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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 tutorial explores some of Mathcad's built-in programming operators and facilities.</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">Here are the topics covered in this tutorial:</p>
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<p style="list" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<link href="#toolbar" title="Links to section" popup="false">To Program Operators and Local Assignments</link>
</p>
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<text use-page-width="false" push-down="false" lock-width="false">
<p style="list" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<link href="#combine" title="Links to section" popup="false">To Combine Multiple Operations and <b>for</b> Loops</link>
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<p style="list" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<link href="#branch" title="Links to section" popup="false">To Branch with<b> if</b> and <b>otherwise</b> Operators</link>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="list" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<link href="#while" title="Links to section" popup="false">To Loop and Exit with the <b>while</b> Operator</link>
</p>
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<p style="list" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<link href="#errors" title="Links to section" popup="false">To Trap Errors with the <b>on error</b> Operator</link>
</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">Other tutorials show how you can use constructs in Mathcad to <b>
<u>
<link href=".\..\Primers\tu_06.xmcd" title="Links to section" popup="false">create your own functions</link>
</u>
</b> and to iterate through calculations using <b>
<u>
<link href="./feat_03.xmcd#iteration" title="Links to section" popup="false">range variables and arrays</link>
</u>
</b>. Mathcad programs enable you to build more complicated compounds and iterative calculations.</p>
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<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Program Operators and Local Assignments</p>
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<phrase>programming toolbar</phrase>
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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">Mathcad programs are constructed with operators, just like many calculus or matrix expressions. You cannot type the Mathcad programming keywords, such as <b>for</b>, <b>if</b>, and <b>while</b>. You must use the Programming toolbar or the appropriate keystrokes to enter the operators, which show the desired keyword along with placeholders for the arguments.</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 make assignments in Mathcad programs just as you can in your worksheet. When the assignments occur in programs, they are local assignments, that is, they are only true with the program operator that contains them, and are not recognized elsewhere in the worksheet. They can even override other worksheet definitions just within the program.</p>
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<b>
<c val="#008080">1.</c>
</b>
<sp count="2"></sp>To view the <b>Programming</b> toolbar, choose <b>Toolbars &gt; Programming </b>from the <b>View</b> menu, or use the icon shown at right on the <b>Math</b> toolbar.</p>
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<b>
<c val="#008080">2.</c>
</b>
<sp count="2"></sp>To begin creating programs, choose <b>Add Line</b> from the toolbar, or type <f family="Verdana" charset="0" size="10">
<b>]</b>
</f>.</p>
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<b>
<c val="#008080">3.</c>
</b>
<sp count="2"></sp>In the first placeholder, enter the name of a local variable (for example, <inlineAttr font-weight="normal">x</inlineAttr>). </p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">4.</c>
</b>
<sp count="2"></sp>Choose the <b>local definition operator</b> (the <b>left-arrow</b>) from the toolbar, or type <f family="Verdana" charset="0" size="10">
<b>{</b>
</f>
<b>
<sp></sp>
</b>and type a value or expression for x, such as <f family="Verdana" charset="0" size="10">
<b>6*34</b>
</f>.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">5.</c>
</b>
<sp count="2"></sp>In the following placeholder, type <f family="Verdana" charset="0" size="10">
<b>x</b>
</f>, then type <f family="Verdana" charset="0" size="10">
<b>[Spacebar]=</b>
</f> to select the whole program and evaluate it.</p>
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<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:program>
<ml:localDefine>
<ml:id xml:space="preserve">x</ml:id>
<ml:apply>
<ml:mult style="dot"></ml:mult>
<ml:real>6</ml:real>
<ml:real>34</ml:real>
</ml:apply>
</ml:localDefine>
<ml:id xml:space="preserve">x</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>204</ml:real>
</result>
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</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">The last line of this program simply returns the value x. If you wish, you can use the return operator (type <f family="Verdana" charset="0" size="10">
<b>[Ctrl] [|]</b>
</f>) to specifically show what this last line does. Note that the variable<b>
<sp></sp>
</b>
