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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The keyword <b>explicit</b> can be used in symbolic calculations to return expressions with the values of variables in place, but without reducing numerical expressions. For example,</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">This is a way to show intermediate values in place before arriving at a full numerical result. You might use</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Instead of just </p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">so that all substituted values for the variables a, b, and c are visible along with the result of the computation. </p>
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<f family="Verdana" charset="0" size="10">Excluding Substitutions</f>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The keyword is entered just like any symbolic keyword, either by typing it in the placeholder for the symbolic keyword operator, <b>[Ctrl] [Shift] [.]</b>, or entering it from the toolbar. The explicit keyword has modifiers that allow you to specify which variables receive substitution if assigned:</p>
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<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can use as many or as few modifiers as you wish.</p>
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</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">d</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>30.7</ml:real>
<ml:id xml:space="preserve">m</ml:id>
</ml:apply>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>5.8</ml:real>
<ml:id xml:space="preserve">sec</ml:id>
</ml:apply>
</ml:parens>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2.36</ml:real>
<ml:parens>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">m</ml:id>
<ml:id xml:space="preserve">sec</ml:id>
</ml:apply>
</ml:parens>
</ml:apply>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="11"></rendering>
</region>
<region region-id="1137" left="6" top="636.75" width="329.25" height="42.75" align-x="6" align-y="648" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Names not appearing in the calculation are ignored. Using all the variable names substitutes all variables. Using no modifiers has the same effect as redefining variable names before other types of symbolic calculations:</p>
</text>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:command>
<ml:id xml:space="preserve">explicit</ml:id>
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<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
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</ml:symResult>
</ml:symEval>
</ml:eval>
</math>
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</region>
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<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>7.653103448275862069</ml:real>
<ml:id xml:space="preserve">m</ml:id>
</ml:apply>
</ml:parens>
<ml:id xml:space="preserve">sec</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
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</region>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">In order to do this without the keyword,</p>
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<math optimize="false" disable-calc="false">
<ml:define>
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<ml:id xml:space="preserve">a</ml:id>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">b</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:define>
</math>
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</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">c</ml:id>
</ml:define>
</math>
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</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
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<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
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</ml:apply>
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</ml:symEval>
</ml:eval>
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<pageBreak></pageBreak>
</region>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can use <b>explicit</b> to display formulas in terms of variables, without substituting values for the variables defined elsewhere in the worksheet. For example, </p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
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<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
<ml:id xml:space="preserve">y</ml:id>
<ml:id xml:space="preserve">z</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:id xml:space="preserve">tan</ml:id>
<ml:id xml:space="preserve">z</ml:id>
</ml:apply>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">x</ml:id>
<ml:id xml:space="preserve">y</ml:id>
</ml:apply>
</ml:apply>
</ml:define>
</math>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>2</ml:real>
</ml:define>
</math>
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</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">y</ml:id>
<ml:real>3</ml:real>
</ml:define>
</math>
<rendering item-idref="20"></rendering>
</region>
<region region-id="1191" left="150" top="966.75" width="29.25" height="15.75" align-x="162.75" align-y="978" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">z</ml:id>
<ml:id xml:space="preserve">π</ml:id>
</ml:define>
</math>
<rendering item-idref="21"></rendering>
</region>
<region region-id="1188" left="36" top="988.5" width="159.75" height="33.75" align-x="135.75" align-y="1008" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:id xml:space="preserve">f</ml:id>
