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    <title>bertiniTrackHomotopy -- a main method to track using a user-defined homotopy</title>
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o6 = {{-1.41421}, {1.41421}}

o6 : List</code></pre>
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              <pre><code class="language-macaulay2">i7 : peek S0_0

o7 = Point{cache => CacheTable{...9...}}
           Coordinates => {-1.41421}</code></pre>
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          <p>In the previous example, we solved $x^2-2$ by moving from $x^2-1$ with a linear homotopy. <span class="tt">Bertini</span> tracks homotopies starting at $t=1$ and ending at $t=0$. Final solutions are of the type Point.</p>
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              <pre><code class="language-macaulay2">i8 : R=CC[x,y,t]; -- include the path variable in the ring</code></pre>
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              <pre><code class="language-macaulay2">i9 : f1=(x^2-y^2);</code></pre>
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              <pre><code class="language-macaulay2">i10 : f2=(2*x^2-3*x*y+5*y^2);</code></pre>
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              <pre><code class="language-macaulay2">i11 : H = { f1*t + f2*(1-t)}; --H is a list of polynomials in x,y,t</code></pre>
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              <pre><code class="language-macaulay2">i12 : sol1=    point{{1,1}}--{{x,y}} coordinates

o12 = sol1

o12 : Point</code></pre>
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              <pre><code class="language-macaulay2">i13 : sol2=    point{{ -1,1}}

o13 = sol2

o13 : Point</code></pre>
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              <pre><code class="language-macaulay2">i14 : S1={sol1,sol2}--solutions to H when t=1

o14 = {sol1, sol2}

o14 : List</code></pre>
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              <pre><code class="language-macaulay2">i15 : S0=bertiniTrackHomotopy(t, H, S1, IsProjective=>1) --solutions to H when t=0

o15 = {{-.482114-.646009*ii, .215048-.462233*ii}, {4.1398-4.7253*ii,
      -----------------------------------------------------------------------
      -1.389-3.72253*ii}}

o15 : List</code></pre>
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          <p>Variables must begin with a letter (lowercase or capital) and can only contain letters, numbers, underscores, and square brackets.</p>
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          <h2>Ways to use <span class="tt">bertiniTrackHomotopy</span>:</h2>
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            <li><kbd>bertiniTrackHomotopy(RingElement,List,List)</kbd></li>
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          <h2>For the programmer</h2>
          <p>The object <a title="a main method to track using a user-defined homotopy" href="_bertini__Track__Homotopy.html">bertiniTrackHomotopy</a> is <span>a <a title="a type of method function" href="../../Macaulay2Doc/html/___Method__Function__With__Options.html">method function with options</a></span>.</p>
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          <p>The source of this document is in <span class="tt">Bertini.m2:2845:0</span>.</p>
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Edit File: _bertini__Track__Homotopy.html

Edit File: _bertiniTrackHomotopy.html