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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">Newer versions of Mathcad make some changes to program behavior so that the same construct produces the same results regardless of where it is used. These changes introduced some incompatibilities between Mathcad versions, due to fixing some bugs in earlier versions. This worksheet catalogs the changes and shows ways to make programs consistent and clear.</p>
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<p style="Header 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Return Value of Local Assignments</p>
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<b>MC11, MC13, and MC14:</b> Local assignments return the right-hand side of the expression.</p>
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<b>MC12:</b> Local assignments return the left-hand side of the expression.</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">In Mathcad 12, the left-side of a local assignment is returned, which results in different values when the local assignment is the last statement used in a program loop. In all other versions of Mathcad, the right-side of a local assignment is the return value:</p>
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<b>Mathcad</b>
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<b>Mathcad 12</b>
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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">To make all versions of Mathcad return the same value, use a return operator on a separate line. Your programs will also be clearer:</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">Mathcad 13 and higher versions have a <b>
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</b> on the "Compatibility" tab of <b>Worksheet Options</b> under the <b>Tools</b> menu that allows you to set the behavior of this construct. Use the switch only to see how an earlier version would have calculated the result. We recommend that you use explicit return statements to clarify what the program should return in all cases.</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">Note that there is a bug in Mathcad 11 that causes it to return the left side of a local evaluation when a matrix column is assigned. This kind of assignment has been made consistent in Mathcad to return the right-hand evaluation, </p>
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<ml:real>0</ml:real>
<ml:real>2</ml:real>
<ml:real>0</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="8"></rendering>
</region>
<region region-id="1776" left="6" top="876.75" width="349.5" height="28.5" align-x="6" align-y="888" 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, as before, explicitly return the whole matrix, B, if you want a result consistent with version 11:</p>
</text>
</region>
<region region-id="1781" left="30" top="909.75" width="143.25" height="83.25" align-x="120.75" align-y="942" 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:program>
<ml:localDefine>
<ml:id xml:space="preserve">A</ml:id>
<ml:apply>
<ml:id xml:space="preserve">identity</ml:id>
<ml:real>3</ml:real>
</ml:apply>
</ml:localDefine>
<ml:localDefine>
<ml:apply>
<ml:matcol></ml:matcol>
<ml:id xml:space="preserve">B</ml:id>
<ml:real>1</ml:real>
</ml:apply>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2</ml:real>
<ml:apply>
<ml:matcol></ml:matcol>
<ml:id xml:space="preserve">A</ml:id>
<ml:real>1</ml:real>
</ml:apply>
</ml:apply>
</ml:localDefine>
<ml:return>
<ml:id xml:space="preserve">B</ml:id>
</ml:return>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="3" cols="2">
<ml:real>0</ml:real>
<ml:real>0</ml:real>
<ml:real>0</ml:real>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
<ml:real>0</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="9"></rendering>
</region>
<region region-id="1687" left="6" top="1004.25" width="210" height="12" align-x="6" align-y="1014" 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="Header 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Evaluation Order of Local Assignments</p>
</text>
<indexes>
<phrase>local assignments, evaluation order</phrase>
</indexes>
</region>
<region region-id="1688" left="6" top="1028.25" width="308.25" height="24" align-x="25.5" align-y="1038" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC11, MC13, and MC14:</b> Expressions with local assignments are evaluated right to left.</p>
</text>
