></dt>
<dd><p>Symbolic constant: zero</p>
<dl class="field-list simple">
<dt class="field-odd">Returns<span class="colon">:</span></dt>
<dd class="field-odd"><p>0</p>
</dd>
<dt class="field-even">Return type<span class="colon">:</span></dt>
<dd class="field-even"><p>symbolic</p>
</dd>
</dl>
<div class="highlight-pycon notranslate"><div class="highlight"><pre><span></span><span class="gp">>>> </span><span class="kn">from</span><span class="w"> </span><span class="nn">spatialmath.base.symbolic</span><span class="w"> </span><span class="kn">import</span> <span class="o">*</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">=</span> <span class="n">symbol</span><span class="p">(</span><span class="s1">'x'</span><span class="p">)</span>
<span class="gp">>>> </span><span class="n">zero</span><span class="p">()</span>
<span class="go">0</span>
<span class="gp">>>> </span><span class="n">x</span> <span class="o">+</span> <span class="n">zero</span><span class="p">()</span>
<span class="go">x</span>
</pre></div>
</div>
<dl class="field-list simple">
<dt class="field-odd">Seealso<span class="colon">:</span></dt>
<dd class="field-odd"><p><code class="xref py py-func docutils literal notranslate"><span class="pre">sympy.S.Zero()</span></code></p>
</dd>
</dl>
</dd></dl>
</section>
</div>
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