<rss xmlns:itunes="http://www.itunes.com/dtds/podcast-1.0.dtd" version="2.0">
  <channel>
    <title>MaplePrimes - Maple 2025 Posts and Questions</title>
    <link>http://www.mapleprimes.com/products/Maple/Maple 2025</link>
    <language>en-us</language>
    <copyright>2026 Maplesoft, A Division of Waterloo Maple Inc.</copyright>
    <generator>Maplesoft Document System</generator>
    <lastBuildDate>Mon, 22 Jun 2026 13:09:09 GMT</lastBuildDate>
    <pubDate>Mon, 22 Jun 2026 13:09:09 GMT</pubDate>
    <itunes:subtitle />
    <itunes:summary />
    <description>Maple 2025 Questions and Posts on MaplePrimes</description>
    <image>
      <url>http://www.mapleprimes.com/images/mapleprimeswhite.jpg</url>
      <title>MaplePrimes - Maple 2025 Posts and Questions</title>
      <link>http://www.mapleprimes.com/products/Maple/Maple 2025</link>
    </image>
    <item>
      <title>Why do the indices on tensor expressions move to different locations? </title>
      <link>http://www.mapleprimes.com/questions/243647-Why-Do-The-Indices-On-Tensor-Expressions?ref=Feed:MaplePrimes:Version Maple 2025</link>
      <itunes:summary>&lt;p&gt;The title says it all. Nevertheless, I am doing some symbolic computation/manipulations with tensors in the Physics pacakge. When I type out my expressions and execute it changes some positions of the indices -- example below. Why?&amp;nbsp;&lt;br&gt;
**Sorry, contents will not post.&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243647_question/IndexQuestion.mw"&gt;Download IndexQuestion.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;The title says it all. Nevertheless, I am doing some symbolic computation/manipulations with tensors in the Physics pacakge. When I type out my expressions and execute it changes some positions of the indices -- example below. Why?&amp;nbsp;&lt;br&gt;
**Sorry, contents will not post.&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243647_question/IndexQuestion.mw"&gt;Download IndexQuestion.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243647</guid>
      <pubDate>Sat, 20 Jun 2026 00:47:56 Z</pubDate>
      <itunes:author>Hullzie16</itunes:author>
      <author>Hullzie16</author>
    </item>
    <item>
      <title>How to simplify this radical expression</title>
      <link>http://www.mapleprimes.com/questions/243634-How-To-Simplify-This-Radical-Expression?ref=Feed:MaplePrimes:Version Maple 2025</link>
      <itunes:summary>&lt;p&gt;The below problem has already occured several times to me. In all such instances Maple did not realise that extracting a factor from a square root is the key for further simplification. Doing this by hand is obvious and often easy when extracted factors are positive.&amp;nbsp;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;Did I overlook something? Are there other ways avoid disassembling an expression with the op command?&lt;br&gt;
Should simplify or other commands be improved to adress such problems?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="12DA639F41D2DC4DBB563D7E2F543298"&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:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=243634_question/0664076378bacabef75654bf3a5af638.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;How to transform the left-hand side by commands that it matches the right-hand side&lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="sqrt(x__0+1)*sqrt(-2*beta^2*x__0-2*beta^2+4)*sqrt(-(x__0+1)*(beta^2-1))/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/(sqrt(-beta^2+1)*sqrt(-2*beta^2*x__0-2*beta^2+4))" height="72" src="/view.aspx?sf=243634_question/1c5cd0e0c09cced8ebda383a297eb15e.gif" style="vertical-align:-31px" width="606"&gt;&lt;/p&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="(x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="72" src="/view.aspx?sf=243634_question/e459a1030c6cedd3e7981750baf8c1e6.gif" style="vertical-align:-31px" width="603"&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;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="assumptions := 0 &amp;lt; x__0 and x__0 &amp;lt; 1, 0 &amp;lt; beta and beta &amp;lt; 1" height="30" src="/view.aspx?sf=243634_question/3cfabee9ce7c376bb5dfcd402ae17db7.gif" style="vertical-align:-11px" width="241"&gt;&lt;/p&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="0 &amp;lt; x__0 and x__0 &amp;lt; 1, 0 &amp;lt; beta and beta &amp;lt; 1" height="30" src="/view.aspx?sf=243634_question/cccba500e3699d177d7f32f2ad36830c.gif" style="vertical-align:-11px" width="241"&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;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="`assuming`([simplify(lhs((x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))))], [assumptions])" height="23" src="/view.aspx?sf=243634_question/8519a1613e94af5619e854d61817fb28.gif" style="vertical-align:-6px" width="251"&gt;&lt;/p&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="-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2))" height="72" src="/view.aspx?sf=243634_question/da67b6ee7bdd4ad245f4e21c4f2a1aac.gif" style="vertical-align:-31px" width="227"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;I have tried the usual simplify and combine commands to remove the square root from the numerator.&lt;/span&gt;&lt;br&gt;
			&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Extracting a factor for -2 from the square root would probably make further simplification possible but there is no simple command to do so.&lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Factor_ := -2" height="23" src="/view.aspx?sf=243634_question/6a83b4470e4904e6dd4c48ae270283dd.gif" style="vertical-align:-6px" width="101"&gt;&lt;/p&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="-2" height="23" src="/view.aspx?sf=243634_question/3675cb864bf79a8ab817a0751c18d343.gif" style="vertical-align:-6px" width="101"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="old := simplify([op(denom(-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2))))])" height="23" src="/view.aspx?sf=243634_question/f1ff6b0a5e6ade5cd6cbd84a6ee4ac4c.gif" style="vertical-align:-6px" width="224"&gt;&lt;/p&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="[(-beta^2+1)^(1/2), -2+(x__0+1)*beta^2]" height="38" src="/view.aspx?sf=243634_question/8dc55b584cd9bf347ad91fb2eaac472f.gif" style="vertical-align:-11px" width="250"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="new := old; new[1] := old[1]/Factor_; new[2] := old[2]*Factor_" height="59" src="/view.aspx?sf=243634_question/0b987e74a76c9e3c9e5fda7c2a03b6ac.gif" style="vertical-align:-42px" width="768"&gt;&lt;/p&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="[-(1/2)*(-beta^2+1)^(1/2), 4-2*(x__0+1)*beta^2]" height="53" src="/view.aspx?sf=243634_question/89a6011409d56a54abbb0ea6a89257a2.gif" style="vertical-align:-16px" width="275"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="subs(1/old[1] = 1/new[1], 1/old[2] = 1/new[2], -(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2)))" height="42" src="/view.aspx?sf=243634_question/a80af2f6b16604aa2e5d288a700401ea.gif" style="vertical-align:-16px" width="323"&gt;&lt;/p&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="2*(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(4-2*(x__0+1)*beta^2))" height="72" src="/view.aspx?sf=243634_question/836247b95b3b51765774803ee7078069.gif" style="vertical-align:-31px" 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;(7)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="expand(simplify(2*(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(4-2*(x__0+1)*beta^2))))" height="23" src="/view.aspx?sf=243634_question/f02dd2c753a2d757910618eed69865ed.gif" style="vertical-align:-6px" width="141"&gt;&lt;/p&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="2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="57" src="/view.aspx?sf=243634_question/e561b0c78f60cd9e33895f7c5c45919e.gif" style="vertical-align:-31px" width="229"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)) = rhs((x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)))" height="23" src="/view.aspx?sf=243634_question/19c70be8179b03dd8cab267904fac0c3.gif" style="vertical-align:-6px" width="103"&gt;&lt;/p&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="2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="57" src="/view.aspx?sf=243634_question/686920bf6fc9a648d69375efc12e7cea.gif" style="vertical-align:-31px" width="468"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="is(2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)))" height="23" src="/view.aspx?sf=243634_question/b6fda6a9032eb1788d5f6ec19f20b83c.gif" style="vertical-align:-6px" width="47"&gt;&lt;/p&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="true" height="23" src="/view.aspx?sf=243634_question/142ffd0cb6861cbeef2f2cd36610e5e7.gif" style="vertical-align:-6px" width="30"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Second approach after &amp;quot;discovering&amp;quot; that content works also on square roots &lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[op(-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2)))]" height="23" src="/view.aspx?sf=243634_question/49cf3d3c722a0c352518c5e190bf85c2.gif" style="vertical-align:-6px" width="65"&gt;&lt;/p&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="[-1, 1/(-beta^2+1)^(1/2), (4+(-2*x__0-2)*beta^2)^(1/2), 1/(-2+(x__0+1)*beta^2)]" height="54" src="/view.aspx?sf=243634_question/6c171181400fa574703b4c26633d0cff.gif" style="vertical-align:-27px" width="399"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="mul(`~`[`*`](`~`[content]([-1, 1/(-beta^2+1)^(1/2), (4+(-2*x__0-2)*beta^2)^(1/2), 1/(-2+(x__0+1)*beta^2)]), `~`[primpart]([-1, 1/(-beta^2+1)^(1/2), (4+(-2*x__0-2)*beta^2)^(1/2), 1/(-2+(x__0+1)*beta^2)])))" height="23" src="/view.aspx?sf=243634_question/06361b8d3d449076dbaf992675e10bc3.gif" style="vertical-align:-6px" width="250"&gt;&lt;/p&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="-2^(1/2)*(-beta^2*x__0-beta^2+2)^(1/2)/((-beta^2+1)^(1/2)*(beta^2*x__0+beta^2-2))" height="72" src="/view.aspx?sf=243634_question/2dec0ecbd298ff5bae393caa86f5b40e.gif" style="vertical-align:-31px" width="208"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="simplify(-2^(1/2)*(-beta^2*x__0-beta^2+2)^(1/2)/((-beta^2+1)^(1/2)*(beta^2*x__0+beta^2-2))) = rhs((x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)))" height="23" src="/view.aspx?sf=243634_question/608ddee2e0e68712b931cacaa60ebd4b.gif" style="vertical-align:-6px" width="157"&gt;&lt;/p&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="2^(1/2)/((2+(-x__0-1)*beta^2)^(1/2)*(-beta^2+1)^(1/2)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="61" src="/view.aspx?sf=243634_question/03ffdf51f27f2bac7dc4f0b5fddf66db.gif" style="vertical-align:-31px" width="457"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="is(%)" height="23" src="/view.aspx?sf=243634_question/83a53d0e2c416a115124a841c8d6f894.gif" style="vertical-align:-6px" width="42"&gt;&lt;/p&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="true" height="23" src="/view.aspx?sf=243634_question/21bbc77e4e4068a892b37d059f08e1d2.gif" style="vertical-align:-6px" width="30"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=243634_question/3b16d1b9e653aff71438e0979e9905f4.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Context: The left-hand side in an integrand which was produced by a change of variables in a elliptic integral. Maple simplifies only halfway which makes validation of the result of the variable change difficult. &amp;nbsp;&lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=243634_question/3023baa5df1741a789889c322bd9e0da.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Related functional programming question: Is a onliner &lt;/span&gt;&lt;img alt="`...`(-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2)))" height="23" src="/view.aspx?sf=243634_question/40c1e4e84efa0012a7f02d19e6495d93.gif" style="vertical-align:-6px" width="64"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;from the above content-primpart construct possible?&lt;/span&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=243634_question/7cdc8f9052d7aba885c3bd9d77cf3eb6.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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=243634_question/Simplify_radical_02.mw"&gt;Download Simplify_radical_02.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;The below problem has already occured several times to me. In all such instances Maple did not realise that extracting a factor from a square root is the key for further simplification. Doing this by hand is obvious and often easy when extracted factors are positive.&amp;nbsp;&amp;nbsp;&lt;/p&gt;