</region>
<region region-id="1689" left="6" top="1058.25" width="308.25" height="24" align-x="25.5" align-y="1068" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC12:</b> Expressions with local assignments are evaluated left to right.</p>
</text>
</region>
<region region-id="1782" left="0" top="1092" width="6000" height="6" align-x="0" align-y="1092" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1534" left="6" top="1098.75" width="320.25" height="57" align-x="6" align-y="1110" 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 order of evaluation of local assignments is different in Mathcad 12 than in other versions of Mathcad. Most versions of Mathcad perform the rightmost assignment first. Mathcad 12 evaluates the leftmost assignment first.</p>
</text>
</region>
<region region-id="1539" left="186" top="1176.75" width="30.75" height="15.75" align-x="200.25" align-y="1188" 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">k</ml:id>
<ml:real>0</ml:real>
</ml:define>
</math>
<rendering item-idref="10"></rendering>
</region>
<region region-id="1530" left="30" top="1161.75" width="116.25" height="80.25" align-x="108" align-y="1194" 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:program>
<ml:localDefine>
<ml:id xml:space="preserve">k</ml:id>
<ml:real>0</ml:real>
</ml:localDefine>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">k</ml:id>
</ml:apply>
<ml:localDefine>
<ml:id xml:space="preserve">k</ml:id>
<ml:real>2</ml:real>
</ml:localDefine>
</ml:localDefine>
<ml:id xml:space="preserve">X</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="3" cols="1">
<ml:real>0</ml:real>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="11"></rendering>
</region>
<region region-id="1540" left="186" top="1200.75" width="62.25" height="17.25" align-x="207.75" align-y="1212" 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">X</ml:id>
<ml:id xml:space="preserve">k</ml:id>
</ml:apply>
<ml:localDefine>
<ml:id xml:space="preserve">k</ml:id>
<ml:real>2</ml:real>
</ml:localDefine>
</ml:define>
</math>
<rendering item-idref="12"></rendering>
</region>
<region region-id="1542" left="186" top="1224.75" width="49.5" height="15.75" align-x="201.75" align-y="1236" 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:id xml:space="preserve">X</ml:id>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="1" cols="1">
<ml:real>2</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="13"></rendering>
</region>
<region region-id="1629" left="6" top="1260.75" width="270.75" height="14.25" align-x="6" align-y="1272" 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 following construction works in all versions of Mathcad:</p>
</text>
</region>
<region region-id="1632" left="36" top="1281.75" width="101.25" height="101.25" align-x="99" align-y="1314" 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:program>
<ml:localDefine>
<ml:id xml:space="preserve">k</ml:id>
<ml:real>0</ml:real>
</ml:localDefine>
<ml:localDefine>
<ml:id xml:space="preserve">k</ml:id>
<ml:real>2</ml:real>
</ml:localDefine>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">X</ml:id>
<ml:id xml:space="preserve">k</ml:id>
</ml:apply>
<ml:id xml:space="preserve">k</ml:id>
</ml:localDefine>
<ml:id xml:space="preserve">X</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="3" cols="1">
<ml:real>0</ml:real>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="14"></rendering>
</region>
<region region-id="1476" left="6" top="1400.25" width="193.5" height="12" align-x="6" align-y="1410" 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="Header 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Referencing of Worksheet Variables</p>
</text>
<indexes>
<phrase>Referencing of worksheet variables</phrase>
<phrase>variables, referencing</phrase>
</indexes>
</region>
<region region-id="1692" left="6" top="1424.25" width="308.25" height="36" align-x="25.5" align-y="1434" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC11:</b> Worksheet names always reference on the right-hand side of local assignments in function definitions.</p>
</text>
</region>
<region region-id="1693" left="6" top="1466.25" width="308.25" height="36" align-x="25.5" 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="true">
<p style="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC12:</b> Worksheet names reference on the right-hand side of local assignments <i>until</i> reassigned in program, <i>except</i> built-in names.</p>