<ml:sequence>
<ml:id xml:space="preserve">x</ml:id>
<ml:id xml:space="preserve">y</ml:id>
<ml:id xml:space="preserve">z</ml:id>
</ml:sequence>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">f</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:id xml:space="preserve">tan</ml:id>
<ml:id xml:space="preserve">z</ml:id>
</ml:apply>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">x</ml:id>
<ml:id xml:space="preserve">y</ml:id>
</ml:apply>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="22"></rendering>
</region>
<region region-id="973" left="6" top="1034.25" width="114" height="12" align-x="6" align-y="1044" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Subhead" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<f family="Verdana" charset="0" size="10">Chaining Evaluations</f>
</p>
</text>
</region>
<region region-id="984" left="6" top="1050.75" width="329.25" height="42.75" align-x="6" align-y="1062" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can use the explicit keyword and its modifiers chained with other symbolic keywords and evaluations, just as you can with other symbolics operations. The settings persist throughout the calculation.</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>30.7</ml:real>
<ml:id xml:space="preserve">m</ml:id>
</ml:apply>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">float</ml:id>
<ml:real>2</ml:real>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">c</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>31.0</ml:real>
<ml:id xml:space="preserve">m</ml:id>
</ml:apply>
</ml:parens>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="23"></rendering>
</region>
<region region-id="988" left="6" top="1140.75" width="9.75" height="14.25" align-x="6" align-y="1152" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">or</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:sequence>
</ml:command>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">float</ml:id>
<ml:real>2</ml:real>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">c</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>0.17</ml:real>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
</ml:parens>
<ml:id xml:space="preserve">sec</ml:id>
</ml:apply>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="24"></rendering>
</region>
<region region-id="991" left="6" top="1206.75" width="9.75" height="14.25" align-x="6" align-y="1218" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">or</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">B</ml:id>
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">b</ml:id>
<ml:id xml:space="preserve">c</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>5.8</ml:real>
<ml:id xml:space="preserve">sec</ml:id>
</ml:apply>
</ml:parens>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2.36</ml:real>
<ml:parens>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">m</ml:id>
<ml:id xml:space="preserve">sec</ml:id>
</ml:apply>
</ml:parens>
</ml:apply>
</ml:apply>
</ml:symResult>
</ml:symEval>
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</math>
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</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">B</ml:id>
</ml:eval>
</math>
<rendering item-idref="26"></rendering>
</region>
<region region-id="1005" left="6" top="1302.75" width="79.5" height="14.25" align-x="6" align-y="1314" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">are all valid, as is </p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">a</ml:id>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>5.8</ml:real>
<ml:id xml:space="preserve">sec</ml:id>
</ml:apply>
</ml:parens>
</ml:apply>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
</ml:eval>
</math>
<rendering item-idref="27"></rendering>
</region>
<region region-id="1014" left="6" top="1380.75" width="336.75" height="71.25" align-x="6" align-y="1392" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">In this way, explicit calculation is used to revert to the named value of variables in symbolic computations without redefining the variables. Once the value has been masked, you can proceed with a multi-step symbolic or symbolic/numeric computation while treating some variables as names and some as their numeric assignments.</p>
</text>
<indexes>
<phrase>explicit calculation</phrase>
</indexes>
</region>
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<pageBreak></pageBreak>
</region>
<region region-id="1150" left="6" top="1466.25" width="274.5" height="12" align-x="6" align-y="1476" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Subhead" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Substituting Values Dependent on Previous Values</p>
</text>
</region>
<region region-id="1109" left="6" top="1482.75" width="336" height="28.5" align-x="6" align-y="1494" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="true" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can chain definitions, but you have to include the whole sequence of variables to substitute all values, for example</p>
</text>
</region>
<region region-id="1139" left="24" top="1524.75" width="30" height="15.75" align-x="37.5" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">a</ml:id>
<ml:real>2</ml:real>
</ml:define>
</math>
<rendering item-idref="28"></rendering>
</region>
<region region-id="1140" left="84" top="1524.75" width="30.75" height="15.75" align-x="98.25" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">b</ml:id>
