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    <title>MaplePrimes - Maple 2026 Posts and Questions</title>
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    <lastBuildDate>Sat, 01 Aug 2026 17:07:58 GMT</lastBuildDate>
    <pubDate>Sat, 01 Aug 2026 17:07:58 GMT</pubDate>
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    <description>Maple 2026 Questions and Posts on MaplePrimes</description>
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      <title>MaplePrimes - Maple 2026 Posts and Questions</title>
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      <title>How to check if a parameter set is in SI base units</title>
      <link>http://www.mapleprimes.com/questions/243711-How-To-Check-If-A-Parameter-Set-Is-In?ref=Feed:MaplePrimes:Version Maple 2026</link>
      <itunes:summary>&lt;p&gt;For a numericial integration I want to check if all physical parameters are given in SI base units (before stripping of the units for the integration). Right now I am doing this&lt;/p&gt;

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									&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="font-size:16px;"&gt;&lt;span style="color: rgb(0, 0, 0); font-family: Trebuchet MS, sans-serif; font-weight: normal; font-style: normal;"&gt;Parameters&lt;/span&gt;&lt;/span&gt;&lt;/p&gt;
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									&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="font-size:16px;"&gt;&lt;img align="middle" alt="H = 0.1e-1*Unit('m'), R = 0.6e-2*Unit('m'), r_sub = 0.3e-2*Unit('m'), k = .540*Unit('W'/('m'*'K')), rho = 1060.0*Unit('kg'/'m'^3), Cp = 3745*Unit('J'/('kg'*'K')), Q_flux = 5000*Unit('W'/'m'^2), T_amb = 0*Unit('K'), Nz = 20, Nr = 20, t_final = 30*Unit('s'), t_step = Unit('s'), test_1 = Unit('kW'), test_2 = 2*Unit('N')" height="328" src="/view.aspx?sf=243711_question/9505006d0dd9c8b2e247125febd55b5e.gif" style="vertical-align:-311px" width="372"&gt;&lt;/span&gt;&lt;/p&gt;

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												&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
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									&lt;p&gt;H: length of rod&lt;br&gt;
									R: outer radius&lt;br&gt;
									r_sub: outer radius of heat flux&lt;br&gt;
									k: conductance&lt;br&gt;
									&amp;rho;: density&lt;br&gt;
									Cp: heat capacity&lt;br&gt;
									Q_flux: heat flux&lt;br&gt;
									T_amb: initial Tempearture&lt;br&gt;
									Nz: number of axial grid points&lt;br&gt;
									Nr: number of radial grid points&lt;br&gt;
									t_final: integration time&lt;br&gt;
									t_step: sampling interval for temperature fields&lt;br&gt;
									test_1: unit given in kilos&lt;br&gt;
									test_2: unit given in derived base units&lt;/p&gt;
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												&lt;td&gt;(2)&lt;/td&gt;
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									&lt;p&gt;&amp;alpha;: thermal diffusivity&lt;/p&gt;
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						&lt;td align="left" style="font-weight:bold"&gt;&amp;nbsp;&lt;/td&gt;
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			&lt;p&gt;One way is to check whether the value of a physical parameter has not changed after simplification&lt;/p&gt;

			&lt;p&gt;&lt;img alt="`minus`(map(convert, simplify(`~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)})), unit_free), map(convert, `~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)}), unit_free))" height="23" src="/view.aspx?sf=243711_question/21bd93ad2777245081e960755b76c4de.gif" style="vertical-align:-6px" width="570"&gt;&lt;/p&gt;

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						&lt;td&gt;(3)&lt;/td&gt;
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			&lt;p&gt;&lt;img align="middle" alt="if is(`minus`(map(convert, simplify(`~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)})), unit_free), map(convert, `~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)}), unit_free)) &amp;lt;&amp;gt; {}) then print(&amp;quot;Not all units are in SI base units&amp;quot;) end if" height="40" src="/view.aspx?sf=243711_question/671e5d56c50a3a43c42295ec63304134.gif" style="vertical-align:-23px" width="768"&gt;&lt;/p&gt;

