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<div class="section" id="module-esys.escript.symbolic">
<span id="esys-escript-symbolic-package"></span><h1>esys.escript.symbolic Package<a class="headerlink" href="#module-esys.escript.symbolic" title="Permalink to this headline">¶</a></h1>
<ul class="simple">
<li></li>
</ul>
<div class="section" id="classes">
<h2>Classes<a class="headerlink" href="#classes" title="Permalink to this headline">¶</a></h2>
<ul class="simple">
<li><a class="reference internal" href="#esys.escript.symbolic.Evaluator" title="esys.escript.symbolic.Evaluator"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Evaluator</span></code></a></li>
<li><a class="reference internal" href="#esys.escript.symbolic.Symbol" title="esys.escript.symbolic.Symbol"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Symbol</span></code></a></li>
</ul>
<dl class="class">
<dt id="esys.escript.symbolic.Evaluator">
<em class="property">class </em><code class="descclassname">esys.escript.symbolic.</code><code class="descname">Evaluator</code><span class="sig-paren">(</span><em>*expressions</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Evaluator" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<dl class="method">
<dt id="esys.escript.symbolic.Evaluator.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><em>*expressions</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Evaluator.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a symbolic evaluator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>expressions</strong> – optional expressions to initialise with</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Evaluator.addExpression">
<code class="descname">addExpression</code><span class="sig-paren">(</span><em>expression</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Evaluator.addExpression" title="Permalink to this definition">¶</a></dt>
<dd><p>Adds an expression to this evaluator.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">the modified Evaluator object</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Evaluator.evaluate">
<code class="descname">evaluate</code><span class="sig-paren">(</span><em>evalf=False</em>, <em>**args</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Evaluator.evaluate" title="Permalink to this definition">¶</a></dt>
<dd><p>Evaluates all expressions in this evaluator and returns the result
as a tuple.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">the evaluated expressions in the order they were added to
this Evaluator.</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Evaluator.subs">
<code class="descname">subs</code><span class="sig-paren">(</span><em>**args</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Evaluator.subs" title="Permalink to this definition">¶</a></dt>
<dd><p>Symbol substitution.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">the modified Evaluator object</td>
</tr>
</tbody>
</table>
</dd></dl>
</dd></dl>
<dl class="class">
<dt id="esys.escript.symbolic.Symbol">
<em class="property">class </em><code class="descclassname">esys.escript.symbolic.</code><code class="descname">Symbol</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol" title="Permalink to this definition">¶</a></dt>
<dd><p>Bases: <code class="xref py py-class docutils literal notranslate"><span class="pre">object</span></code></p>
<p><a class="reference internal" href="#esys.escript.symbolic.Symbol" title="esys.escript.symbolic.Symbol"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Symbol</span></code></a> objects are placeholders for a single mathematical symbol, such as
‘x’, or for arbitrarily complex mathematical expressions such as
‘c*x**4+alpha*exp(x)-2*sin(beta*x)’, where ‘alpha’, ‘beta’, ‘c’, and ‘x’
are also Symbols (the symbolic ‘atoms’ of the expression).</p>
<p>With the help of the ‘Evaluator’ class these symbols and expressions can
be resolved by substituting numeric values and/or escript <code class="xref py py-obj docutils literal notranslate"><span class="pre">Data</span></code> objects
for the atoms. To facilitate the use of <code class="xref py py-obj docutils literal notranslate"><span class="pre">Data</span></code> objects a <a class="reference internal" href="#esys.escript.symbolic.Symbol" title="esys.escript.symbolic.Symbol"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Symbol</span></code></a> has a
shape (and thus a rank) as well as a dimension (see constructor).
