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<div><span class="kw">theorem </span><a NAME="T20"><span class="comment"><font color="firebrick">:: POLYEQ_5:20</font></span><br/></a><div class="add"> for <font color="Olive" title="b1">z</font>, <font color="Olive" title="b2">a0</font>, <font color="Olive" title="b3">a1</font>, <font color="Olive" title="b4">a2</font>, <font color="Olive" title="b5">a3</font> being   <a href="xcmplx_0.html#NM1" title="XCMPLX_0:NM.1">Complex</a>  st <font color="Olive" title="b5">a3</font> <a href="hidden.html#NR2" title="HIDDEN:NR.2">&lt;&gt;</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  holds <br/>( <span class="p1">(<span class="default"><span class="p2">(<span class="default"><span class="p3">(<span class="default"><font color="Olive" title="b5">a3</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">z</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 3</span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p3">(<span class="default"><font color="Olive" title="b4">a2</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <span class="p4">(<span class="default"><font color="Olive" title="b1">z</font> <a href="newton.html#K1" title="NEWTON:func.1">|^</a> 2</span>)</span></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <span class="p2">(<span class="default"><font color="Olive" title="b3">a1</font> <a href="xcmplx_0.html#K3" title="XCMPLX_0:func.3">*</a> <font color="Olive" title="b1">z</font></span>)</span></span>)</span> <a href="xcmplx_0.html#K2" title="XCMPLX_0:func.2">+</a> <font color="Olive" title="b2">a0</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="numbers.html#K5" title="NUMBERS:func.5">0</a>  iff ( <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_5.html#K2" title="POLYEQ_5:func.2">1_root_of_cubic</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a0</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a1</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">a2</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>) or <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_5.html#K3" title="POLYEQ_5:func.3">2_root_of_cubic</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a0</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a1</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">a2</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>) or <font color="Olive" title="b1">z</font> <a href="hidden.html#R1" title="HIDDEN:pred.1">=</a>  <a href="polyeq_5.html#K4" title="POLYEQ_5:func.4">3_root_of_cubic</a> (<span class="p1">(<span class="default"><font color="Olive" title="b2">a0</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b3">a1</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>,<span class="p1">(<span class="default"><font color="Olive" title="b4">a2</font> <a href="xcmplx_0.html#K7" title="XCMPLX_0:func.7">/</a> <font color="Olive" title="b5">a3</font></span>)</span>) ) )</div></div>