</text>
</region>
<region region-id="1695" left="6" top="1508.25" width="308.25" height="36" align-x="25.5" align-y="1518" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC13 and higher:</b> Worksheet names reference on the right-hand side of local assignments <i>until</i> reassigned in program, <i>including</i> built-in names.</p>
</text>
</region>
<region region-id="1543" left="6" top="1554.75" width="332.25" height="99.75" align-x="6" align-y="1566" 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">All versions of Mathcad reference worksheet variables when the name is defined. Mathcad 12 and higher override definitions when the name is reused locally. In previous versions, direct program evaluation worked this way, while function definitions always referenced the worksheet variable. For example, Mathcad 11 assigns the gg on the right of the local assignment below to be the worksheet value on each pass, producing the result 1 from function ff.</p>
</text>
</region>
<region region-id="1783" left="0" top="1662" width="6000" height="6" align-x="0" align-y="1662" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1571" left="36" top="1668.75" width="35.25" height="15.75" align-x="54.75" align-y="1680" 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">gg</ml:id>
<ml:real>0</ml:real>
</ml:define>
</math>
<rendering item-idref="15"></rendering>
</region>
<region region-id="1590" left="192" top="1692.75" width="126.75" height="57.75" align-x="222.75" align-y="1704" 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">ff</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">n</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:for>
<ml:id xml:space="preserve">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:range>
<ml:localDefine>
<ml:id xml:space="preserve">gg</ml:id>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">gg</ml:id>
<ml:real>1</ml:real>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">gg</ml:id>
</ml:program>
</ml:define>
</math>
<rendering item-idref="16"></rendering>
</region>
<region region-id="1573" left="30" top="1698.75" width="114.75" height="57.75" align-x="123" align-y="1710" 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:program>
<ml:for>
<ml:id xml:space="preserve">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:range>
<ml:localDefine>
<ml:id xml:space="preserve">gg</ml:id>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve">gg</ml:id>
<ml:real>1</ml:real>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">gg</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>3</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="17"></rendering>
</region>
<region region-id="1591" left="192" top="1758.75" width="52.5" height="15.75" align-x="222.75" align-y="1770" 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:provenance expr-id="1">
<originRef doc-id="D04A7CB8-311E-4402-9D91-C3559B19D041" version-id="E1957667-D4C5-4687-B95E-6C3CDBC5AB0D" branch-id="00000000-0000-0000-0000-000000000000" revision-num="46590988" is-modified="true" region-id="0" href="C:\Mathcad 13\Documentation\ResourceCenter\EN\qsheet\tutorial\migration\all_incompatibilities.mcd" xmlns="http://schemas.mathsoft.com/provenance10">
<hash></hash>
</originRef>
<parentRef doc-id="D04A7CB8-311E-4402-9D91-C3559B19D041" version-id="E1957667-D4C5-4687-B95E-6C3CDBC5AB0D" branch-id="00000000-0000-0000-0000-000000000000" revision-num="320375900" is-modified="true" region-id="0" href="C:\Mathcad 13\Documentation\ResourceCenter\EN\qsheet\tutorial\migration\all_incompatibilities.mcd" xmlns="http://schemas.mathsoft.com/provenance10">
<hash></hash>
</parentRef>
<comment xmlns="http://schemas.mathsoft.com/provenance10"></comment>
<originComment xmlns="http://schemas.mathsoft.com/provenance10"></originComment>
<contentHash xmlns="http://schemas.mathsoft.com/provenance10">1d72e2e41f4643c816ef12dad9ed9eda</contentHash>
<ml:apply>
<ml:id xml:space="preserve">ff</ml:id>
<ml:real>1</ml:real>
</ml:apply>
</ml:provenance>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>3</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="18">
<element-image-map>
<box left="1.5" top="0.75" width="22.5" height="14.25" expr-idref="1"></box>
</element-image-map>
</rendering>
</region>