&lt;p&gt;Did I overlook something? Are there other ways avoid disassembling an expression with the op command?&lt;br&gt;
Should simplify or other commands be improved to adress such problems?&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="12DA639F41D2DC4DBB563D7E2F543298"&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:0px; padding-bottom:0px"&gt;&lt;img alt="restart" height="23" src="/view.aspx?sf=243634_question/0664076378bacabef75654bf3a5af638.gif" style="vertical-align:-6px" width="58"&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;How to transform the left-hand side by commands that it matches the right-hand side&lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="sqrt(x__0+1)*sqrt(-2*beta^2*x__0-2*beta^2+4)*sqrt(-(x__0+1)*(beta^2-1))/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/(sqrt(-beta^2+1)*sqrt(-2*beta^2*x__0-2*beta^2+4))" height="72" src="/view.aspx?sf=243634_question/1c5cd0e0c09cced8ebda383a297eb15e.gif" style="vertical-align:-31px" width="606"&gt;&lt;/p&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="(x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="72" src="/view.aspx?sf=243634_question/e459a1030c6cedd3e7981750baf8c1e6.gif" style="vertical-align:-31px" width="603"&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;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="assumptions := 0 &amp;lt; x__0 and x__0 &amp;lt; 1, 0 &amp;lt; beta and beta &amp;lt; 1" height="30" src="/view.aspx?sf=243634_question/3cfabee9ce7c376bb5dfcd402ae17db7.gif" style="vertical-align:-11px" width="241"&gt;&lt;/p&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="0 &amp;lt; x__0 and x__0 &amp;lt; 1, 0 &amp;lt; beta and beta &amp;lt; 1" height="30" src="/view.aspx?sf=243634_question/cccba500e3699d177d7f32f2ad36830c.gif" style="vertical-align:-11px" width="241"&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;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="`assuming`([simplify(lhs((x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))))], [assumptions])" height="23" src="/view.aspx?sf=243634_question/8519a1613e94af5619e854d61817fb28.gif" style="vertical-align:-6px" width="251"&gt;&lt;/p&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="-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2))" height="72" src="/view.aspx?sf=243634_question/da67b6ee7bdd4ad245f4e21c4f2a1aac.gif" style="vertical-align:-31px" width="227"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;I have tried the usual simplify and combine commands to remove the square root from the numerator.&lt;/span&gt;&lt;br&gt;
			&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Extracting a factor for -2 from the square root would probably make further simplification possible but there is no simple command to do so.&lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="Factor_ := -2" height="23" src="/view.aspx?sf=243634_question/6a83b4470e4904e6dd4c48ae270283dd.gif" style="vertical-align:-6px" width="101"&gt;&lt;/p&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="-2" height="23" src="/view.aspx?sf=243634_question/3675cb864bf79a8ab817a0751c18d343.gif" style="vertical-align:-6px" width="101"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="old := simplify([op(denom(-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2))))])" height="23" src="/view.aspx?sf=243634_question/f1ff6b0a5e6ade5cd6cbd84a6ee4ac4c.gif" style="vertical-align:-6px" width="224"&gt;&lt;/p&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="[(-beta^2+1)^(1/2), -2+(x__0+1)*beta^2]" height="38" src="/view.aspx?sf=243634_question/8dc55b584cd9bf347ad91fb2eaac472f.gif" style="vertical-align:-11px" width="250"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img align="middle" alt="new := old; new[1] := old[1]/Factor_; new[2] := old[2]*Factor_" height="59" src="/view.aspx?sf=243634_question/0b987e74a76c9e3c9e5fda7c2a03b6ac.gif" style="vertical-align:-42px" width="768"&gt;&lt;/p&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="[-(1/2)*(-beta^2+1)^(1/2), 4-2*(x__0+1)*beta^2]" height="53" src="/view.aspx?sf=243634_question/89a6011409d56a54abbb0ea6a89257a2.gif" style="vertical-align:-16px" width="275"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="subs(1/old[1] = 1/new[1], 1/old[2] = 1/new[2], -(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2)))" height="42" src="/view.aspx?sf=243634_question/a80af2f6b16604aa2e5d288a700401ea.gif" style="vertical-align:-16px" width="323"&gt;&lt;/p&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="2*(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(4-2*(x__0+1)*beta^2))" height="72" src="/view.aspx?sf=243634_question/836247b95b3b51765774803ee7078069.gif" style="vertical-align:-31px" 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;(7)&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="expand(simplify(2*(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(4-2*(x__0+1)*beta^2))))" height="23" src="/view.aspx?sf=243634_question/f02dd2c753a2d757910618eed69865ed.gif" style="vertical-align:-6px" width="141"&gt;&lt;/p&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="2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="57" src="/view.aspx?sf=243634_question/e561b0c78f60cd9e33895f7c5c45919e.gif" style="vertical-align:-31px" width="229"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)) = rhs((x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)))" height="23" src="/view.aspx?sf=243634_question/19c70be8179b03dd8cab267904fac0c3.gif" style="vertical-align:-6px" width="103"&gt;&lt;/p&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="2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="57" src="/view.aspx?sf=243634_question/686920bf6fc9a648d69375efc12e7cea.gif" style="vertical-align:-31px" width="468"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="is(2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)))" height="23" src="/view.aspx?sf=243634_question/b6fda6a9032eb1788d5f6ec19f20b83c.gif" style="vertical-align:-6px" width="47"&gt;&lt;/p&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="true" height="23" src="/view.aspx?sf=243634_question/142ffd0cb6861cbeef2f2cd36610e5e7.gif" style="vertical-align:-6px" width="30"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Second approach after &amp;quot;discovering&amp;quot; that content works also on square roots &lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="[op(-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2)))]" height="23" src="/view.aspx?sf=243634_question/49cf3d3c722a0c352518c5e190bf85c2.gif" style="vertical-align:-6px" width="65"&gt;&lt;/p&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="[-1, 1/(-beta^2+1)^(1/2), (4+(-2*x__0-2)*beta^2)^(1/2), 1/(-2+(x__0+1)*beta^2)]" height="54" src="/view.aspx?sf=243634_question/6c171181400fa574703b4c26633d0cff.gif" style="vertical-align:-27px" width="399"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="mul(`~`[`*`](`~`[content]([-1, 1/(-beta^2+1)^(1/2), (4+(-2*x__0-2)*beta^2)^(1/2), 1/(-2+(x__0+1)*beta^2)]), `~`[primpart]([-1, 1/(-beta^2+1)^(1/2), (4+(-2*x__0-2)*beta^2)^(1/2), 1/(-2+(x__0+1)*beta^2)])))" height="23" src="/view.aspx?sf=243634_question/06361b8d3d449076dbaf992675e10bc3.gif" style="vertical-align:-6px" width="250"&gt;&lt;/p&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="-2^(1/2)*(-beta^2*x__0-beta^2+2)^(1/2)/((-beta^2+1)^(1/2)*(beta^2*x__0+beta^2-2))" height="72" src="/view.aspx?sf=243634_question/2dec0ecbd298ff5bae393caa86f5b40e.gif" style="vertical-align:-31px" width="208"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="simplify(-2^(1/2)*(-beta^2*x__0-beta^2+2)^(1/2)/((-beta^2+1)^(1/2)*(beta^2*x__0+beta^2-2))) = rhs((x__0+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)*(-(x__0+1)*(beta^2-1))^(1/2)/((beta^2*x__0+beta^2-2)*(beta^2*x__0+beta^2-x__0-1)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2)))" height="23" src="/view.aspx?sf=243634_question/608ddee2e0e68712b931cacaa60ebd4b.gif" style="vertical-align:-6px" width="157"&gt;&lt;/p&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="2^(1/2)/((2+(-x__0-1)*beta^2)^(1/2)*(-beta^2+1)^(1/2)) = 2/((-beta^2+1)^(1/2)*(-2*beta^2*x__0-2*beta^2+4)^(1/2))" height="61" src="/view.aspx?sf=243634_question/03ffdf51f27f2bac7dc4f0b5fddf66db.gif" style="vertical-align:-31px" width="457"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="is(%)" height="23" src="/view.aspx?sf=243634_question/83a53d0e2c416a115124a841c8d6f894.gif" style="vertical-align:-6px" width="42"&gt;&lt;/p&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="true" height="23" src="/view.aspx?sf=243634_question/21bbc77e4e4068a892b37d059f08e1d2.gif" style="vertical-align:-6px" width="30"&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;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=243634_question/3b16d1b9e653aff71438e0979e9905f4.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Context: The left-hand side in an integrand which was produced by a change of variables in a elliptic integral. Maple simplifies only halfway which makes validation of the result of the variable change difficult. &amp;nbsp;&lt;/span&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=243634_question/3023baa5df1741a789889c322bd9e0da.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;Related functional programming question: Is a onliner &lt;/span&gt;&lt;img alt="`...`(-(4+(-2*x__0-2)*beta^2)^(1/2)/((-beta^2+1)^(1/2)*(-2+(x__0+1)*beta^2)))" height="23" src="/view.aspx?sf=243634_question/40c1e4e84efa0012a7f02d19e6495d93.gif" style="vertical-align:-6px" width="64"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Trebuchet MS,sans-serif;font-weight:normal;font-style:normal;"&gt;from the above content-primpart construct possible?&lt;/span&gt;&lt;img alt="NULL" height="23" src="/view.aspx?sf=243634_question/7cdc8f9052d7aba885c3bd9d77cf3eb6.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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=243634_question/Simplify_radical_02.mw"&gt;Download Simplify_radical_02.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243634</guid>