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						&lt;td&gt;(4)&lt;/td&gt;
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&lt;p&gt;&lt;a href="/view.aspx?sf=243711_question/check_for_SI_base_units.mw"&gt;Download check_for_SI_base_units.mw&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;I am interested in simpler ways to perform the test. The statement is quite long and not easy to understand.&lt;/p&gt;

&lt;p&gt;Given the size of the unit package, there might be a command that I have overlooked to check whether units are in SI base units.&lt;/p&gt;

&lt;p&gt;Have I missed test cases to make the check fool proof?&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Update&lt;/strong&gt;: A variant with split was added and attempts with functional programming&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243711_question/check_for_SI_base_units_02.mw"&gt;check_for_SI_base_units_02.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;For a numericial integration I want to check if all physical parameters are given in SI base units (before stripping of the units for the integration). Right now I am doing this&lt;/p&gt;

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									&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="font-size:16px;"&gt;&lt;img align="middle" alt="H = 0.1e-1*Unit('m'), R = 0.6e-2*Unit('m'), r_sub = 0.3e-2*Unit('m'), k = .540*Unit('W'/('m'*'K')), rho = 1060.0*Unit('kg'/'m'^3), Cp = 3745*Unit('J'/('kg'*'K')), Q_flux = 5000*Unit('W'/'m'^2), T_amb = 0*Unit('K'), Nz = 20, Nr = 20, t_final = 30*Unit('s'), t_step = Unit('s'), test_1 = Unit('kW'), test_2 = 2*Unit('N')" height="328" src="/view.aspx?sf=243711_question/9505006d0dd9c8b2e247125febd55b5e.gif" style="vertical-align:-311px" width="372"&gt;&lt;/span&gt;&lt;/p&gt;

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												&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
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									&lt;p&gt;H: length of rod&lt;br&gt;
									R: outer radius&lt;br&gt;
									r_sub: outer radius of heat flux&lt;br&gt;
									k: conductance&lt;br&gt;
									&amp;rho;: density&lt;br&gt;
									Cp: heat capacity&lt;br&gt;
									Q_flux: heat flux&lt;br&gt;
									T_amb: initial Tempearture&lt;br&gt;
									Nz: number of axial grid points&lt;br&gt;
									Nr: number of radial grid points&lt;br&gt;
									t_final: integration time&lt;br&gt;
									t_step: sampling interval for temperature fields&lt;br&gt;
									test_1: unit given in kilos&lt;br&gt;
									test_2: unit given in derived base units&lt;/p&gt;
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									&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="alpha = k/(rho*Cp); simplify(subs(H = 0.1e-1*Units:-Unit(m), R = 0.6e-2*Units:-Unit(m), r_sub = 0.3e-2*Units:-Unit(m), k = .540*Units:-Unit(W/(m*K)), rho = 1060.0*Units:-Unit(kg/m^3), Cp = 3745*Units:-Unit(J/(kg*K)), Q_flux = 5000*Units:-Unit(W/m^2), T_amb = 0, Nz = 20, Nr = 20, t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N), %))" height="45" src="/view.aspx?sf=243711_question/bc98d94b2531fb179d2313ae73cf6198.gif" style="vertical-align:-19px" width="225"&gt;&lt;/p&gt;

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												&lt;td&gt;(2)&lt;/td&gt;
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									&lt;p&gt;&amp;alpha;: thermal diffusivity&lt;/p&gt;
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						&lt;td align="left" style="font-weight:bold"&gt;&amp;nbsp;&lt;/td&gt;
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			&lt;p&gt;One way is to check whether the value of a physical parameter has not changed after simplification&lt;/p&gt;

			&lt;p&gt;&lt;img alt="`minus`(map(convert, simplify(`~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)})), unit_free), map(convert, `~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)}), unit_free))" height="23" src="/view.aspx?sf=243711_question/21bd93ad2777245081e960755b76c4de.gif" style="vertical-align:-6px" width="570"&gt;&lt;/p&gt;