<region region-id="1575" left="6" top="1782.75" width="339" height="71.25" align-x="6" align-y="1794" 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">In Mathcad 12 and previous versions, there are further problems if the name of the worksheet and local variables are the same as a built-in variable. In Mathcad 13 and higher, all versions of this construct perform in the same way, regardless of the name used. We recommend that you use different names for variables, to clarify meaning.</p>
</text>
</region>
<region region-id="1764" left="6" top="1874.25" width="115.5" height="12" align-x="32.25" align-y="1884" 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="Header 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Namespace Operator</p>
</text>
<indexes>
<phrase>namespace operator</phrase>
</indexes>
</region>
<region region-id="1696" left="6" top="1896.75" width="338.25" height="57" align-x="6" align-y="1908" 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">If you wish to explicitly reference a name in the worksheet on each pass, mimicking the Mathcad 11 and previous version behavior, use the namespace operator to clarify whether the local or worksheet name is meant:</p>
</text>
</region>
<region region-id="1580" left="36" top="1962.75" width="156" height="62.25" align-x="71.25" align-y="1974" 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">ff2</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">n</ml:id>
</ml:boundVars>
</ml:function>
<ml:program>
<ml:for>
<ml:id xml:space="preserve">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:range>
<ml:localDefine>
<ml:id xml:space="preserve">gg</ml:id>
<ml:apply>
<ml:plus></ml:plus>
<ml:id xml:space="preserve" module="doc">gg</ml:id>
<ml:real>1</ml:real>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">gg</ml:id>
</ml:program>
</ml:define>
</math>
<rendering item-idref="19"></rendering>
</region>
<region region-id="1788" left="204" top="2010.75" width="57" height="15.75" align-x="239.25" align-y="2022" 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">ff2</ml:id>
<ml:real>1</ml:real>
</ml:apply>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>1</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="20"></rendering>
</region>
<region region-id="1594" left="6" top="2046.75" width="321" height="57" align-x="6" align-y="2058" 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 behavior for referencing external functions and assigning them to local variables of the same name works the same way; these will fail in Mathcad 12 and higher. In the following example, the name <i>Q1</i> is reassigned to a local variable and can no longer be used as a function. </p>
</text>
</region>
<region region-id="1599" left="36" top="2113.5" width="59.25" height="21" align-x="74.25" align-y="2130" 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">Q1</ml:id>
<ml:boundVars>
<ml:id xml:space="preserve">x</ml:id>
</ml:boundVars>
</ml:function>
<ml:apply>
<ml:pow></ml:pow>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>2</ml:real>
</ml:apply>
</ml:define>
</math>
<rendering item-idref="21"></rendering>
</region>
<region region-id="1600" left="36" top="2154.75" width="120" height="59.25" align-x="135" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math error="This value must be an array." optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:program>
<ml:for>
<ml:id xml:space="preserve">j</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>3</ml:real>
</ml:range>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">Q1</ml:id>
<ml:id xml:space="preserve">j</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve">Q1</ml:id>
<ml:id xml:space="preserve">j</ml:id>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">Q1</ml:id>
</ml:program>
</ml:eval>
</math>
<metadata>
<customValue name="Mathsoft_expected_error" type="text">must be array	[any1]	f(Unitless) =&gt; any1</customValue>
</metadata>
<rendering item-idref="22"></rendering>
</region>
<region region-id="1610" left="162" top="2154.75" width="9.75" height="14.25" align-x="162" align-y="2166" 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">or</p>
</text>
</region>
<region region-id="1611" left="198" top="2154.75" width="99" height="36.75" align-x="276" align-y="2166" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math error="This function refers to itself inconsistently." optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:for>
<ml:id xml:space="preserve">j</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>3</ml:real>
</ml:range>
<ml:localDefine>
<ml:id xml:space="preserve">Q1</ml:id>
<ml:apply>