      <pubDate>Sat, 13 Jun 2026 07:40:12 Z</pubDate>
      <itunes:author>C_R</itunes:author>
      <author>C_R</author>
    </item>
    <item>
      <title>Creating a Bar Chart</title>
      <link>http://www.mapleprimes.com/questions/243633-Creating-A-Bar-Chart?ref=Feed:MaplePrimes:Version Maple 2025</link>
      <itunes:summary>&lt;p&gt;Help me rewrite the code to create visible Bar chart of different colors. I can&amp;#39;t figure out why this code is not giving me a visible bar graph&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="ACDD616157E72D342139C6C309E23201"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&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: Courier New,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;img align="middle" alt="restart; with(Statistics); with(plots); Data := [45, 38, 51, 67, 74, 91]; P := BarChart(Data, tickmarks = [[1 = &amp;quot;Chemical Vector Control&amp;quot;, 2 = &amp;quot;Resistant Cultivars&amp;quot;, 3 = &amp;quot;Roguing &amp;amp; Sanitation&amp;quot;, 4 = &amp;quot;u1+u2&amp;quot;, 5 = &amp;quot;u1+u3&amp;quot;, 6 = &amp;quot;Integrated&amp;quot;], default], width = .75); T := textplot([[1, 48, &amp;quot;45%&amp;quot;], [2, 41, &amp;quot;38%&amp;quot;], [3, 54, &amp;quot;51%&amp;quot;], [4, 70, &amp;quot;67%&amp;quot;], [5, 77, &amp;quot;74%&amp;quot;], [6, 94, &amp;quot;91%&amp;quot;]], font = [&amp;quot;TIMES&amp;quot;, &amp;quot;BOLD&amp;quot;, 12]); display([P, T], title = &amp;quot;Figure 20: Comparative Effectiveness of Optimal Control Strategies&amp;quot;, labels = [&amp;quot;Control Strategies&amp;quot;, &amp;quot;Reduction in Coinfection Burden (%)&amp;quot;], labelfont = [&amp;quot;TIMES&amp;quot;, &amp;quot;BOLD&amp;quot;, 14], titlefont = [&amp;quot;TIMES&amp;quot;, &amp;quot;BOLD&amp;quot;, 16], axes = boxed, gridlines = true, view = [.5 .. 6.5, 0 .. 100], size = [1000, 650])" height="811" src="/view.aspx?sf=243633_question/2fd6d2cc6ce0b1d1d3f2bba3ea44d272.gif" style="vertical-align:-794px" width="768"&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 align="middle" height="499" src="/view.aspx?sf=243633_question/310921ce0904c159d82efcdea64b33ce.gif" style="border:none" width="768"&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 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: Courier New,monospace;font-weight:bold;font-style:normal;"&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;img alt="NULL" height="23" src="/view.aspx?sf=243633_question/be7944879375c3b97deb268162dc1b9d.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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=243633_question/Bargraph.mw"&gt;Download Bargraph.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Help me rewrite the code to create visible Bar chart of different colors. I can&amp;#39;t figure out why this code is not giving me a visible bar graph&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="ACDD616157E72D342139C6C309E23201"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&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: Courier New,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;img align="middle" alt="restart; with(Statistics); with(plots); Data := [45, 38, 51, 67, 74, 91]; P := BarChart(Data, tickmarks = [[1 = &amp;quot;Chemical Vector Control&amp;quot;, 2 = &amp;quot;Resistant Cultivars&amp;quot;, 3 = &amp;quot;Roguing &amp;amp; Sanitation&amp;quot;, 4 = &amp;quot;u1+u2&amp;quot;, 5 = &amp;quot;u1+u3&amp;quot;, 6 = &amp;quot;Integrated&amp;quot;], default], width = .75); T := textplot([[1, 48, &amp;quot;45%&amp;quot;], [2, 41, &amp;quot;38%&amp;quot;], [3, 54, &amp;quot;51%&amp;quot;], [4, 70, &amp;quot;67%&amp;quot;], [5, 77, &amp;quot;74%&amp;quot;], [6, 94, &amp;quot;91%&amp;quot;]], font = [&amp;quot;TIMES&amp;quot;, &amp;quot;BOLD&amp;quot;, 12]); display([P, T], title = &amp;quot;Figure 20: Comparative Effectiveness of Optimal Control Strategies&amp;quot;, labels = [&amp;quot;Control Strategies&amp;quot;, &amp;quot;Reduction in Coinfection Burden (%)&amp;quot;], labelfont = [&amp;quot;TIMES&amp;quot;, &amp;quot;BOLD&amp;quot;, 14], titlefont = [&amp;quot;TIMES&amp;quot;, &amp;quot;BOLD&amp;quot;, 16], axes = boxed, gridlines = true, view = [.5 .. 6.5, 0 .. 100], size = [1000, 650])" height="811" src="/view.aspx?sf=243633_question/2fd6d2cc6ce0b1d1d3f2bba3ea44d272.gif" style="vertical-align:-794px" width="768"&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 align="middle" height="499" src="/view.aspx?sf=243633_question/310921ce0904c159d82efcdea64b33ce.gif" style="border:none" width="768"&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 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: Courier New,monospace;font-weight:bold;font-style:normal;"&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;img alt="NULL" height="23" src="/view.aspx?sf=243633_question/be7944879375c3b97deb268162dc1b9d.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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=243633_question/Bargraph.mw"&gt;Download Bargraph.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243633</guid>
      <pubDate>Fri, 12 Jun 2026 12:14:21 Z</pubDate>
      <itunes:author>Elisha</itunes:author>
      <author>Elisha</author>
    </item>
    <item>
      <title>HTML entities in 2D Input mode</title>
      <link>http://www.mapleprimes.com/questions/243621-HTML-Entities-In-2D-Input-Mode?ref=Feed:MaplePrimes:Version Maple 2025</link>
      <itunes:summary>&lt;p&gt;The HTML characters in the attached document cause problems here on MaplePrimes. You have to open the worksheet&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243621_question/HTML_characters_in_math_mode.mw"&gt;Download HTML_characters_in_math_mode.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;The HTML characters in the attached document cause problems here on MaplePrimes. You have to open the worksheet&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243621_question/HTML_characters_in_math_mode.mw"&gt;Download HTML_characters_in_math_mode.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243621</guid>
      <pubDate>Sun, 31 May 2026 10:48:32 Z</pubDate>
      <itunes:author>C_R</itunes:author>
      <author>C_R</author>
    </item>
    <item>
      <title>Explore, and plot involving fsolve</title>
      <link>http://www.mapleprimes.com/questions/243617-Explore-And-Plot-Involving-Fsolve?ref=Feed:MaplePrimes:Version Maple 2025</link>
      <itunes:summary>&lt;p&gt;I am trying to plot a function where one of the variables is determind via a procedure that uses fsolve and depends on some parameters. When I go to try and make a plot using Explore to vary the parameters I get the following error:&lt;br&gt;
&amp;quot;in fsolve&amp;nbsp; S&amp;nbsp; is in the equation, and is not solved for&amp;quot;&lt;br&gt;
My worksheet is seen below:&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="959DC542D05631439945F7612EEAFB03"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;restart;&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;T := 2^(2/3)*(16*CC(S,mu,Z,Pr)^2*Pi^2 + 2*Pi^2*Z^2 + 16*Pi*S*CC(S,mu,Z,Pr) + 3*S^2)*Pr^(1/3)/(4*(4*CC(S,mu,Z,Pr)*Pi + S)^(2/3)*(2*Pi^2*Z^2 + 4*Pi*S*CC(S,mu,Z,Pr) + S^2)^(2/3)*CC(S,mu,Z,Pr)^(1/3)*Pi^(2/3))&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="(1/4)*2^(2/3)*(16*CC(S, mu, Z, Pr)^2*Pi^2+2*Pi^2*Z^2+16*Pi*S*CC(S, mu, Z, Pr)+3*S^2)*Pr^(1/3)/((4*CC(S, mu, Z, Pr)*Pi+S)^(2/3)*(2*Pi^2*Z^2+4*Pi*S*CC(S, mu, Z, Pr)+S^2)^(2/3)*CC(S, mu, Z, Pr)^(1/3)*Pi^(2/3))" height="60" src="/view.aspx?sf=243617_question/e9c4b0da315025f7af1087397c252ba0.gif" style="vertical-align:-27px" width="655"&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;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;mu = 2^(2/3)*S*(16*C^2*Pi^2 - 2*Pi^2*Z^2 - S^2)*Pr^(1/3)/(4*(4*C*Pi + S)^(2/3)*(2*Pi^2*Z^2 + 4*C*Pi*S + S^2)^(2/3)*C^(4/3)*Pi^(2/3))&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="mu = (1/4)*2^(2/3)*S*(16*C^2*Pi^2-2*Pi^2*Z^2-S^2)*Pr^(1/3)/((4*C*Pi+S)^(2/3)*(2*Pi^2*Z^2+4*C*Pi*S+S^2)^(2/3)*C^(4/3)*Pi^(2/3))" height="60" src="/view.aspx?sf=243617_question/06c9961f19423e4c3e0a839da3eca9ca.gif" style="vertical-align:-27px" width="390"&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;
				&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;CC:=proc(S,mu,Z,Pr)&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;fsolve(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(2)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;,C,C=0.01..100)&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;end proc;&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 align="middle" alt="proc (S, mu, Z, Pr) fsolve(mu = (1/4)*2^(2/3)*S*(16*C^2*Pi^2-2*Pi^2*Z^2-S^2)*Pr^(1/3)/((4*C*Pi+S)^(2/3)*(2*Pi^2*Z^2+4*C*Pi*S+S^2)^(2/3)*C^(4/3)*Pi^(2/3)), C, C = 0.1e-1 .. 100) end proc" height="83" src="/view.aspx?sf=243617_question/9fe499dbabf0f1927f276bab20000ecb.gif" style="vertical-align:-64px" width="738"&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;CC(1,0,0.5,0.2)&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=".1938622552" height="23" src="/view.aspx?sf=243617_question/c388b5e503bd09640b053b379f2f32e1.gif" style="vertical-align:-6px" width="92"&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;Explore(plot(T,0..15),parameters=[[mu=0 .. 1,minorticks=0.25],[Z=0..0.5,minorticks=0.1],[Pr=0..1,minorticks=0.25]])&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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;
When I try to move the sliders on my parameters this is where I get the error. I want to plot over S, but I can only get CC once I have all the other values including S. I assume it has something to do with the fact that my plotting variable is in the procedure?&lt;/p&gt;

