﻿<?xml version="1.0" encoding="utf-8" standalone="yes"?>
<?application progid="SMath Studio Desktop" version="0.98.6179.21440"?>
<regions>
  <settings>
    <identity>
      <id>f5f96f42-63ab-4b0e-b0dd-a68242719136</id>
      <revision>11</revision>
    </identity>
    <calculation>
      <precision>4</precision>
      <exponentialThreshold>5</exponentialThreshold>
      <fractions>decimal</fractions>
    </calculation>
    <pageModel active="true" printAreas="true" simpleEqualsOnly="false" printBackgroundImages="true">
      <paper id="1" orientation="Portrait" width="850" height="1100" />
      <margins left="39" right="39" top="39" bottom="39" />
      <header alignment="Center" color="#a9a9a9">&amp;[DATE] &amp;[TIME] - &amp;[FILENAME]</header>
      <footer alignment="Center" color="#a9a9a9">&amp;[PAGENUM] / &amp;[COUNT]</footer>
      <backgrounds />
    </pageModel>
    <dependencies>
      <assembly name="SMath Studio Desktop" version="0.98.6179.21440" guid="a37cba83-b69c-4c71-9992-55ff666763bd" />
      <assembly name="Math Region" version="0.98.6179.21440" guid="02f1ab51-215b-466e-a74d-5d8b1cf85e8d" />
      <assembly name="Special Functions" version="1.11.6179.21442" guid="2814e667-4e12-48b1-8d51-194e480eabc5" />
      <assembly name="Text Region" version="1.10.6179.21446" guid="485d28c5-349a-48b6-93be-12a35a1c1e39" />
      <assembly name="Plot Region" version="1.9.6179.21450" guid="c451c2b5-798b-4f08-b9ec-b90963d1ddaa" />
    </dependencies>
  </settings>
  <region id="0" top="18" color="#000000" bgColor="#ffffff">
    <area collapsed="true">
      <title lang="eng">
        <p>     Hatch      </p>
      </title>
    </area>
    <region id="1" left="54" top="45" width="449" height="274" border="true" color="#000000" bgColor="#ffffff" fontSize="10">
      <math>
        <description active="true" position="Top" lang="ger">
          <p>Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und g(x) im Bereich von x1 bis x2 mit 2*n Linien.</p>
        </description>
        <description active="true" position="Top" lang="eng">
          <p>Generates a matrix for 2*N vertical lines (hatching) between functions f(x) and g(x) in x-range from x1 to x2</p>
        </description>
        <input>
          <e type="operand">f</e>
          <e type="operand">g</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
          <e type="operand">N</e>
          <e type="function" args="5">hatch</e>
          <e type="operand">dx</e>
          <e type="operand">x.2</e>
          <e type="operand">x.1</e>
          <e type="operator" args="2">-</e>
          <e type="operand">N</e>
          <e type="operator" args="2">/</e>
          <e type="bracket">(</e>
          <e type="operator" args="2">:</e>
          <e type="operand">h</e>
          <e type="operand">x.1</e>
          <e type="operand">x.1</e>
          <e type="function" args="1">f</e>
          <e type="operand">x.1</e>
          <e type="operand">x.1</e>
          <e type="function" args="1">g</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>
          <e type="operand">x</e>
          <e type="operand">x.1</e>
          <e type="operand">x.2</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">-</e>
          <e type="operand">x.1</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" preserve="true" args="3">range</e>
          <e type="operand">h</e>
          <e type="operand">h</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">g</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operand">2</e>
          <e type="operator" args="2">/</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">f</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">f</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="operand">x</e>
          <e type="operand">dx</e>
          <e type="operator" args="2">+</e>
          <e type="function" args="1">g</e>
          <e type="operand">4</e>
          <e type="operand">2</e>
          <e type="function" preserve="true" args="10">mat</e>
          <e type="function" preserve="true" args="2">stack</e>
          <e type="operator" args="2">:</e>
          <e type="function" preserve="true" args="3">for</e>
          <e type="operand">h</e>
          <e type="operand">4</e>
          <e type="operand">1</e>
          <e type="function" preserve="true" args="6">line</e>
          <e type="operator" args="2">:</e>
        </input>
      </math>
    </region>
    <region id="2" top="369" color="#000000" bgColor="#ffffff">
      <area terminator="true" />
    </region>
  </region>
  <region id="3" left="36" top="405" width="464" height="31" color="#000000" bgColor="#80ffff" fontSize="14">
    <text lang="eng">
      <p bold="true">Cumulative integration via transit algo</p>
    </text>
  </region>
  <region id="4" left="36" top="441" width="237" height="65" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math optimize="2" decimalPlaces="6">
      <description active="true" position="Top" lang="eng">
        <p>SineIntegral classical ΣTransit algo definition</p>
      </description>
      <input>
        <e type="operand">u</e>
        <e type="function" args="1">Si</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operand">0</e>
        <e type="operand">30</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="5" left="324" top="441" width="292" height="92" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math>
      <description active="true" position="Top" lang="eng">
        <p>Si(x) Cumulative Integration∫(z) =&gt; symbol from Maple </p>
      </description>
      <input>
        <e type="operand">z</e>
        <e type="function" args="1">∫</e>
        <e type="operand">u</e>
        <e type="function" args="1">Si</e>
        <e type="operand">u</e>
        <e type="operand">0</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="function" args="1">∫</e>
        <e type="operand">z</e>
        <e type="function" args="1">∫</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operand">z</e>
        <e type="function" args="1">∫_</e>
        <e type="operand">u</e>
        <e type="function" args="1">Si</e>
        <e type="operand">u</e>
        <e type="operand">x</e>
