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      <p>This function appeared in Mathematica"StackExchange" forum... unanswered !Glorious Maxima X_Y plot is genious, but stays blind for "Human Eye".If you extend the 'X' axis, Maxima loses the plot, probably due to the granularityof the 32 bits.</p>
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      <p>--------------- Tip -----------------Often, it's not practical to turn Offcalculations on long work sheet and if you want to delete some item that wereor are active, it forces the all worksheet recalculate,,, nasty minutes !To delete such item(s), click on theright end of the argument, press backspace until everyting is gone .Work sheet does not recalculate.</p>
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      <p bold="true">Human Eye fake parametric equation</p>
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        <p>Human eye ... β level plane contour</p>
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      <p>Here, Smath in sympathic with its Maple companion. Mathcad 11 and its Maple takes a "huge while" to plot, plot 4 solutions. Smath spits Maple two solutions in NO time.This function is only positive in the 3Ddomain, i.e:  β &gt; 0X_Y does NOT like something in there ?</p>
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      <p>Memo: Remember that all those are by default 100 values [native]So, if you want to see 0.125*sin(100*x), you will start plottinga "FlintStones" saw tooth ! that you will have to manage later.</p>
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  <region id="38" left="18" top="3573" width="381" height="208" color="#000000" bgColor="#ffffff" fontSize="10">
    <xyplot width="371" height="200" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="-62.832" xmax="62.832" xtick="20" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-0.25" ymax="0.25" ytick="0.0625" numberformat="General" decimalplaces="4" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="Title" titlefont="Arial, 12pt" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 10pt" labelfontcolor="Black" tickfont="Courier New, 10pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="false" legendbackcolor="White" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="NorthEast" textcolor="Black" />
      <traces>
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Red" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
      </traces>
      <input>
        <e type="operand">0.125</e>
        <e type="operand">20</e>
        <e type="operand">x</e>
        <e type="operator" args="2">*</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operator" args="2">*</e>
        <e type="operand">x</e>
        <e type="function" args="1">datum</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">sys</e>
      </input>
    </xyplot>
  </region>
  <region id="39" left="594" top="3573" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">X</e>
        <e type="operand">5</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="40" left="666" top="3573" width="43" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">m</e>
        <e type="operand">1</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="41" left="414" top="3591" width="91" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="42" left="594" top="3600" width="139" height="148" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">XY</e>
        <e type="operand">X</e>
        <e type="operand">m</e>
        <e type="operator" args="2">-</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">m</e>
        <e type="operator" args="2">+</e>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">1</e>
        <e type="operator" args="2">-</e>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">X</e>
        <e type="operand">m</e>
        <e type="operator" args="2">+</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">7</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="16">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="43" left="414" top="3636" width="78" height="44" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">Y</e>
        <e type="operand">0</e>
        <e type="operand">3</e>
        <e type="operand">0</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="6">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="44" left="414" top="3690" width="167" height="33" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4" exponentialThreshold="3">
      <input>
        <e type="operand">U</e>
        <e type="operand">10</e>
        <e type="operand">12</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">15</e>
        <e type="operand">0.01</e>
        <e type="function" preserve="true" args="3">range</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="45" left="414" top="3726" width="154" height="52" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4" exponentialThreshold="3">
      <input>
        <e type="operand">i</e>
        <e type="operand">1</e>
        <e type="operand">U</e>
        <e type="function" preserve="true" args="1">rows</e>
        <e type="function" preserve="true" args="2">range</e>
        <e type="operand">p</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="operand">U</e>
        <e type="operand">i</e>
        <e type="function" preserve="true" args="2">el</e>
        <e type="function" args="1">f</e>
        <e type="operator" args="2">:</e>
        <e type="function" preserve="true" args="3">for</e>
      </input>
    </math>
  </region>
  <region id="46" left="603" top="3744" width="105" height="64" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">xy</e>
        <e type="operand">10</e>
        <e type="operand">4</e>
        <e type="operand">0</e>
        <e type="operand">4</e>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">3</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="8">mat</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="47" left="414" top="3780" width="162" height="26" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4" exponentialThreshold="3">
      <input>
        <e type="operand">Plot</e>
        <e type="operand">U</e>
        <e type="operand">p</e>
        <e type="function" preserve="true" args="2">augment</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="48" left="9" top="3825" width="387" height="208" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <xyplot width="377" height="200" smoothing="false" points="100">
      <propertiessource index="1" sourcetype="PropertyGrid" />
      <grid gridcolor="LightGray" gridpattern="Solid" gridthickness="1" isxgrid="true" isygrid="true" />
      <xaxes xmin="-5" xmax="20" xtick="5" numberformat="General" decimalplaces="3" />
      <yaxes ymin="-2" ymax="5" ytick="1" numberformat="General" decimalplaces="3" />
      <y2axes isy2axis="false" y2min="-1" y2max="1" y2tick="0.5" numberformat="General" decimalplaces="3" />
      <title2d title="Title" titlefont="Arial, 12pt" titlefontcolor="Black" />
      <xylabel labelfont="Arial, 10pt" labelfontcolor="Black" tickfont="Courier New, 10pt" tickfontcolor="Black" xlabel="x" ylabel="y" y2label="y2" />
      <legend isbordervisible="true" islegendvisible="false" legendbackcolor="White" legendbordercolor="Black" legendfont="Arial, 8pt" legendposition="NorthEast" textcolor="Black" />
      <traces>
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Blue" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Red" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Green" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="Fuchsia" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
        <trace seriesname="" isy2data="false" isvisible="true" plotmethod="Lines" linecolor="DarkOrange" linethickness="1" linepattern="Solid" symbolsize="8" symboltype="None" symbolborderthickness="1" symbolbordercolor="Black" symbolfillcolor="White" />
      </traces>
      <input>
        <e type="operand">Plot</e>
        <e type="operand">x</e>
        <e type="function" args="1">datum</e>
        <e type="operand">Y</e>
        <e type="operand">XY</e>
        <e type="operand">xy</e>
        <e type="operand">5</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="7">sys</e>
      </input>
    </xyplot>
  </region>
  <region id="49" left="504" top="3852" width="170" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">Forget me not </p>
    </text>
  </region>
  <region id="50" left="243" top="3861" width="150" height="28" color="#000000" bgColor="#ffff80" fontSize="10">
    <math fractionType="none" decimalPlaces="2">
      <input>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
        <e type="operand">1.61</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="51" left="414" top="3888" width="298" height="66" color="#000000" bgColor="#ffffff" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">Notes</e>
        <e type="operand">n</e>
        <e type="operand">n</e>
        <e type="function" preserve="true" args="1">ln</e>
        <e type="operand" style="string">+</e>
        <e type="operand">20</e>
        <e type="operand" style="string">blue</e>
        <e type="operand">1</e>
        <e type="operand">5</e>
        <e type="function" preserve="true" args="7">mat</e>
        <e type="operand" style="string">X_Y plot takes 2 cols</e>
        <e type="operand" style="string">does NOT take conditional</e>
        <e type="operand">3</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="5">mat</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="52" left="414" top="3951" width="364" height="40" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>If you attempt "Legend", too many  objectsin the plot ... Legend will scrap the plot.</p>
    </text>
  </region>
  <region id="53" left="513" top="4005" width="166" height="28" color="#000000" bgColor="#ffff80" fontSize="10">
    <math fractionType="none" decimalPlaces="4">
      <input>
        <e type="operand">X</e>
        <e type="operand">X</e>
        <e type="function" args="1">f</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">5</e>
        <e type="operand">1.6094</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
</regions>