&lt;p&gt;Any help would be greatly appreciated, thanks.&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243617_question/Explore_Plot_Problem.mw"&gt;Download Explore_Plot_Problem.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;I am trying to plot a function where one of the variables is determind via a procedure that uses fsolve and depends on some parameters. When I go to try and make a plot using Explore to vary the parameters I get the following error:&lt;br&gt;
&amp;quot;in fsolve&amp;nbsp; S&amp;nbsp; is in the equation, and is not solved for&amp;quot;&lt;br&gt;
My worksheet is seen below:&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="959DC542D05631439945F7612EEAFB03"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;restart;&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;T := 2^(2/3)*(16*CC(S,mu,Z,Pr)^2*Pi^2 + 2*Pi^2*Z^2 + 16*Pi*S*CC(S,mu,Z,Pr) + 3*S^2)*Pr^(1/3)/(4*(4*CC(S,mu,Z,Pr)*Pi + S)^(2/3)*(2*Pi^2*Z^2 + 4*Pi*S*CC(S,mu,Z,Pr) + S^2)^(2/3)*CC(S,mu,Z,Pr)^(1/3)*Pi^(2/3))&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="(1/4)*2^(2/3)*(16*CC(S, mu, Z, Pr)^2*Pi^2+2*Pi^2*Z^2+16*Pi*S*CC(S, mu, Z, Pr)+3*S^2)*Pr^(1/3)/((4*CC(S, mu, Z, Pr)*Pi+S)^(2/3)*(2*Pi^2*Z^2+4*Pi*S*CC(S, mu, Z, Pr)+S^2)^(2/3)*CC(S, mu, Z, Pr)^(1/3)*Pi^(2/3))" height="60" src="/view.aspx?sf=243617_question/e9c4b0da315025f7af1087397c252ba0.gif" style="vertical-align:-27px" width="655"&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;
				&lt;/tbody&gt;
			&lt;/table&gt;