<inlineAttr font-weight="normal">x</inlineAttr> is not defined outside of the program.</p>
</text>
</region>
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<ml:id xml:space="preserve">x</ml:id>
</ml:return>
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<math error="This variable is undefined." optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">x</ml:id>
</ml:eval>
</math>
<metadata>
<customValue name="Mathsoft_expected_error" type="text">bad_variable	mc_x	mc_x		value_zone</customValue>
</metadata>
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<region region-id="3861" left="6" top="914.25" width="336" height="12" align-x="22.5" align-y="924" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="combine">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Combine Multiple Operations and for Loops</p>
</text>
</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">Any combination of Mathcad expressions can be conveniently wrapped in a program, either to group expressions for compactness, or to iterate in a particular way that would be difficult to do with range variables and other worksheet-level constructs. Let's build a program that calculates the residuals and the sum of squares error from a polynomial regression all in one step.</p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">1.</c>
</b>
<sp count="2"></sp>Define a function Res(X,Y,n). Choose <b>Add Line</b>
<inlineAttr font-weight="normal">
<sp></sp>
</inlineAttr>from the <b>Programming</b> toolbar (or type <f family="Verdana" charset="0" size="10">
<b>]</b>
</f>) to begin a new program.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">2.</c>
</b>
<sp count="2"></sp>In the first placeholder, locally assign (<b>
<f family="Verdana" charset="0" size="10">{</f>
</b>) the output of the regress function to <inlineAttr font-weight="normal">c</inlineAttr>.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">3.</c>
</b>
<sp count="2"></sp>Using the<b> for</b> operator from the toolbar (or type <f family="Verdana" charset="0" size="10">
<b>[Ctrl]"</b>
</f>), enter a range over which to loop in the placeholders by typing <f family="Verdana" charset="0" size="10">
<b>i[Tab]0;last(X)</b>
</f>.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">4.</c>
</b>
<sp count="2"></sp>In the placeholder below the <b>for</b> operator, type <f family="Verdana" charset="0" size="10">
<b>e[i [Spacebar] {Y[i [Spacebar] - interp(c,X,Y,X[i)</b>
</f>.</p>
</text>
</region>
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<pageBreak></pageBreak>
</region>
<region region-id="3918" left="12" top="1182" width="181.5" height="48.75" align-x="12" align-y="1182" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<picture>
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</picture>
<rendering item-idref="10"></rendering>
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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">
<b>
<c val="#008080">Note: </c>
</b>To add lines after a <b>for </b>loop, you have to select the whole expression, otherwise you'll nest more instructions inside the loop.</p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">5.</c>
</b>
<sp count="2"></sp>Select the whole<b> for </b>expression in the editing lines, and add another line to the program. In the placeholder below the loop, type <f family="Verdana" charset="0" size="10">
<b>out[0 [Spacebar] { e</b>
</f>.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">6.</c>
</b> Once again, select the whole line that assigns out<sub>0</sub>, add another line, and type <f family="Verdana" charset="0" size="10">
<b>out[1 [Spacebar] { [Ctrl]4 e^2</b>
</f>.<sp count="2"></sp>
</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<c val="#008080">
<b>7.</b>
</c> Once again, select the whole line that assigns out<sub>1</sub>, add another line, and type <f family="Verdana" charset="0" size="10">
<b>[Ctrl]| out</b>
</f>. </p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Example </p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
<ml:id xml:space="preserve">Res</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:localDefine>
<ml:id xml:space="preserve">c</ml:id>
<ml:apply>
<ml:id xml:space="preserve">regress</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">n</ml:id>
</ml:sequence>
</ml:apply>
</ml:localDefine>
<ml:for>
<ml:id xml:space="preserve">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:apply>
<ml:id xml:space="preserve">last</ml:id>
<ml:id xml:space="preserve">X</ml:id>
</ml:apply>
</ml:range>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">e</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
<ml:apply>
<ml:minus></ml:minus>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">Y</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve">interp</ml:id>
<ml:sequence>
<ml:id xml:space="preserve">c</ml:id>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
</ml:sequence>
</ml:apply>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">out</ml:id>
<ml:real>0</ml:real>
</ml:apply>
<ml:id xml:space="preserve">e</ml:id>
</ml:localDefine>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">out</ml:id>
<ml:real>1</ml:real>
</ml:apply>
<ml:apply>
<ml:vectorSum></ml:vectorSum>
<ml:apply>
<ml:pow></ml:pow>
<ml:id xml:space="preserve">e</ml:id>
<ml:real>2</ml:real>
</ml:apply>
</ml:apply>
</ml:localDefine>
<ml:return>
