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<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="with(Client):" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJ0NsaWVudEYnRi9GMi8lK2V4ZWN1dGFibGVHUSZmYWxzZUYnL0YzUSdub3JtYWxGJ0ZALUkjbW9HRiQ2LVEiOkYnRkAvJSZmZW5jZUdGPy8lKnNlcGFyYXRvckdGPy8lKXN0cmV0Y2h5R0Y/LyUqc3ltbWV0cmljR0Y/LyUobGFyZ2VvcEdGPy8lLm1vdmFibGVsaW1pdHNHRj8vJSdhY2NlbnRHRj8vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZWRj1GQA==">QyQtSSV3aXRoRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiNJJ0NsaWVudEdGKCEiIg==</Equation></Text-field>
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<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="GapServer := "chrystal.mcs.st-andrews.ac.uk":" display="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">QyQ+SSpHYXBTZXJ2ZXJHNiJRPmNocnlzdGFsLm1jcy5zdC1hbmRyZXdzLmFjLnVrRiUhIiI=</Equation></Text-field>
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<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Querying the server about its properties:</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=</Equation></Text-field>
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<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="GetServiceDescription(GapServer);" display="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">QyQtSTZHZXRTZXJ2aWNlRGVzY3JpcHRpb25HNiI2I0kqR2FwU2VydmVyR0YlIiIi</Equation></Text-field>
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<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">UWhzR0FQflNDU0NQfnNlcnZpY2V+R0FQfjQuNS4yKGJldGEpfit+U0NTQ1B+Mi4wLjB+U3RhcnRlZH53aXRofnRoZX5jb25maWd1cmF0aW9ufmZpbGV+c2NzY3AvZXhhbXBsZS9teXNlcnZlci5nfn5vbn5Nb25+SmFufjMwfjIyOjA0OjE3fkdNVH4yMDEyNiI=</Equation></Text-field>
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<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="GetAllowedHeads(GapServer);" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEwR2V0QWxsb3dlZEhlYWRzRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYkLUYjNiQtRiw2JVEqR2FwU2VydmVyRidGL0YyL0YzUSdub3JtYWxGJ0Y9LUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjEvJSlzdHJldGNoeUdGRS8lKnN5bW1ldHJpY0dGRS8lKGxhcmdlb3BHRkUvJS5tb3ZhYmxlbGltaXRzR0ZFLyUnYWNjZW50R0ZFLyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJStleGVjdXRhYmxlR0ZFRj0=">QyQtSTBHZXRBbGxvd2VkSGVhZHNHNiI2I0kqR2FwU2VydmVyR0YlIiIi</Equation></Text-field>
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<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LSUnUmVjb3JkRzYnL0kkb21zRzYiN1A3JFEyc2NzY3BfdHJhbnNpZW50XzFGKFElU2l6ZUYoNyRGK1EnTGVuZ3RoRig3JEYrUTNOckNvbmp1Z2FjeUNsYXNzZXNGKDckRitRKWFkZGl0aW9uRig3JEYrUTJTQ1NDUF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</Section>
<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title>
<Text-field style="Heading 2" layout="Heading 2">Ask GAP to compute something</Text-field></Title><Presentation-Block>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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<Input>
<Text-field style="Text" layout="Normal">Evaluate 20! in GAP.</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "WS_Factorial", [20]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRLVdTX0ZhY3RvcmlhbEYlNyMiIz8iIiI=</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IjQrK2t3IjM/IUhWIw==</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L13" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Is 26562357 prime?