			&lt;p align="left" style="margin:0 0 0 0; padding-top:0px; padding-bottom:0px"&gt;&lt;span style="color:#000000;font-size: 100%;font-family: Times New Roman,serif;font-weight:normal;font-style:normal;"&gt;&amp;nbsp; &lt;/span&gt;&lt;/p&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;mu = 2^(2/3)*S*(16*C^2*Pi^2 - 2*Pi^2*Z^2 - S^2)*Pr^(1/3)/(4*(4*C*Pi + S)^(2/3)*(2*Pi^2*Z^2 + 4*C*Pi*S + S^2)^(2/3)*C^(4/3)*Pi^(2/3))&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="mu = (1/4)*2^(2/3)*S*(16*C^2*Pi^2-2*Pi^2*Z^2-S^2)*Pr^(1/3)/((4*C*Pi+S)^(2/3)*(2*Pi^2*Z^2+4*C*Pi*S+S^2)^(2/3)*C^(4/3)*Pi^(2/3))" height="60" src="/view.aspx?sf=243617_question/06c9961f19423e4c3e0a839da3eca9ca.gif" style="vertical-align:-27px" width="390"&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;
				&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;CC:=proc(S,mu,Z,Pr)&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;fsolve(&lt;/span&gt;&lt;span style="color:#000000; font-weight:bold; font-style:normal;"&gt;(2)&lt;/span&gt;&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;,C,C=0.01..100)&lt;/span&gt;&lt;br&gt;
						&lt;span style="color:#78000e;font-size: 100%;font-family: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;end proc;&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 align="middle" alt="proc (S, mu, Z, Pr) fsolve(mu = (1/4)*2^(2/3)*S*(16*C^2*Pi^2-2*Pi^2*Z^2-S^2)*Pr^(1/3)/((4*C*Pi+S)^(2/3)*(2*Pi^2*Z^2+4*C*Pi*S+S^2)^(2/3)*C^(4/3)*Pi^(2/3)), C, C = 0.1e-1 .. 100) end proc" height="83" src="/view.aspx?sf=243617_question/9fe499dbabf0f1927f276bab20000ecb.gif" style="vertical-align:-64px" width="738"&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;CC(1,0,0.5,0.2)&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=".1938622552" height="23" src="/view.aspx?sf=243617_question/c388b5e503bd09640b053b379f2f32e1.gif" style="vertical-align:-6px" width="92"&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: Courier New,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: Courier New,monospace;font-weight:bold;font-style:normal;"&gt;Explore(plot(T,0..15),parameters=[[mu=0 .. 1,minorticks=0.25],[Z=0..0.5,minorticks=0.1],[Pr=0..1,minorticks=0.25]])&lt;/span&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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;
When I try to move the sliders on my parameters this is where I get the error. I want to plot over S, but I can only get CC once I have all the other values including S. I assume it has something to do with the fact that my plotting variable is in the procedure?&lt;/p&gt;