<ml:id xml:space="preserve">out</ml:id>
</ml:return>
</ml:program>
</ml:define>
</math>
<rendering item-idref="11"></rendering>
</region>
<region region-id="3925" left="6" top="1548.75" width="316.5" height="57" align-x="6" align-y="1560" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
<c val="#000">This function takes a pair </c>
<f family="Times New Roman" charset="0">
<inlineAttr font-style="normal" line-through="false">
<c val="#000">of X-Y data vectors and an integer regression polynomial order n. It doesn't explicitly say to return the vector </c>
</inlineAttr>
</f>
<f family="Times New Roman" charset="0">
<b>
<inlineAttr font-style="normal" line-through="false">
<c val="#000">out</c>
</inlineAttr>
</b>
</f>
<f family="Times New Roman" charset="0">
<inlineAttr font-style="normal" line-through="false">
<c val="#000"> because programs return the last thing they calculate by default.</c>
</inlineAttr>
</f>
</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">X</ml:id>
<ml:matrix rows="5" cols="1">
<ml:real>0</ml:real>
<ml:real>0.1</ml:real>
<ml:real>0.35</ml:real>
<ml:real>0.7</ml:real>
<ml:real>1</ml:real>
</ml:matrix>
</ml:define>
</math>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">Y</ml:id>
<ml:matrix rows="5" cols="1">
<ml:real>0</ml:real>
<ml:real>1</ml:real>
<ml:real>9</ml:real>
<ml:real>1</ml:real>
<ml:real>4</ml:real>
</ml:matrix>
</ml:define>
</math>
<rendering item-idref="13"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:id xml:space="preserve">n</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">poly2</ml:id>
<ml:apply>
<ml:id xml:space="preserve">Res</ml:id>
<ml:sequence>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">Y</ml:id>
<ml:real>2</ml:real>
</ml:sequence>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="15"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">poly2</ml:id>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="2" cols="1">
<ml:matrix rows="5" cols="1">
<ml:real>-0.52661830083428862</ml:real>
<ml:real>-1.1152842867526083</ml:real>
<ml:real>4.2676321996941082</ml:real>
<ml:real>-4.1452892362984537</ml:real>
<ml:real>1.5195596241912384</ml:real>
</ml:matrix>
<ml:real>39.226354770960874</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="16"></rendering>
</region>
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<pageBreak></pageBreak>
</region>
<region region-id="3938" left="6" top="1764.75" width="301.5" height="28.5" align-x="6" align-y="1776" 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 program returns the residuals as a vector nested in the first element of the return vector.</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:transpose></ml:transpose>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">poly2</ml:id>
<ml:real>0</ml:real>
</ml:apply>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="1" cols="5">
<ml:real>-0.52661830083428862</ml:real>
<ml:real>-1.1152842867526083</ml:real>
<ml:real>4.2676321996941082</ml:real>
<ml:real>-4.1452892362984537</ml:real>
<ml:real>1.5195596241912384</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="17"></rendering>
</region>
<region region-id="3947" left="6" top="1842.75" width="310.5" height="99.75" align-x="6" align-y="1854" 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">Since programs, like any Mathcad expression, can only have one result, it's convenient to return multiple calculation results stacked into a single vector. </p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"></p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">The function Res now behaves like any other user-defined function. For example, we can call it with a range variable as the argument defining the order of the polynomial, to compare the fits.</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define warning="WarnRedefinedBIFunction">
<ml:id xml:space="preserve">or</ml:id>
<ml:range>
<ml:real>1</ml:real>
<ml:real>4</ml:real>
</ml:range>
</ml:define>
</math>
<rendering item-idref="18"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">err</ml:id>
<ml:apply>
<ml:minus></ml:minus>
<ml:id xml:space="preserve">or</ml:id>
<ml:real>1</ml:real>
</ml:apply>
</ml:apply>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:apply>
<ml:id xml:space="preserve">Res</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">or</ml:id>
</ml:sequence>
</ml:apply>
<ml:real>1</ml:real>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="19"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:id xml:space="preserve">err</ml:id>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="4" cols="1">
<ml:real>50.776504297994265</ml:real>
<ml:real>39.226354770960874</ml:real>
<ml:real>13.988391841485679</ml:real>
<ml:real>3.5507122382063504E-27</ml:real>
</ml:matrix>
</result>
</ml:eval>
<resultFormat>
<general precision="3" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
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</region>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Branch with the if and otherwise Operators</p>
</text>
<indexes>
<phrase>programming, branching</phrase>
<phrase>if operator</phrase>
<phrase>while operator</phrase>
</indexes>
</region>
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<text use-page-width="false" push-down="false" lock-width="true">
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">1.</c>
</b>
