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MapleWorksheet-HyperTypeSeq-examples.mw
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MapleWorksheet-HyperTypeSeq-examples.mw
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<?xml version="1.0" encoding="UTF-8"?>
<Worksheet>
<Version major="2023" minor="2"/>
<Label-Scheme value="2" prefix=""/>
<View-Properties presentation="false" autoexpanding_sections="true" UserProfileName="Maple Default Profile" NumericFormat-ApplyInteger="true" NumericFormat-ApplyRational="true" NumericFormat-ApplyExponent="false" editable="true">
</View-Properties>
<MapleNet-Properties prettyprint="3" warnlevel="3" compactdisplay="false" preplot="" helpbrowser="standard" displayprecision="-1" echo="1" scientificx="true" unitattributes=""fontweight" = "bold"" imaginaryunit="I" longdelim="true" elisiontermsthreshold="10000" elisiondigitsafter="100" elisiondigitsbefore="100" plotdevice="inline" errorbreak="1" plotoptions="" plotdriver="opengl" quiet="false" elisiontermsbefore="100" elisiontermsafter="100" historytimestamp="false" screenwidth="79" indentamount="4" plotoutput="terminal" screenpixelheight="1080" rtablesize="[10, 10]" useclientjvm="true" format="worksheet" labelwidth="20" postplot="" typesetting="extended" ansi="false" ansicolor="[]" elisiondigitsthreshold="10000" showassumed="1" ansilprint="false" trailingsemicolon="true" errorcursor="false" labelling="true" screenheight="25" prompt="> " verboseproc="1" latexwidth="8.0" ShowLabels="true"/>
<Styles>
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<Font name="Warning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" strikethrough="false" placeholder="false"/>
<Font name="2D Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" strikethrough="false" placeholder="false"/>
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<Font name="Line Printed Output" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="false" strikethrough="false" placeholder="false"/>
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<Font name="Maple Output" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" strikethrough="false" placeholder="false"/>
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<Font name="Annotation Title" background="[255,255,255]" bold="true" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="18" subscript="false" superscript="false" underline="false" strikethrough="false" placeholder="false"/>
<Font name="Header and Footer" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="10" subscript="false" superscript="false" underline="false" strikethrough="false" placeholder="false"/>
<Font name="HyperlinkError" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[255,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" strikethrough="false" placeholder="false"/>
<Font name="Atomic Variable" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[175,0,175]" italic="true" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" strikethrough="false" placeholder="false"/>
<Font name="HyperlinkWarning" background="[255,255,255]" bold="false" executable="false" family="Courier New" foreground="[0,0,255]" italic="false" opaque="false" readonly="true" size="12" subscript="false" superscript="false" underline="true" strikethrough="false" placeholder="false"/>
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<Layout name="Heading 2" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="2" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Maple Output" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.3" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
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<Layout name="Dash Item" alignment="left" bullet="dash" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="3" spacebelow="3" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Error" alignment="left" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="0" spacebelow="0" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
<Layout name="Title" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="12" spacebelow="12" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
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<Layout name="Author" alignment="centred" bullet="none" firstindent="0" leftmargin="0" rightmargin="0" linespacing="0.0" spaceabove="8" spacebelow="8" linebreak="space" pagebreak-before="false" initial="0" bulletsuffix=""/>
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</Styles>
<Startup-Code startupcode=""/>
<Task-table>
<Task-category name="<default>"/>
</Task-table>
<Task/>
<Group labelreference="L179" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">restart</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L178" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">with(HyperTypeSeq)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4964" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L4963" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal"><Font size="18" bold="true">mfoldInd</Font></Text-field><Text-field style="Text" layout="Normal"><Font bold="true">New (March 2024): command to evaluate an $m$-fold indicator term or write it symbolically</Font></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4968" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">mfoldInd(n,7,1)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4967" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">mfoldInd(15,7,1)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4970" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">mfoldInd(23,7,1)</Text-field>
</Input>
</Group>
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<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L222" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" size="18" layout="Normal"><Font size="18" bold="true">HolonomiRE</Font></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L213" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L185" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(n!+1/n!,a(n))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L237" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(sin(n*Pi/4)^2,a(n))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L234" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(sin(cos(n*Pi)*Pi/6)*sin(n*Pi/4),a(n))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L254" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(sin(cos(n*Pi)*Pi/6)*sin(n*Pi/4),a(n),reshift=2)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L296" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal"><Font bold="true">New (March 2024): HolonomicRE can now compute recurrence equations from normal forms. </Font></Text-field><Text-field style="Text" layout="Normal"><Font bold="true">Moreover, one can use mfoldInd to write m-fold indicator terms (interlacements)</Font></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L295" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s:=n!*chi[{modp*(n,3)=1}]</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L256" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(s,a(n))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L298" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s:=n^2*chi[{modp*(n,2)=1}]+1/n!*chi[{modp*(n,4)=3}]</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L297" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(s,a(n))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4956" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal">Or equivalently using mfoldInd,</Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4955" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s:=n!