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  <div class="section" id="roots">
<span id="id1"></span><h1>Roots<a class="headerlink" href="#roots" title="Permalink to this headline">¶</a></h1>
<p>Functions to compute roots of simple equations.</p>
<div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="c1">#include &lt;Imath/ImathRoots.h&gt;</span>
</pre></div>
</div>
<dl class="cpp function">
<dt id="_CPPv4I0EN5Imath11solveLinearEi1T1TR1T">
<span id="_CPPv3I0EN5Imath11solveLinearE1T1TR1T"></span><span id="_CPPv2I0EN5Imath11solveLinearE1T1TR1T"></span>template&lt;class <code class="sig-name descname">T</code>&gt;<br /><span class="target" id="_imath_roots_8h_1ab74b6481dec757db3aabf3afad53b42b"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveLinear</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Imath::solveLinear::T">T</a> <em>a</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Imath::solveLinear::T">T</a> <em>b</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Imath::solveLinear::T">T</a> &amp;<em>x</em><span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath11solveLinearEi1T1TR1T" title="Permalink to this definition">¶</a><br /></dt>
<dd><p>Solve for x in the linear equation: </p>
<p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">b</span> <span class="o">==</span> <span class="mi">0</span>
</pre></div>
</div>
 <dl class="simple">
<dt><strong>Return</strong></dt><dd><p>1 if the equation has a solution, 0 if there is no solution, and -1 if all real numbers are solutions. </p>
</dd>
</dl>
</p>
</dd></dl>

<dl class="cpp function">
<dt id="_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T">
<span id="_CPPv3I0EN5Imath14solveQuadraticE1T1T1TAL2E_1T"></span><span id="_CPPv2I0EN5Imath14solveQuadraticE1T1T1TA2_1T"></span>template&lt;class <code class="sig-name descname">T</code>&gt;<br /><span class="target" id="_imath_roots_8h_1a94c654a5ec9ce534aaf83016ba2f265a"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveQuadratic</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>a</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>b</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>c</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Imath::solveQuadratic::T">T</a> <em>x</em>[2]<span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath14solveQuadraticEi1T1T1TAL2E_1T" title="Permalink to this definition">¶</a><br /></dt>
<dd><p>Solve for x in the quadratic equation: </p>
<p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">*</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">b</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">c</span> <span class="o">==</span> <span class="mi">0</span>
</pre></div>
</div>
 <dl class="simple">
<dt><strong>Return</strong></dt><dd><p>2 if the equation has two solutions, 1 if the equation has a single solution, 0 if there is no solution, and -1 if all real numbers are solutions. </p>
</dd>
</dl>
</p>
</dd></dl>

<dl class="cpp function">
<dt id="_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T">
<span id="_CPPv3I0EN5Imath20solveNormalizedCubicE1T1T1TAL3E_1T"></span><span id="_CPPv2I0EN5Imath20solveNormalizedCubicE1T1T1TA3_1T"></span>template&lt;class <code class="sig-name descname">T</code>&gt;<br /><span class="target" id="_imath_roots_8h_1a0266743eb556a3eb3b340d0ed9d3ded9"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveNormalizedCubic</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>r</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>s</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>t</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Imath::solveNormalizedCubic::T">T</a> <em>x</em>[3]<span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath20solveNormalizedCubicEi1T1T1TAL3E_1T" title="Permalink to this definition">¶</a><br /></dt>
<dd><p>Solve for x in the normalized cubic equation: </p>
<p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">r</span> <span class="o">*</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">s</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">t</span> <span class="o">==</span> <span class="mi">0</span>
</pre></div>
</div>
 The equation is solved using Cardano’s Formula; even though only real solutions are produced, some intermediate results are complex (std::complex&lt;T&gt;).</p>
<p><dl class="simple">
<dt><strong>Return</strong></dt><dd><p>0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions. </p>
</dd>
</dl>
</p>
</dd></dl>

<dl class="cpp function">
<dt id="_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T">
<span id="_CPPv3I0EN5Imath10solveCubicE1T1T1T1TAL3E_1T"></span><span id="_CPPv2I0EN5Imath10solveCubicE1T1T1T1TA3_1T"></span>template&lt;class <code class="sig-name descname">T</code>&gt;<br /><span class="target" id="_imath_roots_8h_1a2a27d3e8ea4d2aadc1c506b3a3d77bf5"></span><em class="property">constexpr</em> int <code class="sig-prename descclassname">Imath<code class="sig-prename descclassname">::</code></code><code class="sig-name descname">solveCubic</code><span class="sig-paren">(</span><a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>a</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>b</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>c</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>d</em>, <a class="reference internal" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Imath::solveCubic::T">T</a> <em>x</em>[3]<span class="sig-paren">)</span><a class="headerlink" href="#_CPPv4I0EN5Imath10solveCubicEi1T1T1T1TAL3E_1T" title="Permalink to this definition">¶</a><br /></dt>
<dd><p>Solve for x in the cubic equation: </p>
<p><div class="highlight-default notranslate"><div class="highlight"><pre><span></span><span class="n">a</span> <span class="o">*</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">b</span> <span class="o">*</span> <span class="n">x</span><span class="o">*</span><span class="n">x</span> <span class="o">+</span> <span class="n">c</span> <span class="o">*</span> <span class="n">x</span> <span class="o">+</span> <span class="n">d</span> <span class="o">==</span> <span class="mi">0</span>
</pre></div>
</div>
 The equation is solved using Cardano’s Formula; even though only real solutions are produced, some intermediate results are complex (std::complex&lt;T&gt;).</p>
<p><dl class="simple">
<dt><strong>Return</strong></dt><dd><p>0 if there is no solution, and -1 if all real numbers are solutions, otherwise return the number of solutions. </p>
</dd>
</dl>
</p>
</dd></dl>

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