<sp count="2"></sp>Define a function PW(x,n). Choose <b>Add Line</b>
<inlineAttr font-weight="normal">
<sp></sp>
</inlineAttr>from the <b>Programming</b> toolbar (or type <f family="Verdana" charset="0" size="10">
<b>]</b>
</f>) to begin a new program.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">2.</c>
</b>
<sp count="2"></sp>In the first placeholder, type <f family="Verdana" charset="0" size="10">
<b>sin(x*p[Ctrl]g/n)</b>
</f>. Select the whole <inlineAttr font-weight="normal">sin</inlineAttr> expression and choose the<b> if </b>operator from the <b>Programming</b> toolbar, or type <b>
<f family="Verdana" charset="0" size="10">}</f>
</b>. </p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">3.</c>
</b>
<sp count="2"></sp>In the new placeholder to the right of if, type <f family="Verdana" charset="0" size="10">
<b>0&lt;x&lt;n</b>
</f>.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">4.</c>
</b>
<sp count="2"></sp>Repeat this process for two new if statements, one showing the value for x less than or equal to 0, and one for x greater than or equal to n. </p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Example </p>
</text>
</region>
<region region-id="3996" left="222" top="2226.75" width="117" height="99.75" align-x="222" align-y="2238" 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">This piecewise function may be easier to enter if you use the comparison operators from the <b>Boolean</b> toolbar (choose <b>Toolbars &gt; Boolean</b> from the <b>View</b> menu).</p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
<ml:id xml:space="preserve">PW</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:ifThen>
<ml:apply>
<ml:lessThan></ml:lessThan>
<ml:apply>
<ml:lessThan></ml:lessThan>
<ml:real>0</ml:real>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve">sin</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:id xml:space="preserve">x</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">π</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
</ml:apply>
</ml:apply>
</ml:ifThen>
<ml:ifThen>
<ml:apply>
<ml:lessOrEqual></ml:lessOrEqual>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>0</ml:real>
</ml:apply>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:neg></ml:neg>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
</ml:ifThen>
<ml:ifThen>
<ml:apply>
<ml:greaterOrEqual></ml:greaterOrEqual>
<ml:id xml:space="preserve">x</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:minus></ml:minus>
<ml:id xml:space="preserve">x</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
</ml:ifThen>
</ml:program>
</ml:define>
</math>
<rendering item-idref="21"></rendering>
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<pageBreak></pageBreak>
</region>
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<plot disable-calc="false" item-idref="22"></plot>
<rendering item-idref="23"></rendering>
</region>
<region region-id="4000" left="6" top="2454.75" width="333" height="114" align-x="6" align-y="2466" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Mathcad evaluates each if statement regardless of whether the previous if statements were true or false. It is possible to get the result of an if clause on a lower line than you intended when a subsequent condition also evaluates to true.</p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit"></p>
<p style="Normal" margin-left="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">When the if statements in a program do not cover all the possible inputs and you call the function with a value that <i>falls through</i>, you get the last value evaluated by the program. </p>
</text>
<indexes>
<phrase>if, insufficient casing</phrase>
</indexes>
</region>
<region region-id="4276" left="6" top="2582.25" width="50.25" height="12" align-x="6" align-y="2592" 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="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Example </p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
<ml:id xml:space="preserve">test</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">n</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:localDefine>
<ml:id xml:space="preserve">val</ml:id>
<ml:apply>
<ml:id xml:space="preserve">cos</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">π</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
</ml:apply>
</ml:localDefine>
<ml:ifThen>
<ml:apply>
<ml:equal></ml:equal>
<ml:id xml:space="preserve">val</ml:id>
<ml:real>0.5</ml:real>
</ml:apply>
<ml:real>1</ml:real>
</ml:ifThen>
<ml:ifThen>
<ml:apply>
<ml:lessThan></ml:lessThan>
<ml:id xml:space="preserve">val</ml:id>
<ml:real>0.5</ml:real>
</ml:apply>
<ml:real>2</ml:real>
</ml:ifThen>
</ml:program>
</ml:define>
</math>
<rendering item-idref="24"></rendering>
</region>
<region region-id="4009" left="18" top="2694.75" width="69.75" height="15.75" align-x="66" align-y="2706" 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:apply>
<ml:id xml:space="preserve">test</ml:id>
<ml:real>0.5</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>1</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="25"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">test</ml:id>
<ml:real>6</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>0.86602540378443871</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="26"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">test</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:real>3</ml:real>