Symbols are useful to perform mathematical simplifications, compute
derivatives and as coefficients for nonlinear PDEs which can be solved by
the <code class="xref py py-obj docutils literal notranslate"><span class="pre">NonlinearPDE</span></code> class.</p>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.__init__">
<code class="descname">__init__</code><span class="sig-paren">(</span><em>*args</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.__init__" title="Permalink to this definition">¶</a></dt>
<dd><p>Initialises a new <a class="reference internal" href="#esys.escript.symbolic.Symbol" title="esys.escript.symbolic.Symbol"><code class="xref py py-obj docutils literal notranslate"><span class="pre">Symbol</span></code></a> object in one of three ways:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">u</span><span class="o">=</span><span class="n">Symbol</span><span class="p">(</span><span class="s1">'u'</span><span class="p">)</span>
</pre></div>
</div>
<p>returns a scalar symbol by the name ‘u’.</p>
<blockquote>
<div>alpha=Symbol(‘alpha’, (4,3))</div></blockquote>
<p>returns a rank 2 symbol with the shape (4,3), whose elements are
named ‘[alpha]_i_j’ (with i=0..3, j=0..2).</p>
<blockquote>
<div>a,b,c=symbols(‘a,b,c’)
x=Symbol([[a+b,0,0],[0,b-c,0],[0,0,c-a]])</div></blockquote>
<p>returns a rank 2 symbol with the shape (3,3) whose elements are
explicitly specified by numeric values and other symbols/expressions
within a list or numpy array.</p>
<p>The dimensionality of the symbol can be specified through the <code class="docutils literal notranslate"><span class="pre">dim</span></code>
keyword. All other keywords are passed to the underlying symbolic
library (currently sympy).</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><ul class="first last simple">
<li><strong>args</strong> – initialisation arguments as described above</li>
<li><strong>dim</strong> (<code class="docutils literal notranslate"><span class="pre">int</span></code>) – dimensionality of the new Symbol (default: 2)</li>
</ul>
</td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.applyfunc">
<code class="descname">applyfunc</code><span class="sig-paren">(</span><em>f</em>, <em>on_type=None</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.applyfunc" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the function <code class="xref py py-obj docutils literal notranslate"><span class="pre">f</span></code> to all elements (if on_type is None) or to
all elements of type <code class="xref py py-obj docutils literal notranslate"><span class="pre">on_type</span></code>.</p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.atoms">
<code class="descname">atoms</code><span class="sig-paren">(</span><em>*types</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.atoms" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the atoms that form the current Symbol.</p>
<p>By default, only objects that are truly atomic and cannot be divided
into smaller pieces are returned: symbols, numbers, and number
symbols like I and pi. It is possible to request atoms of any type,
however.</p>
<p>Note that if this symbol contains components such as [x]_i_j then
only their main symbol ‘x’ is returned.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>types</strong> – types to restrict result to</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">list of atoms of specified type</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">set</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.coeff">
<code class="descname">coeff</code><span class="sig-paren">(</span><em>x</em>, <em>expand=True</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.coeff" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the coefficient of the term “x” or 0 if there is no “x”.</p>
<p>If “x” is a scalar symbol then “x” is searched in all components of
this symbol. Otherwise the shapes must match and the coefficients are
checked component by component.</p>
<p>Example:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></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="p">(</span><span class="mi">2</span><span class="p">,</span><span class="mi">2</span><span class="p">))</span>
<span class="n">y</span><span class="o">=</span><span class="mi">3</span><span class="o">*</span><span class="n">x</span>
<span class="nb">print</span> <span class="n">y</span><span class="o">.</span><span class="n">coeff</span><span class="p">(</span><span class="n">x</span><span class="p">)</span>
<span class="nb">print</span> <span class="n">y</span><span class="o">.</span><span class="n">coeff</span><span class="p">(</span><span class="n">x</span><span class="p">[</span><span class="mi">1</span><span class="p">,</span><span class="mi">1</span><span class="p">])</span>
</pre></div>
</div>
<p>will print:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="p">[[</span><span class="mi">3</span> <span class="mi">3</span><span class="p">]</span>
<span class="p">[</span><span class="mi">3</span> <span class="mi">3</span><span class="p">]]</span>
<span class="p">[[</span><span class="mi">0</span> <span class="mi">0</span><span class="p">]</span>
<span class="p">[</span><span class="mi">0</span> <span class="mi">3</span><span class="p">]]</span>
</pre></div>
</div>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>x</strong> (<code class="docutils literal notranslate"><span class="pre">Symbol</span></code>, <code class="docutils literal notranslate"><span class="pre">numpy.ndarray</span></code>, <code class="xref py py-obj docutils literal notranslate"><span class="pre">list</span></code>) – the term whose coefficients are to be found</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">the coefficient(s) of the term</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">Symbol</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.diff">
<code class="descname">diff</code><span class="sig-paren">(</span><em>*symbols</em>, <em>**assumptions</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.diff" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.evalf">
<code class="descname">evalf</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.evalf" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the sympy.evalf operation on all elements in this symbol</p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.expand">
<code class="descname">expand</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.expand" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the sympy.expand operation on all elements in this symbol</p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.getDataSubstitutions">
<code class="descname">getDataSubstitutions</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.getDataSubstitutions" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a dictionary of symbol names and the escript <code class="docutils literal notranslate"><span class="pre">Data</span></code> objects
they represent within this Symbol.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">the dictionary of substituted <code class="docutils literal notranslate"><span class="pre">Data</span></code> objects</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">dict</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.getDim">
<code class="descname">getDim</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.getDim" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the spatial dimensionality of this symbol.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">the symbol’s spatial dimensionality, or -1 if undefined</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">int</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.getRank">
<code class="descname">getRank</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.getRank" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the rank of this symbol.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">the symbol’s rank which is equal to the length of the shape.</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">int</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.getShape">
<code class="descname">getShape</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.getShape" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the shape of this symbol.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Returns:</th><td class="field-body">the symbol’s shape</td>
</tr>
<tr class="field-even field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">tuple</span></code> of <code class="docutils literal notranslate"><span class="pre">int</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.grad">
<code class="descname">grad</code><span class="sig-paren">(</span><em>where=None</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.grad" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns a symbol which represents the gradient of this symbol.