</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "IsPrimeInt", [26562357]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRK0lzUHJpbWVJbnRGJTcjIilkQmNFIiIi</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">SSZmYWxzZUclKnByb3RlY3RlZEc=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L14" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Find the library number (ID) of the group in the GAP Small Groups Library</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "WS_IdGroup", [permgroup(4, {[[1, 2], [3, 4]], [[1, 4], [2, 3]]})]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRK1dTX0lkR3JvdXBGJTcjLUkqcGVybWdyb3VwR0YlNiQiIiU8JDckNyQiIiIiIiM3JCIiJEYuNyQ3JEYyRi43JEYzRjVGMg==</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyQiIiUiIiM=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L15" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Find the number of conjugacy classes of the permutation group</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "NrConjugacyClasses", [permgroup(4, {[[1, 2], [3, 4]], [[1, 4], [2, 3]]})]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRM05yQ29uanVnYWN5Q2xhc3Nlc0YlNyMtSSpwZXJtZ3JvdXBHSShfc3lzbGliR0YlNiQiIiU8JDckNyQiIiIiIiM3JCIiJEYvNyQ3JEYzRi83JEY0RjZGMw==</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">IiIl</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L17" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Check that two-groups are non-isomorphic since they have different IDs in the GAP Small Group Library (using private CD fpgroup1 by A. Konovalov)</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="G := grelgroup({a, b}, {[b, b], [a, b, 1/a, 1/b], [a, a, a, a, a, a, a, a]}):" display="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">QyQ+SSJHRzYiLUkqZ3JlbGdyb3VwR0YlNiQ8JEkiYUdGJUkiYkdGJTwlNyRGK0YrNyZGKkYrKiRGKiEiIiokRitGMDcqRipGKkYqRipGKkYqRipGKkYw</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L18" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "WS_IdGroup", [G]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRK1dTX0lkR3JvdXBGJTcjSSJHR0YlIiIi</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyQiIzsiIiY=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L20" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="G := grelgroup({a, b}, {[b, b], [a, b, a, b], [a, a, a, a, a, a, a, a]}):" display="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">QyQ+SSJHRzYiLUkqZ3JlbGdyb3VwR0koX3N5c2xpYkdGJTYkPCRJImFHRiVJImJHRiU8JTckRixGLDcmRitGLEYrRiw3KkYrRitGK0YrRitGK0YrRishIiI=</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L24" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "WS_IdGroup", [G]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRK1dTX0lkR3JvdXBGJTcjSSJHR0YlIiIi</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyQiIzsiIig=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L39" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="m1 := Matrix([[0, 1, 0, 0, 0], [1, 0, 0, 0, 0], [0, 0, 1, 0, 0], [0, 0, 0, 1, 0], [0, 0, 0, 0, 1]]):" display="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">QyQ+SSNtMUc2Ii1JJ01hdHJpeEdGJTYjNyc3JyIiISIiIkYrRitGKzcnRixGK0YrRitGKzcnRitGK0YsRitGKzcnRitGK0YrRixGKzcnRitGK0YrRitGLCEiIg==</Equation></Text-field>
</Input>
</Group>
<Group view="code" labelreference="L42" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="m2 := Matrix([[0, 0, 1, 0, 0], [1, 0, 0, 0, 0], [0, 1, 0, 0, 0], [0, 0, 0, 0, 1], [0, 0, 0, 1, 0]]):" display="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">QyQ+SSNtMkc2Ii1JJ01hdHJpeEc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJTYjNyc3JyIiIUYuIiIiRi5GLjcnRi9GLkYuRi5GLjcnRi5GL0YuRi5GLjcnRi5GLkYuRi5GLzcnRi5GLkYuRi9GLiEiIg==</Equation></Text-field>
</Input>
</Group>
<Group labelreference="L40" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Find the library number of the group generated by the two matrices from above </Text-field>
<Text-field style="Text" layout="Normal">(using the procedure which accepts the list generators of the group and not the group itself):</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "GroupIdentificationService", [[m1, m2]]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRO0dyb3VwSWRlbnRpZmljYXRpb25TZXJ2aWNlRiU3IzckSSNtMUdGJUkjbTJHRiUiIiI=</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyQiIzciIiU=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L41" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">Now create a remote group generated by two matrices and get a cookie pointing to it so we will be able to use it in further procedure