&lt;p&gt;Any help would be greatly appreciated, thanks.&amp;nbsp;&lt;/p&gt;

&lt;p&gt;&lt;a href="/view.aspx?sf=243617_question/Explore_Plot_Problem.mw"&gt;Download Explore_Plot_Problem.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>243617</guid>
      <pubDate>Thu, 28 May 2026 20:20:34 Z</pubDate>
      <itunes:author>Hullzie16</itunes:author>
      <author>Hullzie16</author>
    </item>
    <item>
      <title>convolution boundaries</title>
      <link>http://www.mapleprimes.com/questions/242383-Convolution-Boundaries?ref=Feed:MaplePrimes:Version Maple 2025</link>
      <itunes:summary>&lt;p&gt;Greetings, Friends.&lt;/p&gt;

&lt;p&gt;I have a function f(t) which is a density function. It has a [0,2] interval and integrates to unity. I convolve f(t) with itself to get g(t). It has a [0,4] interval and integrates to unity. All is well with that and I understand.&lt;/p&gt;

&lt;p&gt;BUT, the boundary of g(t) shouild be on the interval [0,4/sqrt(3)]. This is based upon both my simulation and other analyses.&lt;/p&gt;

&lt;p&gt;At present, the area of the g(t) function on the [4/sqrt(3), 4] interval accounts for 1.408701% of the area under the curve. Not a &amp;quot;trivial&amp;quot; nor &amp;quot;throwaway&amp;quot; amount.&lt;/p&gt;

&lt;p&gt;Does anyone know of a way to &amp;quot;re-scale&amp;quot; or modify my convolved result g(t) so that all of the resultant area under the curve is on the [0,4/sqrt(3)] interval?&lt;/p&gt;