<ml:real>3</ml:real>
</ml:define>
</math>
<rendering item-idref="29"></rendering>
</region>
<region region-id="1141" left="150" top="1524.75" width="48.75" height="15.75" align-x="163.5" align-y="1536" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">c</ml:id>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="30"></rendering>
</region>
<region region-id="1160" left="24" top="1552.5" width="114.75" height="33.75" align-x="91.5" align-y="1572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">c</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:parens>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
</ml:parens>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="31"></rendering>
</region>
<region region-id="1161" left="144" top="1552.5" width="138.75" height="33.75" align-x="234.75" align-y="1572" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:parens>
<ml:apply>
<ml:plus></ml:plus>
<ml:real>2</ml:real>
<ml:real>3</ml:real>
</ml:apply>
</ml:parens>
<ml:real>2</ml:real>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="32"></rendering>
</region>
<region region-id="1151" left="6" top="1602.75" width="312" height="28.5" align-x="6" align-y="1614" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">You can make the value of c show up as a single number by symbolically evaluating it in its definition, for example</p>
</text>
</region>
<region region-id="1152" left="24" top="1644.75" width="72.75" height="15.75" align-x="37.5" align-y="1656" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">c</ml:id>
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">a</ml:id>
<ml:id xml:space="preserve">b</ml:id>
</ml:apply>
<ml:symResult>
<ml:real>5</ml:real>
</ml:symResult>
</ml:symEval>
</ml:define>
</math>
<rendering item-idref="33"></rendering>
</region>
<region region-id="1159" left="24" top="1666.5" width="98.25" height="33.75" align-x="102.75" align-y="1686" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:real>5</ml:real>
<ml:real>2</ml:real>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="34"></rendering>
</region>
<region region-id="1158" left="6" top="1704.75" width="363.75" height="14.25" align-x="6" align-y="1716" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">This can be more complex when there are other operators involved, for example:</p>
</text>
</region>
<region region-id="1162" left="24" top="1726.5" width="39" height="18" align-x="38.25" align-y="1740" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">d</ml:id>
<ml:apply>
<ml:sqrt></ml:sqrt>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="35"></rendering>
</region>
<region region-id="1164" left="24" top="1754.25" width="108.75" height="36" align-x="104.25" align-y="1776" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">d</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">d</ml:id>
<ml:id xml:space="preserve">c</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:sqrt></ml:sqrt>
<ml:real>5</ml:real>
</ml:apply>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="36"></rendering>
</region>
<region region-id="1168" left="6" top="1800.75" width="340.5" height="28.5" align-x="6" align-y="1812" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">So, if you want to replace the square root of c with the numeric value, you'll have to choose which symbolic representation you want for d:</p>
</text>
</region>
<region region-id="1177" left="24" top="1852.5" width="78" height="18" align-x="44.25" align-y="1866" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">d1</ml:id>
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:sqrt></ml:sqrt>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:symResult>
<ml:apply>
<ml:sqrt></ml:sqrt>
<ml:real>5</ml:real>
</ml:apply>
</ml:symResult>
</ml:symEval>
</ml:define>
</math>
<rendering item-idref="37"></rendering>
</region>
<region region-id="1178" left="192" top="1852.5" width="141.75" height="18" align-x="212.25" align-y="1866" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">d2</ml:id>
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:sqrt></ml:sqrt>
<ml:id xml:space="preserve">c</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">float</ml:id>
<ml:real>6</ml:real>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:real>2.23607</ml:real>
</ml:symResult>
</ml:symEval>
</ml:define>
</math>
<rendering item-idref="38"></rendering>
</region>
<region region-id="1174" left="24" top="1898.25" width="120.75" height="36" align-x="116.25" align-y="1920" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">d1</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">d1</ml:id>
<ml:id xml:space="preserve">c</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:sqrt></ml:sqrt>
<ml:real>5</ml:real>
</ml:apply>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="39"></rendering>
</region>
<region region-id="1179" left="186" top="1900.5" width="144.75" height="33.75" align-x="278.25" align-y="1920" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="default" hide-keywords="false" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">d2</ml:id>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">d2</ml:id>
<ml:id xml:space="preserve">c</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:real>2.23607</ml:real>
<ml:id xml:space="preserve">a</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="40"></rendering>
</region>