        <e type="operand">0</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="function" args="1">∫_</e>
        <e type="operand">z</e>
        <e type="function" args="1">∫_</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
    </math>
  </region>
  <region id="6" left="36" top="549" width="102" height="49" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">f</e>
        <e type="operand">x</e>
        <e type="function" args="1">Si</e>
        <e type="operator" args="2">:</e>
        <e type="operand">x</e>
        <e type="function" args="1">g</e>
        <e type="operand">0</e>
        <e type="operator" args="2">:</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">line</e>
      </input>
    </math>
  </region>
  <region id="7" left="324" top="585" width="184" height="75" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math>
      <description active="true" position="Right" lang="eng">
        <p>Integral definition</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Si</e>
        <e type="operand">t</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">t</e>
        <e type="operator" args="2">/</e>
        <e type="operand">t</e>
        <e type="operand">10</e>
        <e type="operand">15</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="4">int</e>
        <e type="operator" args="2">≡</e>
      </input>
    </math>
  </region>
  <region id="8" left="36" top="603" width="101" height="27" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math>
      <input>
        <e type="operand">X</e>
        <e type="operand">4</e>
        <e type="operator" args="2">:</e>
        <e type="operand">U</e>
        <e type="operand">2</e>
        <e type="operator" args="1">-</e>
        <e type="operator" args="2">:</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
    </math>
  </region>
  <region id="9" left="36" top="639" width="226" height="49" color="#000000" bgColor="#e1ffff" fontSize="10">
    <math decimalPlaces="15">
      <input>
        <e type="operand">X</e>
        <e type="function" args="1">∫</e>
        <e type="operand">U</e>
        <e type="function" args="1">∫_</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">7.03281255579621</e>
        <e type="operand">3.2108259536054</e>
        <e type="operator" args="1">-</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="10" left="324" top="657" width="104" height="43" color="#000000" bgColor="#ebebeb" fontSize="10">
    <math>
      <description active="true" position="Right" lang="eng">
        <p>... from which derivative follows</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">D</e>
        <e type="operand">x</e>
        <e type="function" preserve="true" args="1">sin</e>
        <e type="operand">x</e>
        <e type="operator" args="2">/</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="11" left="36" top="702" width="374" height="158" color="#000000" bgColor="#ffffff" fontSize="10" showInputData="False">
    <plot type="2d" render="lines" scale_x="2.51670571529257" scale_y="1.3374806020408" scale_z="3.36604507524903" rotate_x="0" rotate_y="0" rotate_z="0" transpose_x="0" transpose_y="0" transpose_z="0">
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Si</e>
        <e type="operand">f</e>
        <e type="operand">g</e>
        <e type="operand">U</e>
        <e type="operand">0</e>
        <e type="operand">10</e>
        <e type="function" args="5">hatch</e>
        <e type="operand">f</e>
        <e type="operand">g</e>
        <e type="operand">0</e>
        <e type="operand">X</e>
        <e type="operand">20</e>
        <e type="function" args="5">hatch</e>
        <e type="operand">x</e>
        <e type="function" args="1">D</e>
        <e type="operand">4</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="6">sys</e>
      </input>
    </plot>
  </region>
  <region id="12" left="450" top="702" width="237" height="65" color="#000000" bgColor="#ffffff" fontSize="10">
    <math optimize="2" decimalPlaces="6">
      <description active="true" position="Top" lang="eng">
        <p>SineIntegral classical Σ(x)for the point evaluate.</p>
      </description>
      <input>
        <e type="operand">x</e>
        <e type="function" args="1">Si</e>
        <e type="operand">1</e>
        <e type="operator" args="1">-</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operator" args="2">^</e>
        <e type="operand">x</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="operator" args="2">^</e>
        <e type="operator" args="2">*</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operand">1</e>
        <e type="operand">2</e>
        <e type="operand">n</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">+</e>
        <e type="bracket">(</e>
        <e type="operator" args="1">!</e>
        <e type="bracket">(</e>
        <e type="operator" args="2">*</e>
        <e type="operator" args="2">/</e>
        <e type="bracket">(</e>
        <e type="operand">n</e>
        <e type="operand">0</e>
        <e type="operand">30</e>
        <e type="function" preserve="true" args="4">sum</e>
        <e type="operator" args="2">:</e>
      </input>
    </math>
  </region>
  <region id="13" left="450" top="810" width="226" height="49" color="#000000" bgColor="#ffffff" fontSize="10">
    <math decimalPlaces="15">
      <input>
        <e type="operand">U</e>
        <e type="function" args="1">Si</e>
        <e type="operand">X</e>
        <e type="function" args="1">Si</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </input>
      <result action="numeric">
        <e type="operand">1.6054129768027</e>
        <e type="operator" args="1">-</e>
        <e type="operand">1.75820313894905</e>
        <e type="operand">2</e>
        <e type="operand">1</e>
        <e type="function" preserve="true" args="4">mat</e>
      </result>
    </math>
  </region>
  <region id="14" left="369" top="873" width="391" height="24" color="#000000" bgColor="#ffffff" fontSize="10">
    <text lang="eng">
      <p>http://keisan.casio.com/exec/system/1180573427</p>
    </text>
  </region>
  <region id="15" top="927" color="#000000" bgColor="#ffe1e1">
    <area single="true" collapsed="true" />
  </region>
</regions>