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<title>Maple package on MacMahon's partition analysis</title>
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</head>

<body lang=3DZH-CN link=3D"#993333" vlink=3Dpurple style=3D'tab-interval:21=
.0pt;
text-justify-trim:punctuation'>

<div class=3DSection1 style=3D'layout-grid:15.6pt'>

<h3 align=3Dcenter style=3D'margin:0pt;margin-bottom:.0001pt;text-align:cen=
ter;
line-height:150%'><span lang=3DEN-US>Progress on <span class=3DSpellE>MacMa=
hon&#8217;s</span>
Partition Analysis</span></h3>

<h3 align=3Dcenter style=3D'margin:0pt;margin-bottom:.0001pt;text-align:cen=
ter;
line-height:150%'><span lang=3DEN-US><o:p>&nbsp;</o:p></span></h3>

<h3 align=3Dcenter style=3D'margin:0pt;margin-bottom:.0001pt;text-align:cen=
ter;
line-height:150%'><span lang=3DEN-US><o:p>&nbsp;</o:p></span></h3>

<h3 align=3Dcenter style=3D'margin:0pt;margin-bottom:.0001pt;text-align:cen=
ter;
line-height:150%'><span lang=3DEN-US><o:p>&nbsp;</o:p></span></h3>

<h3 align=3Dcenter style=3D'margin:0pt;margin-bottom:.0001pt;text-align:cen=
ter;
line-height:150%'><span lang=3DEN-US style=3D'font-weight:normal;mso-bidi-f=
ont-weight:
bold'>My first Maple package <a
href=3D"http://www.combinatorics.net.cn/homepage/xin/maple/Ell.rar">ELL.mpl=
</a>
is associated to my paper<o:p></o:p></span></h3>

<p style=3D'margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:18=
.0pt;
margin-bottom:.0001pt;line-height:150%'><span lang=3DEN-US><a
href=3D"http://www.combinatorics.net.cn/homepage/xin/files/papers/iterate.p=
df"><span
class=3DGramE><b>A fast algorithm for MacMahon's partition analysis</b></sp=
an></a><span
class=3DGramE>, <i><a
href=3D"http://www.combinatorics.org/Volume_11/Abstracts/v11i1r58.html">Ele=
ctron.</a></i></span></span></p>

<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;mso-pagination:w=
idow-orphan'><span
class=3DMsoHyperlink><i><span lang=3DEN-US style=3D'font-size:12.0pt;mso-fo=
nt-kerning:
0pt'><a href=3D"http://www.combinatorics.org/Volume_11/Abstracts/v11i1r58.h=
tml"><span
style=3D'mso-spacerun:yes'>&nbsp;</span>J. <span class=3DSpellE>Combin</spa=
n>.<span
style=3D'color:windowtext;font-style:normal;text-decoration:none;text-under=
line:
none'><span style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combina=
torics\.org\/Volume_11\/Abstracts\/v11i1r58\.html\0022 "'>,
11 (2004), R58. (<span class=3DGramE>electronic</span>). <span class=3DGram=
E>arXiv</span>:
<span style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/front\.math\.ucdav=
is\.edu\/math\.CO\/0408377\0022 "'><u><span
style=3D'color:#993333'>math.CO/0408377</span></u></span>. (20 pages) </spa=
n><o:p></o:p></span></a></span></i></span></p>

<p style=3D'margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:1=
8.0pt;
margin-bottom:.0001pt;line-height:150%'><span lang=3DEN-US><a
href=3D"http://www.combinatorics.org/Volume_11/Abstracts/v11i1r58.html"><sp=
an
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/front\.math\.ucdavis\.ed=
u\/math\.CO\/0408377\0022 "'>Package
name: ELL.mpl</span></span></a></span></p>