:type where: <code class="docutils literal notranslate"><span class="pre">Symbol</span></code>, <code class="docutils literal notranslate"><span class="pre">FunctionSpace</span></code></p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.inverse">
<code class="descname">inverse</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.inverse" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="esys.escript.symbolic.Symbol.is_Add">
<code class="descname">is_Add</code><em class="property"> = False</em><a class="headerlink" href="#esys.escript.symbolic.Symbol.is_Add" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="attribute">
<dt id="esys.escript.symbolic.Symbol.is_Float">
<code class="descname">is_Float</code><em class="property"> = False</em><a class="headerlink" href="#esys.escript.symbolic.Symbol.is_Float" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.item">
<code class="descname">item</code><span class="sig-paren">(</span><em>*args</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.item" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns an element of this symbol.
This method behaves like the item() method of numpy.ndarray.
If this is a scalar Symbol, no arguments are allowed and the only
element in this Symbol is returned.
Otherwise, ‘args’ specifies a flat or nd-index and the element at
that index is returned.</p>
<table class="docutils field-list" frame="void" rules="none">
<col class="field-name" />
<col class="field-body" />
<tbody valign="top">
<tr class="field-odd field"><th class="field-name">Parameters:</th><td class="field-body"><strong>args</strong> – index of item to be returned</td>
</tr>
<tr class="field-even field"><th class="field-name">Returns:</th><td class="field-body">the requested element</td>
</tr>
<tr class="field-odd field"><th class="field-name">Return type:</th><td class="field-body"><code class="docutils literal notranslate"><span class="pre">sympy.Symbol</span></code>, <code class="docutils literal notranslate"><span class="pre">int</span></code>, or <code class="docutils literal notranslate"><span class="pre">float</span></code></td>
</tr>
</tbody>
</table>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.lambdarepr">
<code class="descname">lambdarepr</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.lambdarepr" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.simplify">
<code class="descname">simplify</code><span class="sig-paren">(</span><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.simplify" title="Permalink to this definition">¶</a></dt>
<dd><p>Applies the sympy.simplify operation on all elements in this symbol</p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.subs">
<code class="descname">subs</code><span class="sig-paren">(</span><em>old</em>, <em>new</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.subs" title="Permalink to this definition">¶</a></dt>
<dd><p>Substitutes an expression.</p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.swap_axes">
<code class="descname">swap_axes</code><span class="sig-paren">(</span><em>axis0</em>, <em>axis1</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.swap_axes" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.tensorProduct">
<code class="descname">tensorProduct</code><span class="sig-paren">(</span><em>other</em>, <em>axis_offset</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.tensorProduct" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.tensorTransposedProduct">
<code class="descname">tensorTransposedProduct</code><span class="sig-paren">(</span><em>other</em>, <em>axis_offset</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.tensorTransposedProduct" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.trace">
<code class="descname">trace</code><span class="sig-paren">(</span><em>axis_offset</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.trace" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the trace of this Symbol.</p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.transpose">
<code class="descname">transpose</code><span class="sig-paren">(</span><em>axis_offset</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.transpose" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns the transpose of this Symbol.</p>
</dd></dl>
<dl class="method">
<dt id="esys.escript.symbolic.Symbol.transposedTensorProduct">
<code class="descname">transposedTensorProduct</code><span class="sig-paren">(</span><em>other</em>, <em>axis_offset</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.Symbol.transposedTensorProduct" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
</dd></dl>
</div>
<div class="section" id="functions">
<h2>Functions<a class="headerlink" href="#functions" title="Permalink to this headline">¶</a></h2>
<dl class="function">
<dt id="esys.escript.symbolic.combineData">