<ml:real>5</ml:real>
</ml:apply>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>0.50000000000000011</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="27"></rendering>
</region>
<region region-id="4015" left="102" top="2728.5" width="173.25" height="33.75" align-x="154.5" align-y="2748" 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:apply>
<ml:id xml:space="preserve">cos</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:apply>
<ml:mult style="auto-select"></ml:mult>
<ml:real>5</ml:real>
<ml:id xml:space="preserve">π</ml:id>
</ml:apply>
<ml:real>3</ml:real>
</ml:apply>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>0.50000000000000011</ml:real>
</result>
</ml:eval>
<resultFormat>
<general precision="17" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="true" simplify-units="true" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="28"></rendering>
</region>
<region region-id="4012" left="6" top="2772.75" width="336" height="129" align-x="6" align-y="2784" 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 perplexing example the variable<i>
<sp></sp>
</i>
<inlineAttr font-style="normal">val</inlineAttr> is the last thing calculated for the first two values of n. Both <b>if </b>tests fail, so <inlineAttr font-style="normal">val</inlineAttr> is returned. You might have expected the last case, cos(5<f family="Symbol" charset="2" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">p</inlineAttr>
</f>
<f family="Times New Roman" charset="0" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">/3), to produce 0.5, but the </inlineAttr>
</f>first test does not <f family="Times New Roman" charset="0" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">catch it because of </inlineAttr>
</f>
<b>
<u>
<link href=".\..\..\Techniques\roundoff.xmcd" title="Links to section" popup="false">small numerical accuracy differences</link>
</u>
</b>
<f family="Times New Roman" charset="0" size="12">
<inlineAttr font-weight="normal" font-style="normal" underline="false" line-through="false">. Although the result is incorrect</inlineAttr>
</f>, it doesn't cause an error, so it can be very hard to spot and debug.</p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit"></p>
<p style="Normal" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<c val="#000">Programs require a statement that can handle the cases you don't want to specify explicitly. This is what you use the </c>
<b>
<c val="#000">otherwise</c>
</b>
<c val="#000"> operator for.</c>
</p>
</text>
</region>
<region region-id="4017" left="0" top="2922" width="6000" height="6" align-x="0" align-y="2922" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
<ml:id xml:space="preserve">test2</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">n</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:localDefine>
<ml:id xml:space="preserve">val</ml:id>
<ml:apply>
<ml:id xml:space="preserve">cos</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">π</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
</ml:apply>
</ml:localDefine>
<ml:ifThen>
<ml:apply>
<ml:equal></ml:equal>
<ml:apply>
<ml:id xml:space="preserve">round</ml:id>
<ml:sequence>
<ml:id xml:space="preserve">val</ml:id>
<ml:real>2</ml:real>
</ml:sequence>
</ml:apply>
<ml:real>0.5</ml:real>
</ml:apply>
<ml:real>1</ml:real>
</ml:ifThen>
<ml:otherwise>
<ml:real>2</ml:real>
</ml:otherwise>
</ml:program>
</ml:define>
</math>
<rendering item-idref="29"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">test2</ml:id>
<ml:real>0.5</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>2</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="30"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">test2</ml:id>
<ml:real>6</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>2</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="31"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">test2</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:real>3</ml:real>
<ml:real>5</ml:real>
</ml:apply>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>1</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="32"></rendering>
</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">Note that the otherwise operator only refers to the <b>if</b> operator that immediately precedes it. If you want to exit from a function when a condition is true, couple the <b>if</b> operator with a <b>return</b> operator, also on the <b>Programming</b> toolbar.</p>
</text>
</region>
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<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Example </p>
</text>
</region>
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<math optimize="false" disable-calc="false">
<ml:define>
<ml:function>
<ml:id xml:space="preserve">type</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:ifThen>
<ml:apply>
<ml:notEqual></ml:notEqual>
<ml:apply>
<ml:id xml:space="preserve">Im</ml:id>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:real>0</ml:real>
</ml:apply>
<ml:return>
<ml:str xml:space="preserve">complex</ml:str>
</ml:return>
</ml:ifThen>
<ml:ifThen>
<ml:apply>
<ml:equal></ml:equal>
<ml:apply>
<ml:id xml:space="preserve">floor</ml:id>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:return>
<ml:str xml:space="preserve">integer</ml:str>
</ml:return>