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						&lt;p&gt;&lt;img alt="{1000}" height="23" src="/view.aspx?sf=243711_question/dd984c9af9ac072e42d55edde3b90a7b.gif" style="vertical-align:-6px" width="51"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p&gt;&lt;img align="middle" alt="if is(`minus`(map(convert, simplify(`~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)})), unit_free), map(convert, `~`[rhs]({Cp = 3745*Units:-Unit(J/(kg*K)), H = 0.1e-1*Units:-Unit(m), Nr = 20, Nz = 20, Q_flux = 5000*Units:-Unit(W/m^2), R = 0.6e-2*Units:-Unit(m), T_amb = 0, k = .540*Units:-Unit(W/(m*K)), r_sub = 0.3e-2*Units:-Unit(m), rho = 1060.0*Units:-Unit(kg/m^3), t_final = 30*Units:-Unit(s), t_step = Units:-Unit(s), test_1 = Units:-Unit(kW), test_2 = 2*Units:-Unit(N)}), unit_free)) &amp;lt;&amp;gt; {}) then print(&amp;quot;Not all units are in SI base units&amp;quot;) end if" height="40" src="/view.aspx?sf=243711_question/671e5d56c50a3a43c42295ec63304134.gif" style="vertical-align:-23px" width="768"&gt;&lt;/p&gt;

			&lt;table&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="&amp;quot;Not all units are in SI base units&amp;quot;" height="23" src="/view.aspx?sf=243711_question/18160d74cb4c71b3261e6c36b557e347.gif" style="vertical-align:-6px" width="210"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td&gt;(4)&lt;/td&gt;
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			&lt;/td&gt;
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&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243711_question/check_for_SI_base_units.mw"&gt;Download check_for_SI_base_units.mw&lt;/a&gt;&lt;/p&gt;

&lt;p&gt;I am interested in simpler ways to perform the test. The statement is quite long and not easy to understand.&lt;/p&gt;

&lt;p&gt;Given the size of the unit package, there might be a command that I have overlooked to check whether units are in SI base units.&lt;/p&gt;

&lt;p&gt;Have I missed test cases to make the check fool proof?&lt;/p&gt;

&lt;p&gt;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;strong&gt;Update&lt;/strong&gt;: A variant with split was added and attempts with functional programming&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243711_question/check_for_SI_base_units_02.mw"&gt;check_for_SI_base_units_02.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243711</guid>
      <pubDate>Thu, 30 Jul 2026 21:08:28 Z</pubDate>
      <itunes:author>C_R</itunes:author>
      <author>C_R</author>
    </item>
    <item>
      <title>Agent Skill for Maple</title>
      <link>http://www.mapleprimes.com/questions/243710-Agent-Skill-For-Maple?ref=Feed:MaplePrimes:Version Maple 2026</link>
      <itunes:summary>&lt;p&gt;Has anyone developed an Agent Skill for Maple compliant with the &lt;a href="https://agentskills.io/home"&gt;Agent Skills Specification&lt;/a&gt;?&lt;/p&gt;

&lt;p&gt;I frequently use Claude Code to create and edit Maple Documents. It does fine alone, but I found adding a script to do a syntax check eliminated a lot of content errors. I also presume some instructions on how it should read the Maple documentation will improve its reliability. Before I go about writing my own Skill against the specification, I just want to check if there is already one in use within the community.&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Has anyone developed an Agent Skill for Maple compliant with the &lt;a href="https://agentskills.io/home"&gt;Agent Skills Specification&lt;/a&gt;?&lt;/p&gt;