&lt;p&gt;My work is attached.&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="86CE4C9244B033FAABBACA01D7184F7E"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&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: Courier New,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;img alt="restart" height="23" src="/view.aspx?sf=242383_question/7b3dba23b56650d3a84d415a321ef0a0.gif" style="vertical-align:-6px" width="54"&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: Courier New,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;img alt="with(Statistics)" height="23" src="/view.aspx?sf=242383_question/65bb6756f97b705e3f79568521623128.gif" style="vertical-align:-6px" width="111"&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: Courier New,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;img alt="f := proc (t) options operator, arrow; piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, 6/5-(3/2)*t^2+(3/4)*t^3-(3/80)*t^5, 2 &amp;lt;= t, 0) end proc" height="42" src="/view.aspx?sf=242383_question/dd8aa506a6faa9ca7fc3e06e6a83bd0b.gif" style="vertical-align:-16px" width="503"&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="proc (t) options operator, arrow; piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, 6/5-(3/2)*t^2+(3/4)*t^3-(3/80)*t^5, 2 &amp;lt;= t, 0) end proc" height="98" src="/view.aspx?sf=242383_question/2d22f4dce540b13728fd92cc0911292a.gif" style="vertical-align:-43px" width="314"&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;
				&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: Courier New,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;img align="middle" alt="plot(f(t), t = 0 .. 2)" height="58" src="/view.aspx?sf=242383_question/5db3c20e91d4a90052551ed9ea332fc2.gif" style="vertical-align:-41px" width="768"&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 align="middle" height="500" src="/view.aspx?sf=242383_question/e80694b8351e82da1df90c6669f95d45.gif" style="border:none" width="500"&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 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: Courier New,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;img alt="int(f(t), t = 0 .. 2)" height="23" src="/view.aspx?sf=242383_question/cf71a31a3dec47e15db290084d507a86.gif" style="vertical-align:-6px" width="120"&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="1" height="23" src="/view.aspx?sf=242383_question/84bba2591bbcc56732b126dbfa20ba69.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;(2)&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: Courier New,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;img alt="simplify(int(f(tau)*f(t-tau), tau = -infinity .. infinity))" height="23" src="/view.aspx?sf=242383_question/9e292fbcea82bdacc0d24db432664120.gif" style="vertical-align:-6px" width="356"&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="(1/1971200)*piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, t^11-220*t^9+1320*t^8+7920*t^7-103488*t^6+147840*t^5+887040*t^4-2365440*t^3+2838528*t, t &amp;lt;= 4, -(t^4+28*t^3+228*t^2+536*t+80)*(t-4)^7, 4 &amp;lt; t, 0)" height="130" src="/view.aspx?sf=242383_question/5736e357a8d5921d9418eea76199f403.gif" style="vertical-align:-16px" width="697"&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: Courier New,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;img alt="g := unapply(simplify(int(f(tau)*f(t-tau), tau = -infinity .. infinity)), t)" height="23" src="/view.aspx?sf=242383_question/f81947147f8da4c609da2410a44e9074.gif" style="vertical-align:-6px" width="462"&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 align="middle" alt="proc (t) options operator, arrow; (1/1971200)*piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, t^11-220*t^9+1320*t^8+7920*t^7-103488*t^6+147840*t^5+887040*t^4-2365440*t^3+2838528*t, t &amp;lt;= 4, -(t^4+28*t^3+228*t^2+536*t+80)*(t-4)^7, 4 &amp;lt; t, 0) end proc" height="147" src="/view.aspx?sf=242383_question/db2f01a4fef739120b260321ff644457.gif" style="vertical-align:-130px" width="738"&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: Courier New,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;img alt="plot(g(t), t = 0 .. 4)" height="23" src="/view.aspx?sf=242383_question/ef5bb1fe43fed2ea5c4b7f3a7989a002.gif" style="vertical-align:-6px" width="127"&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 align="middle" height="500" src="/view.aspx?sf=242383_question/8826fd5b59d3b2e2a38711628a21dbd2.gif" style="border:none" width="500"&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 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: Courier New,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;img alt="int(g(t), t = 0 .. 4)" height="23" src="/view.aspx?sf=242383_question/2d90738efe93efa4746847b81c7d44cf.gif" style="vertical-align:-6px" width="119"&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="1" height="23" src="/view.aspx?sf=242383_question/470b9f7c49b853add06dd2c8fdcb0938.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;(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: Courier New,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;img alt="evalf(int(g(t), t = 0 .. 4/sqrt(3)))" height="42" src="/view.aspx?sf=242383_question/6bd24f4b306c0a8ef8ccf78c3b4a5105.gif" style="vertical-align:-16px" width="220"&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=".98591299" height="23" src="/view.aspx?sf=242383_question/b7fbd453d799fed7d4175d86d2100b42.gif" style="vertical-align:-6px" width="77"&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: Courier New,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;img align="middle" alt="evalf(int(g(t), t = 4/sqrt(3) .. 4))" height="60" src="/view.aspx?sf=242383_question/d2128fcbec011ac20630ecce169116f9.gif" style="vertical-align:-34px" width="768"&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="0.1408701e-1" height="23" src="/view.aspx?sf=242383_question/f0c5f4296df99055ff17410761c54614.gif" style="vertical-align:-6px" width="77"&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: Courier New,monospace;font-weight:bold;font-style:normal;"&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;img alt="NULL" height="23" src="/view.aspx?sf=242383_question/8429a65b4e88d4a09d180eea72630989.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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=242383_question/SphereConvolution.mw"&gt;Download SphereConvolution.mw&lt;/a&gt;&lt;/p&gt;
</itunes:summary>
      <description>&lt;p&gt;Greetings, Friends.&lt;/p&gt;

&lt;p&gt;I have a function f(t) which is a density function. It has a [0,2] interval and integrates to unity. I convolve f(t) with itself to get g(t). It has a [0,4] interval and integrates to unity. All is well with that and I understand.&lt;/p&gt;

&lt;p&gt;BUT, the boundary of g(t) shouild be on the interval [0,4/sqrt(3)]. This is based upon both my simulation and other analyses.&lt;/p&gt;

&lt;p&gt;At present, the area of the g(t) function on the [4/sqrt(3), 4] interval accounts for 1.408701% of the area under the curve. Not a &amp;quot;trivial&amp;quot; nor &amp;quot;throwaway&amp;quot; amount.&lt;/p&gt;

&lt;p&gt;Does anyone know of a way to &amp;quot;re-scale&amp;quot; or modify my convolved result g(t) so that all of the resultant area under the curve is on the [0,4/sqrt(3)] interval?&lt;/p&gt;

&lt;p&gt;My work is attached.&lt;/p&gt;