</ml:ifThen>
<ml:otherwise>
<ml:return>
<ml:str xml:space="preserve">float</ml:str>
</ml:return>
</ml:otherwise>
</ml:program>
</ml:define>
</math>
<rendering item-idref="33"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">type</ml:id>
<ml:real>2.6</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:str xml:space="preserve">float</ml:str>
</result>
</ml:eval>
</math>
<rendering item-idref="34"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">type</ml:id>
<ml:apply>
<ml:sqrt></ml:sqrt>
<ml:real>-1</ml:real>
</ml:apply>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:str xml:space="preserve">complex</ml:str>
</result>
</ml:eval>
</math>
<rendering item-idref="35"></rendering>
</region>
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<math optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">type</ml:id>
<ml:real>-9</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:str xml:space="preserve">integer</ml:str>
</result>
</ml:eval>
</math>
<rendering item-idref="36"></rendering>
</region>
<region region-id="4106" left="6" top="3282.75" width="333.75" height="42.75" align-x="6" align-y="3294" 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">Without the explicit use of the <b>return</b> operator, any complex value with integer components would be listed as type "integer" since both the first and second<b> if</b> statements would evaluate to true as the program executes.</p>
</text>
</region>
<region region-id="4065" left="6" top="3344.25" width="285.75" height="12" align-x="27" align-y="3354" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="while">
<text use-page-width="false" push-down="false" lock-width="true">
<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Loop and Exit with the while Operator</p>
</text>
</region>
<region region-id="4066" left="6" top="3360.75" width="336.75" height="57" align-x="6" align-y="3372" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">Sometimes you don't know exactly how many iterations through a procedure are required before a condition is met. You could pick a huge number of iterations and set up a <b>for</b> loop, but it might be a waste of time and computation and still doesn't guarantee that the program finishes.</p>
</text>
</region>
<region region-id="4116" left="0" top="3432" width="6000" height="6" align-x="0" align-y="3432" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="4067" left="6" top="3444.75" width="321" height="114" align-x="6" align-y="3456" 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="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">1.</c>
</b>
<sp count="2"></sp>Define a function Newton(x). Choose <b>Add Line</b>
<inlineAttr font-weight="normal">
<sp></sp>
</inlineAttr>from the <b>Programming</b> toolbar (or type <f family="Verdana" charset="0" size="10">
<b>]</b>
</f>) to begin a new program.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">2.</c>
</b>
<sp count="2"></sp>In the first placeholder, type <f family="Verdana" charset="0" size="10">
<b>eps{10^-6</b>
</f>.<sp count="2"></sp>In the next placeholder, likewise locally assign r to x/2 by typing <f family="Verdana" charset="0" size="10">
<b>r{x/2</b>
</f>.<sp count="2"></sp>Select the whole expression and add another line.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<c val="#008080">
<b>3.</b>
</c>
<sp count="2"></sp>In the new placeholder, type <f family="Verdana" charset="0" size="10">
<b>rnew{r/2[Spacebar]+x/2*r</b>
</f>. Select the whole expression and add another line.</p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">4.</c>
</b> Choose the <b>while</b> operator from the toolbar, or type <f family="Verdana" charset="0" size="10">
<b>[Ctrl]]</b>
</f>.</p>
</text>
</region>
<region region-id="4280" left="6" top="3572.25" width="50.25" height="12" align-x="6" align-y="3582" 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="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Example </p>
</text>
</region>
<region region-id="4069" left="18" top="3589.5" width="201" height="201" align-x="78" align-y="3606" 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:function>
<ml:id xml:space="preserve">Newton</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:localDefine>
<ml:id xml:space="preserve">eps</ml:id>
<ml:apply>
<ml:pow></ml:pow>
<ml:real>10</ml:real>
<ml:real>-6</ml:real>
</ml:apply>
</ml:localDefine>
<ml:localDefine>
<ml:id xml:space="preserve">r</ml:id>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>2</ml:real>
</ml:apply>
</ml:localDefine>
<ml:localDefine>
<ml:id xml:space="preserve">rnew</ml:id>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">r</ml:id>
<ml:real>2</ml:real>
</ml:apply>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">x</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2</ml:real>
<ml:id xml:space="preserve">r</ml:id>
</ml:apply>
</ml:apply>
</ml:apply>
</ml:localDefine>
<ml:while>
<ml:apply>
<ml:greaterThan></ml:greaterThan>
<ml:apply>
<ml:absval></ml:absval>
<ml:apply>
<ml:minus></ml:minus>
<ml:id xml:space="preserve">rnew</ml:id>
<ml:id xml:space="preserve">r</ml:id>
</ml:apply>
</ml:apply>
<ml:id xml:space="preserve">eps</ml:id>
</ml:apply>
<ml:program>
<ml:localDefine>
<ml:id xml:space="preserve">r</ml:id>
<ml:id xml:space="preserve">rnew</ml:id>
</ml:localDefine>
<ml:localDefine>
<ml:id xml:space="preserve">rnew</ml:id>
<ml:apply>