&lt;p&gt;I frequently use Claude Code to create and edit Maple Documents. It does fine alone, but I found adding a script to do a syntax check eliminated a lot of content errors. I also presume some instructions on how it should read the Maple documentation will improve its reliability. Before I go about writing my own Skill against the specification, I just want to check if there is already one in use within the community.&lt;/p&gt;
</description>
      <guid>243710</guid>
      <pubDate>Wed, 29 Jul 2026 18:36:34 Z</pubDate>
      <itunes:author>OptimusMaplePrime</itunes:author>
      <author>OptimusMaplePrime</author>
    </item>
    <item>
      <title>Simplifications and substitutions</title>
      <link>http://www.mapleprimes.com/questions/243709-Simplifications-And-Substitutions?ref=Feed:MaplePrimes:Version Maple 2026</link>
      <itunes:summary>&lt;p&gt;I am trying to follow a series of substitutions used in a paper. I have given some examples of the substitutions. But I am having difficulty getting them to work. I know if all else fails I can manually recreate an expression with the substitution variables and then check backwards using eval(f,vals).&lt;br&gt;
Would appreciate any insight on substitution techniques here.&lt;br&gt;
&amp;nbsp;&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="89C5EE9877BE4045A1223CA4746573F1"&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;restart&lt;/span&gt;&lt;/p&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;sidrels := [a*c - b^2 = Delta, a + c - 2*b = d, a - b = c__bar, a - c = b__bar, c - b = a__bar];&lt;/span&gt;&lt;/p&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[a*c-b^2 = Delta, a+c-2*b = d, a-b = c__bar, a-c = b__bar, c-b = a__bar]" height="32" src="/view.aspx?sf=243709_question/837318404a37992c739324b038074608.gif" style="vertical-align:-11px" width="496"&gt;&lt;/p&gt;
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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;vals:=&amp;#39;rhs=lhs&amp;#39;~(sidrels)&lt;/span&gt;&lt;/p&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[Delta = a*c-b^2, d = a+c-2*b, c__bar = a-b, b__bar = a-c, a__bar = c-b]" height="32" src="/view.aspx?sf=243709_question/81b30fcc982c88c2dc1787bdd6878d29.gif" style="vertical-align:-11px" width="480"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t1:=a + c - 2*b;&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(t1,sidrels); #this should be d&lt;/span&gt;&lt;/p&gt;
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			&lt;table&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="a+c-2*b" height="23" src="/view.aspx?sf=243709_question/16e5ae53af6b40dc3c9e2e914e962e3e.gif" style="vertical-align:-6px" width="113"&gt;&lt;/p&gt;
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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="d" height="23" src="/view.aspx?sf=243709_question/f7b1dfbc72ee0da25cd42324b51cbfb5.gif" style="vertical-align:-6px" width="13"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t2:=Vector[column](3, [-a + b, c - b, 0]);&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(t2,sidrels) ; # This should be &amp;lt;&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;-c__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;,a__bar,0&amp;gt; or &amp;lt;&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;c__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;,-a__bar,0,&amp;gt;r&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector(3, {(1) = -a+b, (2) = c-b, (3) = 0})" height="23" src="/view.aspx?sf=243709_question/e9ab41b97efde22b9ab2d4c4c1e4f140.gif" style="vertical-align:-6px" width="63"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector[column](%id = 36893490321805397396)" height="23" src="/view.aspx?sf=243709_question/bd62644a066b98d83961da2f76ef09e4.gif" style="vertical-align:-6px" width="26"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t3:=normal(1 - b^2/(a*c));&lt;/span&gt;&lt;/p&gt;
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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(a*c-b^2)/(a*c)" height="46" src="/view.aspx?sf=243709_question/06cd2b48056cc7f529afc9b232519731.gif" style="vertical-align:-16px" width="102"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(5)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;,sidrels); # This should be Delta/(a*c)&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Delta/(b^2+Delta)" height="50" src="/view.aspx?sf=243709_question/977bd70c1c1a1e50d6009f841495c427.gif" style="vertical-align:-21px" width="58"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(6)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(numer(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(5)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;),sidrels,&amp;#39;mindeg&amp;#39;)/(denom(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(5)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;) ); # This works&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Delta/(a*c)" height="45" src="/view.aspx?sf=243709_question/9d0e21a353afdc57d908e33d85c9b299.gif" style="vertical-align:-16px" width="32"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(7)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t4:=[(-b^2 + b*c)/(a*c - b^2), (a*b - b^2)/(a*c - b^2)]&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[(-b^2+b*c)/(a*c-b^2), (a*b-b^2)/(a*c-b^2)]" height="50" src="/view.aspx?sf=243709_question/b3d07af862d906bc450d27740a30cd3d.gif" style="vertical-align:-20px" width="192"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(8)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(t4,sidrels,&amp;#39;mindeg&amp;#39;);# this should be [(b*&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;a__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;)/Delta, (b*&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;b__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;)/Delta]&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[-b*(-c+b)/Delta, b*(a-b)/Delta]" height="45" src="/view.aspx?sf=243709_question/40debfa0587d65c948f75fd0027c4655.gif" style="vertical-align:-19px" width="181"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(9)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t5:=simplify(Vector[column](3, [3*b*c__bar - Delta, -3*a__bar*b + Delta, b*(-c__bar + a__bar)]))&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector(3, {(1) = 3*b*c__bar-Delta, (2) = -3*a__bar*b+Delta, (3) = b*(-c__bar+a__bar)})" height="23" src="/view.aspx?sf=243709_question/a5db620409e4bc8dd0825c514e245d9b.gif" style="vertical-align:-6px" width="63"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(10)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t5[3]:=simplify(t5[3],sidrels) &amp;nbsp;;#This should be &lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;b*b__bar&lt;/span&gt;&lt;/p&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="-a__bar^2+(2*b+d)*a__bar-Delta" height="32" src="/view.aspx?sf=243709_question/3674fb80d2b5e94f5f963c225ffade0c.gif" style="vertical-align:-11px" width="217"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(11)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t5&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector(3, {(1) = 3*b*c__bar-Delta, (2) = -3*a__bar*b+Delta, (3) = -a__bar^2+(2*b+d)*a__bar-Delta})" height="23" src="/view.aspx?sf=243709_question/b73f3e985c4c3baa55015b122bc07089.gif" style="vertical-align:-6px" width="26"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(12)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;subs(sidrels[-2],b*(-c__bar + a__bar))&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="b*(-c__bar+a__bar)" height="28" src="/view.aspx?sf=243709_question/0e08bb8cc1204bc8fdf8649322e38317.gif" style="vertical-align:-11px" width="107"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(13)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;algsubs(sidrels[-2],b*(-c__bar + a__bar))&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="b*(-c__bar+a__bar)" height="28" src="/view.aspx?sf=243709_question/93bb6f1bc432d8cbe0293321dfd908c0.gif" style="vertical-align:-11px" width="107"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(14)&lt;/td&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
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&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;br&gt;
&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243709_question/2026-07-29_Q_Simplifications_and_Substitutions.mw"&gt;Download 2026-07-29_Q_Simplifications_and_Substitutions.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;I am trying to follow a series of substitutions used in a paper. I have given some examples of the substitutions. But I am having difficulty getting them to work. I know if all else fails I can manually recreate an expression with the substitution variables and then check backwards using eval(f,vals).&lt;br&gt;
Would appreciate any insight on substitution techniques here.&lt;br&gt;
&amp;nbsp;&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="89C5EE9877BE4045A1223CA4746573F1"&gt;
&lt;table align="center" width="768"&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;restart&lt;/span&gt;&lt;/p&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
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						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;sidrels := [a*c - b^2 = Delta, a + c - 2*b = d, a - b = c__bar, a - c = b__bar, c - b = a__bar];&lt;/span&gt;&lt;/p&gt;
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			&lt;table&gt;
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						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[a*c-b^2 = Delta, a+c-2*b = d, a-b = c__bar, a-c = b__bar, c-b = a__bar]" height="32" src="/view.aspx?sf=243709_question/837318404a37992c739324b038074608.gif" style="vertical-align:-11px" width="496"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;vals:=&amp;#39;rhs=lhs&amp;#39;~(sidrels)&lt;/span&gt;&lt;/p&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[Delta = a*c-b^2, d = a+c-2*b, c__bar = a-b, b__bar = a-c, a__bar = c-b]" height="32" src="/view.aspx?sf=243709_question/81b30fcc982c88c2dc1787bdd6878d29.gif" style="vertical-align:-11px" width="480"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t1:=a + c - 2*b;&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(t1,sidrels); #this should be d&lt;/span&gt;&lt;/p&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="a+c-2*b" height="23" src="/view.aspx?sf=243709_question/16e5ae53af6b40dc3c9e2e914e962e3e.gif" style="vertical-align:-6px" width="113"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
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			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="d" height="23" src="/view.aspx?sf=243709_question/f7b1dfbc72ee0da25cd42324b51cbfb5.gif" style="vertical-align:-6px" width="13"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t2:=Vector[column](3, [-a + b, c - b, 0]);&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(t2,sidrels) ; # This should be &amp;lt;&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;-c__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;,a__bar,0&amp;gt; or &amp;lt;&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;c__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;,-a__bar,0,&amp;gt;r&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector(3, {(1) = -a+b, (2) = c-b, (3) = 0})" height="23" src="/view.aspx?sf=243709_question/e9ab41b97efde22b9ab2d4c4c1e4f140.gif" style="vertical-align:-6px" width="63"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;&amp;nbsp;&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector[column](%id = 36893490321805397396)" height="23" src="/view.aspx?sf=243709_question/bd62644a066b98d83961da2f76ef09e4.gif" style="vertical-align:-6px" width="26"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(4)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t3:=normal(1 - b^2/(a*c));&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="(a*c-b^2)/(a*c)" height="46" src="/view.aspx?sf=243709_question/06cd2b48056cc7f529afc9b232519731.gif" style="vertical-align:-16px" width="102"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(5)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(5)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;,sidrels); # This should be Delta/(a*c)&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Delta/(b^2+Delta)" height="50" src="/view.aspx?sf=243709_question/977bd70c1c1a1e50d6009f841495c427.gif" style="vertical-align:-21px" width="58"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(6)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(numer(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(5)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;),sidrels,&amp;#39;mindeg&amp;#39;)/(denom(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(5)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;) ); # This works&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Delta/(a*c)" height="45" src="/view.aspx?sf=243709_question/9d0e21a353afdc57d908e33d85c9b299.gif" style="vertical-align:-16px" width="32"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(7)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t4:=[(-b^2 + b*c)/(a*c - b^2), (a*b - b^2)/(a*c - b^2)]&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[(-b^2+b*c)/(a*c-b^2), (a*b-b^2)/(a*c-b^2)]" height="50" src="/view.aspx?sf=243709_question/b3d07af862d906bc450d27740a30cd3d.gif" style="vertical-align:-20px" width="192"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(8)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;simplify(t4,sidrels,&amp;#39;mindeg&amp;#39;);# this should be [(b*&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;a__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;)/Delta, (b*&lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;b__bar&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;)/Delta]&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[-b*(-c+b)/Delta, b*(a-b)/Delta]" height="45" src="/view.aspx?sf=243709_question/40debfa0587d65c948f75fd0027c4655.gif" style="vertical-align:-19px" width="181"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(9)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t5:=simplify(Vector[column](3, [3*b*c__bar - Delta, -3*a__bar*b + Delta, b*(-c__bar + a__bar)]))&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector(3, {(1) = 3*b*c__bar-Delta, (2) = -3*a__bar*b+Delta, (3) = b*(-c__bar+a__bar)})" height="23" src="/view.aspx?sf=243709_question/a5db620409e4bc8dd0825c514e245d9b.gif" style="vertical-align:-6px" width="63"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(10)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t5[3]:=simplify(t5[3],sidrels) &amp;nbsp;;#This should be &lt;/span&gt;&lt;span style="color:#008000;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;b*b__bar&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="-a__bar^2+(2*b+d)*a__bar-Delta" height="32" src="/view.aspx?sf=243709_question/3674fb80d2b5e94f5f963c225ffade0c.gif" style="vertical-align:-11px" width="217"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(11)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;t5&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Vector(3, {(1) = 3*b*c__bar-Delta, (2) = -3*a__bar*b+Delta, (3) = -a__bar^2+(2*b+d)*a__bar-Delta})" height="23" src="/view.aspx?sf=243709_question/b73f3e985c4c3baa55015b122bc07089.gif" style="vertical-align:-6px" width="26"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(12)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;subs(sidrels[-2],b*(-c__bar + a__bar))&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="b*(-c__bar+a__bar)" height="28" src="/view.aspx?sf=243709_question/0e08bb8cc1204bc8fdf8649322e38317.gif" style="vertical-align:-11px" width="107"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(13)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;&amp;gt;&amp;nbsp;&lt;/span&gt;&lt;/td&gt;
						&lt;td&gt;
						&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: monospace,monospace;font-weight:bold;font-style:normal;"&gt;algsubs(sidrels[-2],b*(-c__bar + a__bar))&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
						&lt;td&gt;
						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="b*(-c__bar+a__bar)" height="28" src="/view.aspx?sf=243709_question/93bb6f1bc432d8cbe0293321dfd908c0.gif" style="vertical-align:-11px" width="107"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(14)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;table style="margin-left:0px;margin-right:0px"&gt;
				&lt;tbody&gt;
					&lt;tr valign="baseline"&gt;
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&lt;p&gt;&lt;br&gt;
&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243709_question/2026-07-29_Q_Simplifications_and_Substitutions.mw"&gt;Download 2026-07-29_Q_Simplifications_and_Substitutions.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243709</guid>
      <pubDate>Wed, 29 Jul 2026 16:37:44 Z</pubDate>
      <itunes:author>Ronan</itunes:author>
      <author>Ronan</author>
    </item>
    <item>
      <title>Recalcitrant differential equation</title>
      <link>http://www.mapleprimes.com/questions/243707-Recalcitrant-Differential-Equation?ref=Feed:MaplePrimes:Version Maple 2026</link>
      <itunes:summary>&lt;p&gt;In the attached file, I&amp;#39;d like to solve an ODE as an exercise. Only the &amp;quot;series&amp;quot; option yielded a solution. How can the length of the result series be controlled? Is there a package that leads to a &amp;quot;closed&amp;quot; solution &amp;ndash; even using well-known transcendental functions?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="CB0FEDFF3073DE6C3A4E90EFA6044C71"&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="ode := (1+f(x))*(diff(f(x), x, x)) = 1+x" height="50" src="/view.aspx?sf=243707_question/62891d1f7973d6a7176f502106063918.gif" style="vertical-align:-20px" width="260"&gt;&lt;/p&gt;