calls:</Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="res := CallService(GapServer, "scscp_transient_1", "MatrixGroup", [[m1, m2]], output = cookie);" display="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">QyQ+SSRyZXNHNiItSSxDYWxsU2VydmljZUdGJTYnSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRLE1hdHJpeEdyb3VwRiU3IzckSSNtMUdGJUkjbTJHRiUvSSdvdXRwdXRHRiVJJ2Nvb2tpZUdGJSIiIg==</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknQ29va2llRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkmU0NTQ1BHSShfc3lzbGliR0YoNiNRW29zY3NjcDovL2NocnlzdGFsLm1jcy5zdC1hbmRyZXdzLmFjLnVrOjI2MTMzL1RFTVBWYXJTQ1NDUGhKckxrMFRIRig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L43" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">The cookie returned by the previous command may be now substituted in procedure calls. </Text-field>
<Text-field style="Text" layout="Normal">For example, since the remote object is a group, it is already a valid argument for  WS_IdGroup: </Text-field>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="CallService(GapServer, "scscp_transient_1", "WS_IdGroup", [res]);" display="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">QyQtSSxDYWxsU2VydmljZUc2IjYmSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRK1dTX0lkR3JvdXBGJTcjSSRyZXNHRiUiIiI=</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output">NyQiIzciIiU=</Equation></Text-field>
</Output>
</Group>
<Group view="code" labelreference="L88" drawlabel="true">
<Input>
<Text-field style="Text" layout="Normal">In the next example we compute remotely the Sylow 2-subgroup of the group from the previous example, and then get its order:</Text-field>
</Input>
</Group>
<Group labelreference="L89" drawlabel="true">
<Input>
<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="sylow2 := CallService(GapServer, "scscp_transient_1", "SylowSubgroup", [res, 2], output = cookie);" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkjbWlHRiQ2JVEnc3lsb3cyRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRiw2JVEsQ2FsbFNlcnZpY2VGJ0YvRjItSShtZmVuY2VkR0YkNiQtRiM2Mi1GLDYlUSpHYXBTZXJ2ZXJGJ0YvRjItRjY2LVEiLEYnRjlGOy9GP0YxRkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTlEsMC4zMzMzMzMzZW1GJy1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRmhuL0ZORmluLUkjbXNHRiQ2I1Eyc2NzY3BfdHJhbnNpZW50XzFGJ0ZaRlxvLUZhbzYjUS5TeWxvd1N1Ymdyb3VwRidGWkZcby1GUzYmLUYjNiYtRiw2JVEkcmVzRidGL0YyRlotSSNtbkdGJDYkUSIyRidGOUY5RjkvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGWkZcby1GLDYlUSdvdXRwdXRGJ0YvRjItRjY2LVEiPUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tRiw2JVEnY29va2llRidGL0YyRjlGOS1GNjYtUSI7RidGOUY7RmduRkBGQkZERkZGSEZobkZNLyUrZXhlY3V0YWJsZUdGPUY5">QyQ+SSdzeWxvdzJHNiItSSxDYWxsU2VydmljZUdGJTYnSSpHYXBTZXJ2ZXJHRiVRMnNjc2NwX3RyYW5zaWVudF8xRiVRLlN5bG93U3ViZ3JvdXBGJTckSSRyZXNHRiUiIiMvSSdvdXRwdXRHRiVJJ2Nvb2tpZUdGJSIiIg==</Equation></Text-field>
</Input>
<Output>
<Text-field style="2D Output" layout="Maple Output"><Equation executable="false" style="2D Output" display="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">LUknQ29va2llRzYkJSpwcm90ZWN0ZWRHL0krbW9kdWxlbmFtZUc2IkkmU0NTQ1BHSShfc3lzbGliR0YoNiNRW29zY3NjcDovL2NocnlzdGFsLm1jcy5zdC1hbmRyZXdzLmFjLnVrOjI2MTMzL1RFTVBWYXJTQ1NDUGVPdWhkQUs1Rig=</Equation></Text-field>
</Output>
</Group>
<Group labelreference="L86" drawlabel="true">
<Input>
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<Text-field prompt="> " style="Maple Input" layout="Normal"><Equation executable="true" style="2D Input" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbWlHRiQ2I1EhRicvJStleGVjdXRhYmxlR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRic=">JSFH</Equation></Text-field>
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<Text-field style="Text" layout="Normal"><Equation executable="false" style="2D Math" input-equation="" display="LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbWlHRiQ2I1EhRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYn">JSFH</Equation></Text-field>
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