<p style=3D'margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:1=
8.0pt;
margin-bottom:.0001pt;line-height:150%'><span lang=3DEN-US><a
href=3D"http://front.math.ucdavis.edu/math.CO/0408377"><span style=3D'color=
:windowtext;
text-decoration:none;text-underline:none'><span style=3D'mso-field-code:" H=
YPERLINK \0022http\:\/\/front\.math\.ucdavis\.edu\/math\.CO\/0408377\0022 "=
'>Version:
written in Maple 9.0 (should work for earlier version, but definitely not f=
or
Maple 10)</span></span></a></span></p>

<p style=3D'margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:1=
8.0pt;
margin-bottom:.0001pt;line-height:150%'><span lang=3DEN-US><a
href=3D"http://front.math.ucdavis.edu/math.CO/0408377"><span style=3D'color=
:windowtext;
text-decoration:none;text-underline:none'><span style=3D'mso-field-code:" H=
YPERLINK \0022http\:\/\/front\.math\.ucdavis\.edu\/math\.CO\/0408377\0022 "=
'>Main
procedure: <span style=3D'mso-spacerun:yes'>&nbsp;</span>E_<span class=3DGr=
amE>Oeq(</span>Q,vx,va)</span></span></a></span></p>

<p style=3D'margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:1=
8.0pt;
margin-bottom:.0001pt;line-height:150%'><span lang=3DEN-US><a
href=3D"http://front.math.ucdavis.edu/math.CO/0408377"><span style=3D'color=
:windowtext;
text-decoration:none;text-underline:none'><span style=3D'mso-field-code:" H=
YPERLINK \0022http\:\/\/front\.math\.ucdavis\.edu\/math\.CO\/0408377\0022 "=
'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>E_<span class=3DGramE>Oge(</span>Q,vx,va)</span></span></a></span></=
p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a href=3D"http://front.math.ucdavis.edu/math.CO/0408377"><span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/front\.math\.ucdavis\.ed=
u\/math\.CO\/0408377\0022 "'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span></span></span></a></span></p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a href=3D"http://front.math.ucdavis.edu/math.CO/0408377"><span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/front\.math\.ucdavis\.ed=
u\/math\.CO\/0408377\0022 "'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>The updated version: <span
style=3D'mso-field-code:"HYPERLINK \0022http\:\/\/www\.combinatorics\.net\.=
cn\/homepage\/xin\/maple\/Ell2\.rar\0022"'><u><span
style=3D'color:#993333'>Ell2.mpl</span></u></span></span></span></a></span>=
</p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a href=3D"http://front.math.ucdavis.edu/math.CO/0408377"><span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
.cn\/homepage\/xin\/maple\/Ell2\.mpl\0022 "'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp; </span>New procedure: E_<span
class=3DGramE>OeqS(</span>Q,vxa,va), E_OeqW(Q,vxa,va) (there should be no b=
ug for
these two procedures)</span></span></a></span></p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a href=3D"http://www.combinatorics.net.cn/homepage/xin/maple/=
Ell2.mpl"><span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
.cn\/homepage\/xin\/maple\/Ell2\.mpl\0022 "'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;
</span>E_<span class=3DGramE>OgeS(</span>Q,vxa,va), E_OgeW(Q,vxa,va) (you a=
re
welcome to report bug for these two procedures)</span></span></a></span></p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a href=3D"http://www.combinatorics.net.cn/homepage/xin/maple/=
Ell2.mpl"><span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
.cn\/homepage\/xin\/maple\/Ell2\.mpl\0022 "'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span>Here=
 is a <span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
.cn\/homepage\/xin\/maple\/ManualEll2\.pdf\0022 "'><u><span
style=3D'color:#993333'>draft manual</span></u></span> for the Ell2 package=
.</span></span></a></span></p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a href=3D"http://www.combinatorics.net.cn/homepage/xin/maple/=
Ell2.mpl"><span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
.cn\/homepage\/xin\/maple\/ManualEll2\.pdf\0022 "'><span
style=3D'mso-spacerun:yes'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; </span></sp=
an></span></a></span></p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a
href=3D"http://www.combinatorics.net.cn/homepage/xin/maple/ManualEll2.pdf">=
<span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
.cn\/homepage\/xin\/maple\/ManualEll2\.pdf\0022 "'>Related
talks I gave:</span></span></a></span></p>