&lt;form name="worksheet_form"&gt;&lt;input name="md.ref" type="hidden" value="86CE4C9244B033FAABBACA01D7184F7E"&gt;
&lt;table align="center" width="768"&gt;
	&lt;tbody&gt;
		&lt;tr&gt;
			&lt;td&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: Courier New,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;img alt="restart" height="23" src="/view.aspx?sf=242383_question/7b3dba23b56650d3a84d415a321ef0a0.gif" style="vertical-align:-6px" width="54"&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: Courier New,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;img alt="with(Statistics)" height="23" src="/view.aspx?sf=242383_question/65bb6756f97b705e3f79568521623128.gif" style="vertical-align:-6px" width="111"&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: Courier New,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;img alt="f := proc (t) options operator, arrow; piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, 6/5-(3/2)*t^2+(3/4)*t^3-(3/80)*t^5, 2 &amp;lt;= t, 0) end proc" height="42" src="/view.aspx?sf=242383_question/dd8aa506a6faa9ca7fc3e06e6a83bd0b.gif" style="vertical-align:-16px" width="503"&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="proc (t) options operator, arrow; piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, 6/5-(3/2)*t^2+(3/4)*t^3-(3/80)*t^5, 2 &amp;lt;= t, 0) end proc" height="98" src="/view.aspx?sf=242383_question/2d22f4dce540b13728fd92cc0911292a.gif" style="vertical-align:-43px" width="314"&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;
				&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: Courier New,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;img align="middle" alt="plot(f(t), t = 0 .. 2)" height="58" src="/view.aspx?sf=242383_question/5db3c20e91d4a90052551ed9ea332fc2.gif" style="vertical-align:-41px" width="768"&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 align="middle" height="500" src="/view.aspx?sf=242383_question/e80694b8351e82da1df90c6669f95d45.gif" style="border:none" width="500"&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 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: Courier New,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;img alt="int(f(t), t = 0 .. 2)" height="23" src="/view.aspx?sf=242383_question/cf71a31a3dec47e15db290084d507a86.gif" style="vertical-align:-6px" width="120"&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="1" height="23" src="/view.aspx?sf=242383_question/84bba2591bbcc56732b126dbfa20ba69.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;(2)&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: Courier New,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;img alt="simplify(int(f(tau)*f(t-tau), tau = -infinity .. infinity))" height="23" src="/view.aspx?sf=242383_question/9e292fbcea82bdacc0d24db432664120.gif" style="vertical-align:-6px" width="356"&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="(1/1971200)*piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, t^11-220*t^9+1320*t^8+7920*t^7-103488*t^6+147840*t^5+887040*t^4-2365440*t^3+2838528*t, t &amp;lt;= 4, -(t^4+28*t^3+228*t^2+536*t+80)*(t-4)^7, 4 &amp;lt; t, 0)" height="130" src="/view.aspx?sf=242383_question/5736e357a8d5921d9418eea76199f403.gif" style="vertical-align:-16px" width="697"&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: Courier New,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;img alt="g := unapply(simplify(int(f(tau)*f(t-tau), tau = -infinity .. infinity)), t)" height="23" src="/view.aspx?sf=242383_question/f81947147f8da4c609da2410a44e9074.gif" style="vertical-align:-6px" width="462"&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 align="middle" alt="proc (t) options operator, arrow; (1/1971200)*piecewise(t &amp;lt;= 0, 0, t &amp;lt;= 2, t^11-220*t^9+1320*t^8+7920*t^7-103488*t^6+147840*t^5+887040*t^4-2365440*t^3+2838528*t, t &amp;lt;= 4, -(t^4+28*t^3+228*t^2+536*t+80)*(t-4)^7, 4 &amp;lt; t, 0) end proc" height="147" src="/view.aspx?sf=242383_question/db2f01a4fef739120b260321ff644457.gif" style="vertical-align:-130px" width="738"&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: Courier New,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;img alt="plot(g(t), t = 0 .. 4)" height="23" src="/view.aspx?sf=242383_question/ef5bb1fe43fed2ea5c4b7f3a7989a002.gif" style="vertical-align:-6px" width="127"&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 align="middle" height="500" src="/view.aspx?sf=242383_question/8826fd5b59d3b2e2a38711628a21dbd2.gif" style="border:none" width="500"&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 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: Courier New,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;img alt="int(g(t), t = 0 .. 4)" height="23" src="/view.aspx?sf=242383_question/2d90738efe93efa4746847b81c7d44cf.gif" style="vertical-align:-6px" width="119"&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="1" height="23" src="/view.aspx?sf=242383_question/470b9f7c49b853add06dd2c8fdcb0938.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;(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: Courier New,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;img alt="evalf(int(g(t), t = 0 .. 4/sqrt(3)))" height="42" src="/view.aspx?sf=242383_question/6bd24f4b306c0a8ef8ccf78c3b4a5105.gif" style="vertical-align:-16px" width="220"&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=".98591299" height="23" src="/view.aspx?sf=242383_question/b7fbd453d799fed7d4175d86d2100b42.gif" style="vertical-align:-6px" width="77"&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: Courier New,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;img align="middle" alt="evalf(int(g(t), t = 4/sqrt(3) .. 4))" height="60" src="/view.aspx?sf=242383_question/d2128fcbec011ac20630ecce169116f9.gif" style="vertical-align:-34px" width="768"&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="0.1408701e-1" height="23" src="/view.aspx?sf=242383_question/f0c5f4296df99055ff17410761c54614.gif" style="vertical-align:-6px" width="77"&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: Courier New,monospace;font-weight:bold;font-style:normal;"&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;img alt="NULL" height="23" src="/view.aspx?sf=242383_question/8429a65b4e88d4a09d180eea72630989.gif" style="vertical-align:-6px" width="9"&gt;&lt;/p&gt;
						&lt;/td&gt;
					&lt;/tr&gt;
				&lt;/tbody&gt;
			&lt;/table&gt;
			&lt;/td&gt;
		&lt;/tr&gt;
	&lt;/tbody&gt;
&lt;/table&gt;
&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=242383_question/SphereConvolution.mw"&gt;Download SphereConvolution.mw&lt;/a&gt;&lt;/p&gt;
</description>
      <guid>242383</guid>
      <pubDate>Mon, 06 Apr 2026 17:45:57 Z</pubDate>
      <itunes:author>JoyDivisionMan</itunes:author>
      <author>JoyDivisionMan</author>
    </item>
  </channel>
</rss>