<ml:id xml:space="preserve">Q1</ml:id>
<ml:id xml:space="preserve">j</ml:id>
</ml:apply>
</ml:localDefine>
</ml:for>
</ml:eval>
</math>
<metadata>
<customValue name="Mathsoft_expected_error" type="text">bad_implicit	k0	(Value {})-&gt;a-&gt;a	(Value {})-&gt;((Value {})-&gt;a)-&gt;a	1	1	a	(Value {})-&gt;a</customValue>
</metadata>
<rendering item-idref="23"></rendering>
</region>
<region region-id="1784" left="0" top="2226" width="6000" height="6" align-x="0" align-y="2226" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1698" left="6" top="2226.75" width="171.75" height="14.25" align-x="6" 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">These programs should be changed to</p>
</text>
</region>
<region region-id="1644" left="6" top="2249.25" width="162" height="93.75" align-x="129.75" 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:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:program>
<ml:for>
<ml:id xml:space="preserve">j</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>3</ml:real>
</ml:range>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">Q1</ml:id>
<ml:id xml:space="preserve">j</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve" module="doc">Q1</ml:id>
<ml:id xml:space="preserve">j</ml:id>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">Q1</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="4" cols="1">
<ml:real>0</ml:real>
<ml:real>1</ml:real>
<ml:real>4</ml:real>
<ml:real>9</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="24"></rendering>
</region>
<region region-id="1647" left="186" top="2280.75" width="9.75" height="14.25" align-x="186" align-y="2292" 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">or</p>
</text>
</region>
<region region-id="1646" left="216" top="2249.25" width="137.25" height="90.75" align-x="315" 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:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:program>
<ml:for>
<ml:id xml:space="preserve">j</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>3</ml:real>
</ml:range>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">Q2</ml:id>
<ml:id xml:space="preserve">j</ml:id>
</ml:apply>
<ml:apply>
<ml:id xml:space="preserve">Q1</ml:id>
<ml:id xml:space="preserve">j</ml:id>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">Q2</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="4" cols="1">
<ml:real>0</ml:real>
<ml:real>1</ml:real>
<ml:real>4</ml:real>
<ml:real>9</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="25"></rendering>
</region>
<region region-id="1627" left="6" top="2364.75" width="328.5" height="28.5" align-x="6" align-y="2376" 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">This change makes program functionality consistent with the way reassignments work outside of programs.</p>
</text>
</region>
<region region-id="1766" left="0" top="2400" width="6000" height="6" align-x="0" align-y="2400" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1625" left="6" top="2406.75" width="321.75" height="57" align-x="6" align-y="2418" 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">
<b>
<c val="#008080">Note:</c>
</b> Since the namespace operator was introduced in Mathcad 12, saving and opening files that use it as Mathcad 11 or Mathcad 2001i will not work. Use distinct names in the worksheet and the program for the most version-neutral functionality.</p>
</text>
</region>
<region region-id="1769" left="6" top="2474.25" width="150.75" height="12" align-x="19.5" align-y="2484" 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="Header 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Range Summation Operator</p>
</text>
</region>
<region region-id="1719" left="6" top="2496.75" width="328.5" height="85.5" align-x="6" align-y="2508" 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">Similarly, the range summation operator always refers to worksheet assignments for its range variable in Mathcad 11, even if there is a locally defined variable of the same name. In Mathcad 12 and higher, the local value takes precedence. A program iteration variable is just a scalar for the value of each loop; the range summation gives the error "This value must be a range."</p>
</text>
</region>
<region region-id="1737" left="30" top="2598.75" width="42.75" height="15.75" align-x="40.5" align-y="2610" 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">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:range>
</ml:define>
</math>