<ml:plus></ml:plus>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">r</ml:id>
<ml:real>2</ml:real>
</ml:apply>
<ml:apply>
<ml:div></ml:div>
<ml:id xml:space="preserve">x</ml:id>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2</ml:real>
<ml:id xml:space="preserve">r</ml:id>
</ml:apply>
</ml:apply>
</ml:apply>
</ml:localDefine>
</ml:program>
</ml:while>
<ml:id xml:space="preserve">rnew</ml:id>
</ml:program>
</ml:define>
</math>
<rendering item-idref="37"></rendering>
</region>
<region region-id="4074" left="6" top="3804.75" width="329.25" height="42.75" align-x="14.25" align-y="3816" 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 <b>while</b> operator executes all the statements in the loop until the condition is false. The program above uses a variation of Newton's method to find approximations to square roots within some value of <inlineAttr font-weight="normal">eps.</inlineAttr>
</p>
</text>
</region>
<region region-id="4085" left="18" top="3864.75" width="174.75" height="15.75" align-x="78" align-y="3876" 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:apply>
<ml:id xml:space="preserve">Newton</ml:id>
<ml:real>2</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>1.4142135623730949</ml:real>
</result>
</ml:eval>
<resultFormat>
<general precision="15" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="false" simplify-units="false" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="38"></rendering>
</region>
<region region-id="4086" left="54" top="3886.5" width="137.25" height="18" align-x="76.5" align-y="3900" 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:apply>
<ml:sqrt></ml:sqrt>
<ml:real>2</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>1.4142135623730952</ml:real>
</result>
</ml:eval>
<resultFormat>
<general precision="15" show-trailing-zeros="false" radix="dec" complex-threshold="10" zero-threshold="15" imaginary-value="i" exponential-threshold="3"></general>
<matrix display-style="auto" expand-nested-arrays="false"></matrix>
<unit format-units="false" simplify-units="false" fractional-unit-exponent="false"></unit>
</resultFormat>
</math>
<rendering item-idref="39"></rendering>
</region>
<region region-id="4121" left="6" top="3920.25" width="221.25" height="12" align-x="6" align-y="3930" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="errors">
<text use-page-width="false" push-down="false" lock-width="false">
<p style="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">To Trap Errors with the on error Operator</p>
</text>
</region>
<region region-id="4118" left="6" top="3936.75" width="315" height="28.5" align-x="6" align-y="3948" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">
<f family="Times New Roman" charset="0" size="12">
<c val="#000">The </c>
</f>
<f family="Times New Roman" charset="0" size="12">
<b>
<inlineAttr font-style="normal" line-through="false">
<c val="#000">on error </c>
</inlineAttr>
</b>
</f>
<f family="Times New Roman" charset="0" size="12">
<c val="#000">operator returns the expression on the right, unless it is in error, in which case it returns the expression on the left.</c>
</f>
</p>
</text>
</region>
<region region-id="4135" left="6" top="3978.75" width="321" height="42.75" align-x="6" align-y="3990" 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="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">1.</c>
</b>
<sp count="2"></sp>Define f(x), and in the placeholder after the := type <f family="Verdana" charset="0" size="10">
<b>arg(10^-2)</b>
</f>. </p>
<p style="Normal" margin-left="14.25" margin-right="0" text-indent="-14.25" text-align="left" list-style-type="none" tabs="inherit">
<b>
<c val="#008080">2.</c>
</b>
<sp count="2"></sp>Choose the<b> on error</b> operator, or press <f family="Verdana" charset="0" size="10">
<b>[Ctrl] [']</b>
</f>, and in the placeholder, type <f family="Verdana" charset="0" size="10">
<b>arg(x)</b>
</f>.</p>
</text>
</region>
<region region-id="4255" left="0" top="4032" width="6000" height="6" align-x="0" align-y="4032" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="4282" left="6" top="4040.25" width="50.25" height="12" align-x="6" align-y="4050" 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="Heading 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Example </p>
</text>
</region>
<region region-id="4258" left="6" top="4062.75" width="321" height="28.5" align-x="6" align-y="4074" 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="0" text-align="inherit" list-style-type="none" tabs="inherit">Using the <b>on error</b> operator you can return another value that lets subsequent calculations continue without failing.</p>
</text>
</region>
<region region-id="4248" left="18" top="4099.5" width="167.25" height="21" align-x="45.75" align-y="4116" 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:function>
<ml:id xml:space="preserve">f</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
</ml:boundVars>
</ml:function>
<ml:tryCatch>
<ml:apply>
<ml:id xml:space="preserve">arg</ml:id>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve">arg</ml:id>
<ml:apply>
<ml:pow></ml:pow>
<ml:real>10</ml:real>
<ml:real>-2</ml:real>
</ml:apply>
</ml:apply>
</ml:tryCatch>
</ml:define>
</math>
<rendering item-idref="40"></rendering>
</region>