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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="ics := f(0) = 1, (D(f))(0) = 0" height="23" src="/view.aspx?sf=243707_question/b38c92592dd9a5e67f9ceef74ab76b9a.gif" style="vertical-align:-6px" width="191"&gt;&lt;/p&gt;

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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="dsolve({ics, ode}, f(x), series)" height="23" src="/view.aspx?sf=243707_question/d8dfdc5e5efce239a8f499475170232a.gif" style="vertical-align:-6px" width="199"&gt;&lt;/p&gt;

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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="f(x) = series(1+(1/4)*x^2+(1/12)*x^3-(1/192)*x^4-(1/240)*x^5+O(x^6),x,6)" height="42" src="/view.aspx?sf=243707_question/80db5cf8dc7d5ad04b137703f3063d60.gif" style="vertical-align:-16px" width="359"&gt;&lt;/p&gt;
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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=243707_question/5711fa44c51db4941cc72ed6f88c7b90.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
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&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243707_question/test.mw"&gt;Download test.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;In the attached file, I&amp;#39;d like to solve an ODE as an exercise. Only the &amp;quot;series&amp;quot; option yielded a solution. How can the length of the result series be controlled? Is there a package that leads to a &amp;quot;closed&amp;quot; solution &amp;ndash; even using well-known transcendental functions?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="CB0FEDFF3073DE6C3A4E90EFA6044C71"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&gt;
			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=243707_question/8c470ac7d9aa6659a12088a08f8027e1.gif" style="vertical-align:-6px" width="54"&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="ode := (1+f(x))*(diff(f(x), x, x)) = 1+x" height="50" src="/view.aspx?sf=243707_question/62891d1f7973d6a7176f502106063918.gif" style="vertical-align:-20px" width="260"&gt;&lt;/p&gt;

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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(1)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="ics := f(0) = 1, (D(f))(0) = 0" height="23" src="/view.aspx?sf=243707_question/b38c92592dd9a5e67f9ceef74ab76b9a.gif" style="vertical-align:-6px" width="191"&gt;&lt;/p&gt;