<rendering item-idref="26"></rendering>
</region>
<region region-id="1748" left="216" top="2595.75" width="133.5" height="134.25" align-x="311.25" align-y="2628" 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:program>
<ml:localDefine>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>2</ml:real>
</ml:localDefine>
<ml:for>
<ml:id xml:space="preserve">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:range>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">val</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
<ml:apply>
<ml:summation></ml:summation>
<ml:lambda>
<ml:boundVars>
<ml:id xml:space="preserve">k</ml:id>
</ml:boundVars>
<ml:id xml:space="preserve">k</ml:id>
</ml:lambda>
<ml:bounds>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:bounds>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">val</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="3" cols="1">
<ml:real>3</ml:real>
<ml:real>3</ml:real>
<ml:real>3</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="27"></rendering>
</region>
<region region-id="1739" left="24" top="2622.75" width="101.25" height="101.25" align-x="104.25" align-y="2634" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math error="This value must be a range." optimize="false" disable-calc="false">
<ml:eval placeholderMultiplicationStyle="default" resultMultiplicationStyle="default">
<ml:program>
<ml:localDefine>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>2</ml:real>
</ml:localDefine>
<ml:for>
<ml:id xml:space="preserve">i</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:range>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">val</ml:id>
<ml:id xml:space="preserve">i</ml:id>
</ml:apply>
<ml:apply>
<ml:summation></ml:summation>
<ml:lambda>
<ml:boundVars>
<ml:id xml:space="preserve">i</ml:id>
</ml:boundVars>
<ml:id xml:space="preserve">i</ml:id>
</ml:lambda>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">val</ml:id>
</ml:program>
</ml:eval>
</math>
<metadata>
<customValue name="Mathsoft_expected_error" type="text">must be range</customValue>
</metadata>
<rendering item-idref="28"></rendering>
</region>
<region region-id="1749" left="138" top="2624.25" width="69" height="36" align-x="138" align-y="2634" 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="H5" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">We recommend instead</p>
</text>
</region>
<region region-id="1745" left="6" top="2742.75" width="222" height="14.25" align-x="6" align-y="2754" 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">Or you can change the name of the local variable:</p>
</text>
</region>
<region region-id="1747" left="24" top="2769.75" width="121.5" height="122.25" align-x="107.25" align-y="2802" 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:program>
<ml:localDefine>
<ml:id xml:space="preserve">x</ml:id>
<ml:real>2</ml:real>
</ml:localDefine>
<ml:for>
<ml:id xml:space="preserve">k</ml:id>
<ml:range>
<ml:real>0</ml:real>
<ml:real>2</ml:real>
</ml:range>
<ml:localDefine>
<ml:apply>
<ml:indexer></ml:indexer>
<ml:id xml:space="preserve">val</ml:id>
<ml:id xml:space="preserve">k</ml:id>
</ml:apply>
<ml:apply>
<ml:summation></ml:summation>
<ml:lambda>
<ml:boundVars>
<ml:id xml:space="preserve">i</ml:id>
</ml:boundVars>
<ml:id xml:space="preserve">i</ml:id>
</ml:lambda>
</ml:apply>
</ml:localDefine>
</ml:for>
<ml:id xml:space="preserve">val</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:matrix rows="3" cols="1">
<ml:real>3</ml:real>
<ml:real>3</ml:real>
<ml:real>3</ml:real>
</ml:matrix>
</result>
</ml:eval>
</math>
<rendering item-idref="29"></rendering>
</region>
<region region-id="1770" left="0" top="2898" width="6000" height="6" align-x="0" align-y="2898" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<pageBreak></pageBreak>
</region>
<region region-id="1650" left="6" top="2906.25" width="282.75" height="12" align-x="6" align-y="2916" 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="Header 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Uninitialized Variables and Non-executing Programs</p>
</text>
<indexes>
<phrase>variables in programs, unitialized</phrase>
<phrase>programs, non-executing</phrase>
</indexes>
</region>
<region region-id="1703" left="6" top="2924.25" width="308.25" height="36" align-x="25.5" align-y="2934" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC11, MC13, and MC14:</b> Programs that return unassigned variables are set to 0. Programs that never execute produce an error.</p>