<p style=3D'margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:2=
1.0pt;
margin-bottom:.0001pt;text-indent:-21.0pt;line-height:150%;mso-list:l0 leve=
l1 lfo2;
tab-stops:list 21.0pt'><b style=3D'mso-bidi-font-weight:normal'><span lang=
=3DEN-US><a
href=3D"http://www.combinatorics.net.cn/homepage/xin/maple/ManualEll2.pdf">=
<![if !supportLists]><span
style=3D'mso-fareast-font-family:"Times New Roman";color:windowtext;text-de=
coration:
none;text-underline:none'><span style=3D'mso-list:Ignore'>1.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;
</span></span></span><![endif]><span style=3D'color:windowtext;text-decorat=
ion:
none;text-underline:none'><span style=3D'mso-field-code:" HYPERLINK \0022ht=
tp\:\/\/www\.combinatorics\.net\.cn\/homepage\/xin\/maple\/ManualEll2\.pdf\=
0022 "'><span
style=3D'mso-field-code:"HYPERLINK \0022http\:\/\/www\.combinatorics\.net\.=
cn\/homepage\/xin\/files\/talks\/Iterate\.pdf\0022"'><u><span
style=3D'color:#993333'>Partial fraction algorithm for MacMahon&#8217;s par=
tition
analysis</span></u></span><span style=3D'font-weight:normal'>, Combinatorial
Seminar @ UCSD, August 16, 2007</span></span><o:p></o:p></span></a></span><=
/b></p>

<p style=3D'margin-top:0pt;margin-right:0pt;margin-bottom:0pt;margin-left:2=
1.0pt;
margin-bottom:.0001pt;text-indent:-21.0pt;line-height:150%;mso-list:l0 leve=
l1 lfo2;
tab-stops:list 21.0pt'><b><span lang=3DEN-US><a
href=3D"http://www.combinatorics.net.cn/homepage/xin/maple/ManualEll2.pdf">=
<![if !supportLists]><span
style=3D'mso-fareast-font-family:"Times New Roman";color:windowtext;mso-bid=
i-font-weight:
normal;text-decoration:none;text-underline:none'><span style=3D'mso-list:Ig=
nore'>2.<span
style=3D'font:7.0pt "Times New Roman"'>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;=
&nbsp;
</span></span></span><![endif]><span style=3D'color:windowtext;text-decorat=
ion:
none;text-underline:none'><span style=3D'mso-field-code:" HYPERLINK \0022ht=
tp\:\/\/www\.combinatorics\.net\.cn\/homepage\/xin\/files\/talks\/Iterate\.=
pdf\0022 "'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
.cn\/homepage\/xin\/files\/talks\/macmahonMIT\.pdf\0022 "'><u><span
style=3D'color:#993333'>MacMahon's partition analysis</span></u></span><span
style=3D'font-weight:normal'>, Combinatorics Seminar @ MIT, <i>October 6, 2=
004</i>.
</span></span></span><span style=3D'color:windowtext;mso-bidi-font-weight:n=
ormal;
text-decoration:none;text-underline:none'><o:p></o:p></span></a></span></b>=
</p>

<p style=3D'margin:0pt;margin-bottom:.0001pt;line-height:150%;tab-stops:lis=
t 54.0pt'><span
lang=3DEN-US><a
href=3D"http://www.combinatorics.net.cn/homepage/xin/files/talks/Iterate.pd=
f"><span
style=3D'color:windowtext;text-decoration:none;text-underline:none'><span
style=3D'mso-field-code:" HYPERLINK \0022http\:\/\/www\.combinatorics\.net\=
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