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						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(2)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="dsolve({ics, ode}, f(x), series)" height="23" src="/view.aspx?sf=243707_question/d8dfdc5e5efce239a8f499475170232a.gif" style="vertical-align:-6px" width="199"&gt;&lt;/p&gt;

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						&lt;p align="center" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="f(x) = series(1+(1/4)*x^2+(1/12)*x^3-(1/192)*x^4-(1/240)*x^5+O(x^6),x,6)" height="42" src="/view.aspx?sf=243707_question/80db5cf8dc7d5ad04b137703f3063d60.gif" style="vertical-align:-16px" width="359"&gt;&lt;/p&gt;
						&lt;/td&gt;
						&lt;td align="right" style="color:#000000; font-family:Times, serif; font-weight:bold; font-style:normal;"&gt;(3)&lt;/td&gt;
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			&lt;p align="left" style="margin:0 0 0 0; padding-top:3px; padding-bottom:3px"&gt;&lt;img alt="``" height="23" src="/view.aspx?sf=243707_question/5711fa44c51db4941cc72ed6f88c7b90.gif" style="vertical-align:-6px" width="11"&gt;&lt;/p&gt;
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&lt;input name="sequence" type="hidden" value="1"&gt; &lt;input name="cmd" type="hidden" value="none"&gt;&lt;/form&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243707_question/test.mw"&gt;Download test.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243707</guid>
      <pubDate>Wed, 29 Jul 2026 09:10:23 Z</pubDate>
      <itunes:author>Alfred_F</itunes:author>
      <author>Alfred_F</author>
    </item>
    <item>
      <title>How to Import Converations from ChatGPT</title>
      <link>http://www.mapleprimes.com/questions/243702-How-To-Import-Converations-From-ChatGPT?ref=Feed:MaplePrimes:Version Maple 2026</link>
      <itunes:summary>&lt;p&gt;Responses from the AI assistant in Maple2026 can be copied directly into a Maple Document or Worksheet, Is there a process which allows one to similarly import a external ChatGPT conversation. I have Maple MCP configured in my ChatGPT account.&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Responses from the AI assistant in Maple2026 can be copied directly into a Maple Document or Worksheet, Is there a process which allows one to similarly import a external ChatGPT conversation. I have Maple MCP configured in my ChatGPT account.&lt;/p&gt;
</description>
      <guid>243702</guid>
      <pubDate>Sat, 25 Jul 2026 14:18:57 Z</pubDate>
      <itunes:author>ianmccr</itunes:author>
      <author>ianmccr</author>
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    <item>
      <title>How to integrate a trig function with parameter?</title>
      <link>http://www.mapleprimes.com/questions/243698-How-To-Integrate-A-Trig-Function-With-Parameter?ref=Feed:MaplePrimes:Version Maple 2026</link>
      <itunes:summary>&lt;p&gt;How to integrate this function (n::posint) :&lt;br&gt;
f := (n, x) -&amp;gt; (1 - cos(n*x))/(1 - cos(x))&lt;/p&gt;

&lt;p&gt;Maple is not returning a result. It seems unable to establish the connection with the Dirichlet kernel.&amp;nbsp;Is there a solution that doesn&amp;#39;t require forcing a decomposition into a sum of cosinus?&lt;/p&gt;

&lt;p&gt;Thank you for your help.&lt;/p&gt;

&lt;p&gt;Best regards.&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;How to integrate this function (n::posint) :&lt;br /&gt;
f := (n, x) -&amp;gt; (1 - cos(n*x))/(1 - cos(x))&lt;/p&gt;

&lt;p&gt;Maple is not returning a result. It seems unable to establish the connection with the Dirichlet kernel.&amp;nbsp;Is there a solution that doesn&amp;#39;t require forcing a decomposition into a sum of cosinus?&lt;/p&gt;

&lt;p&gt;Thank you for your help.&lt;/p&gt;

&lt;p&gt;Best regards.&lt;/p&gt;
</description>
      <guid>243698</guid>
      <pubDate>Thu, 23 Jul 2026 11:42:49 Z</pubDate>
      <itunes:author>Aliocha</itunes:author>
      <author>Aliocha</author>
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