*mfoldInd(n,3,1)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4958" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(s,a(n))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4957" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HolonomicRE(n^2*mfoldInd(n,2,1)+1/n!*mfoldInd(n,4,3),a(n))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4960" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L190" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" size="18" layout="Normal"><Font size="18" bold="true">REtoHTS</Font></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L276" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L275" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" bold="true" size="16" layout="Normal"><Font size="16" bold="true">The sequence </Font><Hyperlink linktarget="https://oeis.org/A212579" hyperlink="true"><Font size="16" style="Hyperlink" bold="true">A212579</Font></Hyperlink><Hyperlink linktarget="http://A212579" hyperlink="true"></Hyperlink></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L277" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L228" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">RE:= a(n) = a(n-1)+2*a(n-2)-a(n-3)-2*a(n-4)-a(n-5)+2*a(n-6)+a(n-7)-a(n-8)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L246" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">REtoHTS(RE,a(n),[0, 1, 8, 31, 80, 171, 308, 509, 780, 1137, 1584, 2143, 2812])</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L240" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">U:=proc(n) U(n):=subs([n=n-1,a=U],RE) end proc:
U(0):=0: U(1):=1:U(2):=8:U(3):=31:U(4):=80:U(5):=171:U(6):=308:U(7):=509:U(8):=780:U(9):=1137:U(10):=1584:U(11):=2143:U(12):=2812:</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L231" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">REtoHTS(RE,a(n),U)</Text-field>
</Input>
</Group>
<Group labelreference="L273" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L272" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" bold="true" size="16" layout="Normal"><Font size="16" bold="true">The sequence </Font><Hyperlink linktarget="https://oeis.org/A033481" hyperlink="true"><Font size="16" style="Hyperlink" bold="true">A033481</Font></Hyperlink></Text-field><Text-field style="Text" bold="true" size="16" layout="Normal"><Font size="16" bold="true">Requirement: </Font><Hyperlink linktarget="https://bertrandteguia.com/FPS" hyperlink="true"><Font size="16" style="Hyperlink" bold="true">FPS</Font></Hyperlink><Font size="16" bold="true"> </Font></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L271" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L266" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">f:=(21 + 64*z + 32*z^2 - 5*z^3 - 56*z^4 - 28*z^5 - 14*z^6 - 7*z^7) / ((1 - z)*(1 + z + z^2))</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L264" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">FPS(f,z,n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L265" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">RE:=FPS:-FindRE(f-(7*z^4 + 14*z^3 + 28*z^2 + 63*z + 19),z,u(n))</Text-field>
</Input>
</Group>
<Group labelreference="L270" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">U:=proc(n) U(n):=subs([n=n-1,u=U],solve(RE,u(n+1))) end proc:
U(0):=2:U(1):=1:U(2):=4:U(3):=2:U(4):=1:U(5):=4:</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L267" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">REtoHTS(RE,u(n),U)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L262" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">REtoHTS(RE,u(n),[2,1,4,2,1,4])</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L281" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">REtoHTS(a(n+2)=a(n+1)+a(n),a(n),[0,1,1])</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L293" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">U:= proc(n) U(n):=2*(2*n-1)*U(n-1)/(n+1) end proc: U(0):=1: U(1):=1:</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L294" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">REtoHTS((n+2)*C(n+1)=2*(2*n+1)*C(n),C(n),U)</Text-field>
</Input>
</Group>
<Group labelreference="L280" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L193" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" size="18" layout="Normal"><Font size="18" bold="true">HTS</Font></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L194" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L291" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(sin(n*Pi/4)^2,n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L289" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(sin(Pi*cos(n*Pi)/6)*cos(n*Pi/4),n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L286" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(sin(cos(n*Pi/3)*Pi),n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L288" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(tan(n*Pi/4),n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L290" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(tan(n*Pi/3),n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L287" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(cos(n*arccos(x)),n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L284" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(sin(n*Pi/6)*cos(n*Pi/3)-sin(n*Pi/2),n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L283" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(sin(n*Pi/4)^2*cos(n*Pi/6)^2,n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L285" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS(sin(n*Pi/4)^2*cos(n*Pi/6)^4,n,maxreorder=12)</Text-field>
</Input>
</Group>
<Group labelreference="L168" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L259" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group labelreference="L260" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal"><Font size="18" bold="true">HTSproduct</Font></Text-field><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal"><Font bold="true">New (March 2024): computing product of hypergeometric type terms</Font></Text-field><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4948" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s1:=HTS(sin(n*Pi/4)^2,n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4946" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s2:=HTS(cos(n*Pi/3)^2,n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4947" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">s:=HTSproduct(s1,s2,n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4951" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4949" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field style="Text" layout="Normal"></Text-field><Text-field style="Text" layout="Normal"><Font size="14" italic="true">And we can now have fun with finding equivalent representations by combining <Font bold="true">HTS </Font>and <Font bold="true">HTSproduct</Font></Font></Text-field><Text-field style="Text" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4950" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal">HTS((sin(n*Pi/4)*cos(n*Pi/3))^2,n)</Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4954" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
<Input><Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field>
</Input>
</Group>
<Group hide-input="false" labelreference="L4952" drawlabel="true" applyint="true" applyrational="true" applyexponent="false">
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