<code class="descclassname">esys.escript.symbolic.</code><code class="descname">combineData</code><span class="sig-paren">(</span><em>array</em>, <em>shape</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.combineData" title="Permalink to this definition">¶</a></dt>
<dd></dd></dl>
<dl class="function">
<dt id="esys.escript.symbolic.getTotalDifferential">
<code class="descclassname">esys.escript.symbolic.</code><code class="descname">getTotalDifferential</code><span class="sig-paren">(</span><em>f</em>, <em>x</em>, <em>order=0</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.getTotalDifferential" title="Permalink to this definition">¶</a></dt>
<dd><p>This function computes:</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="o">|</span> <span class="n">Df</span><span class="o">/</span><span class="n">Dx</span> <span class="o">=</span> <span class="n">del_f</span><span class="o">/</span><span class="n">del_x</span> <span class="o">+</span> <span class="n">del_f</span><span class="o">/</span><span class="n">del_grad</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">*</span><span class="n">del_grad</span><span class="p">(</span><span class="n">x</span><span class="p">)</span><span class="o">/</span><span class="n">del_x</span> <span class="o">+</span> <span class="o">...</span>
<span class="o">|</span> \ <span class="o">/</span> \ <span class="o">/</span>
<span class="o">|</span> <span class="n">a</span> <span class="n">b</span>
</pre></div>
</div>
</dd></dl>
<dl class="function">
<dt id="esys.escript.symbolic.isSymbol">
<code class="descclassname">esys.escript.symbolic.</code><code class="descname">isSymbol</code><span class="sig-paren">(</span><em>arg</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.isSymbol" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns True if the argument <code class="docutils literal notranslate"><span class="pre">arg</span></code> is an escript <code class="docutils literal notranslate"><span class="pre">Symbol</span></code> or
<code class="docutils literal notranslate"><span class="pre">sympy.Basic</span></code> object, False otherwise.</p>
</dd></dl>
<dl class="function">
<dt id="esys.escript.symbolic.pprint">
<code class="descclassname">esys.escript.symbolic.</code><code class="descname">pprint</code><span class="sig-paren">(</span><em>expr</em>, <em>use_unicode=None</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.pprint" title="Permalink to this definition">¶</a></dt>
<dd><p>Prints expr in pretty form.</p>
<p>pprint is just a shortcut for this function</p>
</dd></dl>
<dl class="function">
<dt id="esys.escript.symbolic.pretty_print">
<code class="descclassname">esys.escript.symbolic.</code><code class="descname">pretty_print</code><span class="sig-paren">(</span><em>expr</em>, <em>use_unicode=None</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.pretty_print" title="Permalink to this definition">¶</a></dt>
<dd><p>Prints expr in pretty form.</p>
<p>pprint is just a shortcut for this function</p>
</dd></dl>
<dl class="function">
<dt id="esys.escript.symbolic.removeFsFromGrad">
<code class="descclassname">esys.escript.symbolic.</code><code class="descname">removeFsFromGrad</code><span class="sig-paren">(</span><em>sym</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.removeFsFromGrad" title="Permalink to this definition">¶</a></dt>
<dd><p>Returns <code class="docutils literal notranslate"><span class="pre">sym</span></code> with all occurrences grad_n(a,b,c) replaced by grad_n(a,b).
That is, all functionspace parameters are removed.</p>
</dd></dl>
<dl class="function">
<dt id="esys.escript.symbolic.symbols">
<code class="descclassname">esys.escript.symbolic.</code><code class="descname">symbols</code><span class="sig-paren">(</span><em>*names</em>, <em>**kwargs</em><span class="sig-paren">)</span><a class="headerlink" href="#esys.escript.symbolic.symbols" title="Permalink to this definition">¶</a></dt>
<dd><p>Emulates the behaviour of sympy.symbols.</p>
</dd></dl>
</div>
<div class="section" id="others">
<h2>Others<a class="headerlink" href="#others" title="Permalink to this headline">¶</a></h2>
<ul class="simple">
<li>HAVE_SYMBOLS</li>
</ul>
</div>
<div class="section" id="packages">
<h2>Packages<a class="headerlink" href="#packages" title="Permalink to this headline">¶</a></h2>
<div class="toctree-wrapper compound">
</div>
</div>
</div>
</div>
</div>
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<h3><a href="index.html">Table of Contents</a></h3>
<ul>
<li><a class="reference internal" href="#">esys.escript.symbolic Package</a><ul>
<li><a class="reference internal" href="#classes">Classes</a></li>
<li><a class="reference internal" href="#functions">Functions</a></li>
<li><a class="reference internal" href="#others">Others</a></li>
<li><a class="reference internal" href="#packages">Packages</a></li>
</ul>
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</ul>
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