<region region-id="4249" left="18" top="4134.75" width="45.75" height="15.75" align-x="31.5" align-y="4146" 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">n</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>3</ml:real>
</ml:range>
</ml:define>
</math>
<rendering item-idref="41"></rendering>
</region>
<region region-id="4250" left="126" top="4134.75" width="73.5" height="17.25" align-x="146.25" align-y="4146" 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:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">Z</ml:id>
<ml:id xml:space="preserve">n</ml:id>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:id xml:space="preserve">n</ml:id>
<ml:parens>
<ml:apply>
<ml:plus></ml:plus>
<ml:real>1</ml:real>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:id xml:space="preserve">n</ml:id>
<ml:imag symbol="j">1</ml:imag>
</ml:apply>
</ml:apply>
</ml:parens>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="42"></rendering>
</region>
<region region-id="4251" left="18" top="4163.25" width="87.75" height="78.75" align-x="46.5" align-y="4206" 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:apply>
<ml:vectorize></ml:vectorize>
<ml:apply>
<ml:id xml:space="preserve">f</ml:id>
<ml:id xml:space="preserve">Z</ml:id>
</ml:apply>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="4" cols="1">
<ml:real>0</ml:real>
<ml:real>0.78539816339744828</ml:real>
<ml:real>1.1071487177940904</ml:real>
<ml:real>1.2490457723982544</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="43"></rendering>
</region>
<region region-id="4252" left="138" top="4192.5" width="59.25" height="24" align-x="176.25" align-y="4212" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math error="This value cannot be 0." optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:vectorize></ml:vectorize>
<ml:apply>
<ml:id xml:space="preserve">arg</ml:id>
<ml:id xml:space="preserve">Z</ml:id>
</ml:apply>
</ml:apply>
</ml:eval>
</math>
<metadata>
<customValue name="Mathsoft_expected_error" type="text">must be nonzero</customValue>
</metadata>
<rendering item-idref="44"></rendering>
</region>
<region region-id="4265" left="6" top="4254.75" width="325.5" height="42.75" align-x="6" align-y="4266" 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 also use the <b>on error</b> operator to produce a customized error message (click on the evaluation of f(0) below to see it), which might provide a better alternative to the Mathcad error in some situations. </p>
</text>
</region>
<region region-id="4266" left="18" top="4312.5" width="239.25" height="33.75" align-x="45.75" align-y="4332" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math optimize="false" disable-calc="false">
<ml:define warning="WarnRedefinedUDFunction">
<ml:function>
<ml:id xml:space="preserve">f</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
</ml:boundVars>
</ml:function>
<ml:tryCatch>
<ml:apply>
<ml:div></ml:div>
<ml:real>1</ml:real>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:return>
<ml:apply>
<ml:id xml:space="preserve">error</ml:id>
<ml:str xml:space="preserve">x must not be 0</ml:str>
</ml:apply>
</ml:return>
</ml:tryCatch>
</ml:define>
</math>
<rendering item-idref="45"></rendering>
</region>
<region region-id="4267" left="18" top="4356.75" width="48.75" height="15.75" align-x="45.75" align-y="4368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math error="x must not be 0" optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:id xml:space="preserve">f</ml:id>
<ml:real>0</ml:real>
</ml:apply>
</ml:eval>
</math>
<metadata>
<customValue name="Mathsoft_expected_error" type="text">x must not be 0</customValue>
</metadata>
<rendering item-idref="46"></rendering>
</region>
<region region-id="4268" left="102" top="4348.5" width="37.5" height="33.75" align-x="118.5" align-y="4368" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math error="Divide by zero." optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:apply>
<ml:div></ml:div>
<ml:real>1</ml:real>
<ml:real>0</ml:real>
</ml:apply>
</ml:eval>
</math>
<metadata>
<customValue name="Mathsoft_expected_error" type="text">divide by zero</customValue>
</metadata>
<rendering item-idref="47"></rendering>
</region>
<region region-id="4269" left="174" top="4356.75" width="58.5" height="15.75" align-x="201.75" align-y="4368" 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:apply>
<ml:id xml:space="preserve">f</ml:id>
<ml:real>2</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>0.5</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="48"></rendering>
</region>
<region region-id="4178" left="6" top="4398.75" width="339" height="28.5" align-x="6" align-y="4410" 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="0" margin-right="0" text-indent="inherit" text-align="left" list-style-type="inherit" tabs="inherit">For more programming examples and usage tips, see the <link href=".\..\..\Programming\progrtoc.xmcd" title="Links to section" popup="false">
<b>
<u>Programming QuickShee</u>
</b>
<b>
<u>t</u>
</b>
</link>
<b>
<u>s</u>
</b> and online Help.</p>
</text>
</region>
<region region-id="4288" left="6" top="4446.75" width="342.75" height="14.25" align-x="6" align-y="4458" 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 <b>
<u>
<link href="./debug.xmcd" title="Links to section" popup="false">Program Debugging</link>
</u>
</b> tool will help you spot errors in your programs.</p>
</text>
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