<region region-id="1193" left="0" top="1944" width="6000" height="6" align-x="0" align-y="1944" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1024" left="6" top="1958.25" width="84.75" height="12" align-x="6" align-y="1968" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Subhead" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Display Options</p>
</text>
<indexes>
<phrase>display options</phrase>
</indexes>
</region>
<region region-id="1025" left="6" top="1974.75" width="308.25" height="42.75" align-x="6" align-y="1986" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">When using these symbolic results in reports, you can choose to hide or change the display of the operators and keywords. For example,</p>
</text>
</region>
<region region-id="1106" left="36" top="2022.75" width="57.75" height="15.75" align-x="50.25" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">q</ml:id>
<ml:real>56.234</ml:real>
</ml:define>
</math>
<rendering item-idref="41"></rendering>
</region>
<region region-id="1028" left="126" top="2022.75" width="34.5" height="15.75" align-x="138" align-y="2034" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">r</ml:id>
<ml:real>45</ml:real>
</ml:define>
</math>
<rendering item-idref="42"></rendering>
</region>
<region region-id="1107" left="36" top="2050.5" width="107.25" height="33.75" align-x="106.5" align-y="2070" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:symEval style="equals" hide-keywords="true" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">q</ml:id>
<ml:id xml:space="preserve">r</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">q</ml:id>
<ml:id xml:space="preserve">r</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:real>56.234</ml:real>
<ml:real>45</ml:real>
</ml:apply>
</ml:symResult>
</ml:symEval>
</ml:eval>
</math>
<rendering item-idref="43"></rendering>
</region>
<region region-id="1099" left="6" top="2094.75" width="333.75" height="57" align-x="6" align-y="2106" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The expression above has its keywords hidden and the display of the symbolic equals changed to =. Click on the expression to see the original form. All symbolic equations that use the explicit keyword can have these switches set by default.</p>
</text>
</region>
<region region-id="1036" left="6" top="2166.75" width="336.75" height="71.25" align-x="6" align-y="2178" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To modify the appearance of any symbolically evaluated region, right-click on the left-hand side. The menu options allow you to hide the keywords or the entire left-hand side. A submenu for <b>View Evaluation As</b> lets you replace the symbolic evaluation arrow with an equals sign, just as you can with definitions and global definitions.</p>
</text>
<indexes>
<phrase>view evaluation as</phrase>
</indexes>
</region>
<region region-id="1052" left="6" top="2250.75" width="319.5" height="14.25" align-x="6" align-y="2262" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">These options allow you to construct expressions such as the following:</p>
</text>
</region>
<region region-id="1075" left="42" top="2280.75" width="75" height="15.75" align-x="63" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">F1</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2.987</ml:real>
<ml:id xml:space="preserve">N</ml:id>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="44"></rendering>
</region>
<region region-id="1076" left="144" top="2275.5" width="75" height="21" align-x="166.5" align-y="2292" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">A1</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>5.78</ml:real>
<ml:apply>
<ml:pow></ml:pow>
<ml:id xml:space="preserve">m</ml:id>
<ml:real>2</ml:real>
</ml:apply>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="45"></rendering>
</region>
<region region-id="1056" left="42" top="2314.5" width="82.5" height="33.75" align-x="67.5" align-y="2334" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="equals" hide-keywords="true" hide-lhs="false">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">F1</ml:id>
<ml:id xml:space="preserve">A1</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">F1</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2.987</ml:real>
<ml:id xml:space="preserve">N</ml:id>
</ml:apply>
<ml:id xml:space="preserve">A1</ml:id>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="46"></rendering>
</region>
<region region-id="1078" left="42" top="2362.5" width="91.5" height="39" align-x="67.5" align-y="2382" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:symEval style="equals" hide-keywords="true" hide-lhs="true">
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">F1</ml:id>
<ml:id xml:space="preserve">A1</ml:id>
</ml:apply>
<ml:command>
<ml:sequence>
<ml:id xml:space="preserve">explicit</ml:id>
<ml:id xml:space="preserve">F1</ml:id>
<ml:id xml:space="preserve">A1</ml:id>
</ml:sequence>
</ml:command>
<ml:symResult>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2.987</ml:real>
<ml:id xml:space="preserve">N</ml:id>
</ml:apply>
<ml:parens>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>5.78</ml:real>
<ml:apply>
<ml:pow></ml:pow>
<ml:id xml:space="preserve">m</ml:id>
<ml:real>2</ml:real>
</ml:apply>
</ml:apply>
</ml:parens>
</ml:apply>
</ml:symResult>
</ml:symEval>
</math>
<rendering item-idref="47"></rendering>
</region>
<region region-id="1086" left="42" top="2410.5" width="166.5" height="39" align-x="146.25" align-y="2430" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:symEval style="equals" hide-keywords="true" hide-lhs="true">
<ml:apply>
<ml:div></ml:div>
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