</text>
</region>
<region region-id="1704" left="6" top="2966.25" width="308.25" height="24" align-x="25.5" align-y="2976" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC12:</b> Programs that return unassigned variables or that never execute return NaN.</p>
</text>
</region>
<region region-id="1651" left="6" top="3006.75" width="338.25" height="57" align-x="6" align-y="3018" show-border="false" show-highlight="false" is-protected="true" z-order="-2" 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">Mathcad 12 returns NaN from programs that return unassigned variables or from programs that never executed. Mathcad 13 and Mathcad 11 set uninitialized variables to zero, while programs that never execute because of conditional statements return an error.</p>
</text>
</region>
<region region-id="1751" left="36" top="3084.75" width="126.75" height="36.75" align-x="63.75" align-y="3096" 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:program>
<ml:ifThen>
<ml:id xml:space="preserve">x</ml:id>
<ml:localDefine>
<ml:id xml:space="preserve">p</ml:id>
<ml:real>1</ml:real>
</ml:localDefine>
</ml:ifThen>
<ml:ifThen>
<ml:apply>
<ml:mult style="default"></ml:mult>
<ml:real>2</ml:real>
<ml:id xml:space="preserve">x</ml:id>
</ml:apply>
<ml:localDefine>
<ml:id xml:space="preserve">p</ml:id>
<ml:real>2</ml:real>
</ml:localDefine>
</ml:ifThen>
</ml:program>
</ml:define>
</math>
<rendering item-idref="30"></rendering>
</region>
<region region-id="1752" left="36" top="3132.75" width="49.5" height="15.75" align-x="63.75" align-y="3144" 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>1</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>
<region region-id="1753" left="108" top="3132.75" width="48.75" height="15.75" align-x="135.75" align-y="3144" show-border="false" show-highlight="false" is-protected="true" z-order="0" background-color="inherit" tag="">
<math error="This program has no return value. You must account for all cases &#xA;when using conditional statements in a Mathcad program." 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">invalid</customValue>
</metadata>
<rendering item-idref="32"></rendering>
</region>
<region region-id="1659" left="6" top="3168.75" width="340.5" height="28.5" align-x="6" align-y="3180" 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">
<b>
<c val="#008080">Note: </c>
</b>Returning an uninitialized variable in a program will override any worksheet definition:</p>
</text>
</region>
<region region-id="1664" left="36" top="3204.75" width="30.75" height="15.75" align-x="50.25" align-y="3216" 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">p</ml:id>
<ml:real>2</ml:real>
</ml:define>
</math>
<rendering item-idref="33"></rendering>
</region>
<region region-id="1661" left="36" top="3228.75" width="105" height="36.75" align-x="119.25" align-y="3240" 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:program>
<ml:ifThen>
<ml:real>0</ml:real>
<ml:localDefine>
<ml:id xml:space="preserve">p</ml:id>
<ml:real>1</ml:real>
</ml:localDefine>
</ml:ifThen>
<ml:id xml:space="preserve">p</ml:id>
</ml:program>
<result xmlns="http://schemas.mathsoft.com/math30">
<ml:real>0</ml:real>
</result>
</ml:eval>
</math>
<rendering item-idref="34"></rendering>
</region>
<region region-id="1705" left="6" top="3290.25" width="167.25" height="12" align-x="6" align-y="3300" 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="Header 2" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">Recursion Depth in Mathcad 13</p>
</text>
<indexes>
<phrase>recursion depth</phrase>
<phrase>programs, recursion depth</phrase>
<phrase>infinite recursion</phrase>
<phrase>recursion stack limitations</phrase>
</indexes>
</region>
<region region-id="1708" left="6" top="3308.25" width="308.25" height="24" align-x="25.5" align-y="3318" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC11:</b> Infinitely recursing programs sometimes throw errors, sometimes crash Mathcad.</p>
</text>
</region>
<region region-id="1709" left="6" top="3344.25" width="308.25" height="24" align-x="25.5" align-y="3354" 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="comment" margin-left="inherit" margin-right="inherit" text-indent="inherit" text-align="inherit" list-style-type="inherit" tabs="inherit">
<b>MC12:</b> Programs are limited to a stack depth of 100, more instructions throw an error.</p>
</text>
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