open-axiom repository from github
\begin{patch}{CycleIndicatorsXmpPagePatch1}
\begin{paste}{CycleIndicatorsXmpPageFull1}{CycleIndicatorsXmpPageEmpty1}
\pastebutton{CycleIndicatorsXmpPageFull1}{\hidepaste}
\tab{5}\spadcommand{)expose EVALCYC}
\indentrel{3}\begin{verbatim}
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty1}
\begin{paste}{CycleIndicatorsXmpPageEmpty1}{CycleIndicatorsXmpPagePatch1}
\pastebutton{CycleIndicatorsXmpPageEmpty1}{\showpaste}
\tab{5}\spadcommand{)expose EVALCYC}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch2}
\begin{paste}{CycleIndicatorsXmpPageFull2}{CycleIndicatorsXmpPageEmpty2}
\pastebutton{CycleIndicatorsXmpPageFull2}{\hidepaste}
\tab{5}\spadcommand{complete 1}
\indentrel{3}\begin{verbatim}
(1) (1)
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty2}
\begin{paste}{CycleIndicatorsXmpPageEmpty2}{CycleIndicatorsXmpPagePatch2}
\pastebutton{CycleIndicatorsXmpPageEmpty2}{\showpaste}
\tab{5}\spadcommand{complete 1}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch3}
\begin{paste}{CycleIndicatorsXmpPageFull3}{CycleIndicatorsXmpPageEmpty3}
\pastebutton{CycleIndicatorsXmpPageFull3}{\hidepaste}
\tab{5}\spadcommand{complete 2}
\indentrel{3}\begin{verbatim}
1 1 2
(2) � (2) + � (1 )
2 2
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty3}
\begin{paste}{CycleIndicatorsXmpPageEmpty3}{CycleIndicatorsXmpPagePatch3}
\pastebutton{CycleIndicatorsXmpPageEmpty3}{\showpaste}
\tab{5}\spadcommand{complete 2}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch4}
\begin{paste}{CycleIndicatorsXmpPageFull4}{CycleIndicatorsXmpPageEmpty4}
\pastebutton{CycleIndicatorsXmpPageFull4}{\hidepaste}
\tab{5}\spadcommand{complete 3}
\indentrel{3}\begin{verbatim}
1 1 1 3
(3) � (3) + � (2 1) + � (1 )
3 2 6
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty4}
\begin{paste}{CycleIndicatorsXmpPageEmpty4}{CycleIndicatorsXmpPagePatch4}
\pastebutton{CycleIndicatorsXmpPageEmpty4}{\showpaste}
\tab{5}\spadcommand{complete 3}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch5}
\begin{paste}{CycleIndicatorsXmpPageFull5}{CycleIndicatorsXmpPageEmpty5}
\pastebutton{CycleIndicatorsXmpPageFull5}{\hidepaste}
\tab{5}\spadcommand{complete 7}
\indentrel{3}\begin{verbatim}
(4)
1 1 1 1 2 1
� (7) + � (6 1) + �� (5 2) + �� (5 1 ) + �� (4 3)
7 6 10 10 12
+
1 1 3 1 2 1 2
� (4 2 1) + �� (4 1 ) + �� (3 1) + �� (3 2 )
8 24 18 24
+
1 2 1 4 1 3 1 2 3
�� (3 2 1 ) + �� (3 1 ) + �� (2 1) + �� (2 1 )
12 72 48 48
+
1 5 1 7
��� (2 1 ) + ���� (1 )
240 5040
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty5}
\begin{paste}{CycleIndicatorsXmpPageEmpty5}{CycleIndicatorsXmpPagePatch5}
\pastebutton{CycleIndicatorsXmpPageEmpty5}{\showpaste}
\tab{5}\spadcommand{complete 7}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch6}
\begin{paste}{CycleIndicatorsXmpPageFull6}{CycleIndicatorsXmpPageEmpty6}
\pastebutton{CycleIndicatorsXmpPageFull6}{\hidepaste}
\tab{5}\spadcommand{elementary 7}
\indentrel{3}\begin{verbatim}
(5)
1 1 1 1 2 1
� (7) - � (6 1) - �� (5 2) + �� (5 1 ) - �� (4 3)
7 6 10 10 12
+
1 1 3 1 2 1 2
� (4 2 1) - �� (4 1 ) + �� (3 1) + �� (3 2 )
8 24 18 24
+
1 2 1 4 1 3 1 2 3
- �� (3 2 1 ) + �� (3 1 ) - �� (2 1) + �� (2 1 )
12 72 48 48
+
1 5 1 7
- ��� (2 1 ) + ���� (1 )
240 5040
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty6}
\begin{paste}{CycleIndicatorsXmpPageEmpty6}{CycleIndicatorsXmpPagePatch6}
\pastebutton{CycleIndicatorsXmpPageEmpty6}{\showpaste}
\tab{5}\spadcommand{elementary 7}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch7}
\begin{paste}{CycleIndicatorsXmpPageFull7}{CycleIndicatorsXmpPageEmpty7}
\pastebutton{CycleIndicatorsXmpPageFull7}{\hidepaste}
\tab{5}\spadcommand{alternating 7}
\indentrel{3}\begin{verbatim}
(6)
2 1 2 1 1 2 1 2
� (7) + � (5 1 ) + � (4 2 1) + � (3 1) + �� (3 2 )
7 5 4 9 12
+
1 4 1 2 3 1 7
�� (3 1 ) + �� (2 1 ) + ���� (1 )
36 24 2520
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty7}
\begin{paste}{CycleIndicatorsXmpPageEmpty7}{CycleIndicatorsXmpPagePatch7}
\pastebutton{CycleIndicatorsXmpPageEmpty7}{\showpaste}
\tab{5}\spadcommand{alternating 7}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch8}
\begin{paste}{CycleIndicatorsXmpPageFull8}{CycleIndicatorsXmpPageEmpty8}
\pastebutton{CycleIndicatorsXmpPageFull8}{\hidepaste}
\tab{5}\spadcommand{cyclic 7}
\indentrel{3}\begin{verbatim}
6 1 7
(7) � (7) + � (1 )
7 7
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty8}
\begin{paste}{CycleIndicatorsXmpPageEmpty8}{CycleIndicatorsXmpPagePatch8}
\pastebutton{CycleIndicatorsXmpPageEmpty8}{\showpaste}
\tab{5}\spadcommand{cyclic 7}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch9}
\begin{paste}{CycleIndicatorsXmpPageFull9}{CycleIndicatorsXmpPageEmpty9}
\pastebutton{CycleIndicatorsXmpPageFull9}{\hidepaste}
\tab{5}\spadcommand{dihedral 7}
\indentrel{3}\begin{verbatim}
3 1 3 1 7
(8) � (7) + � (2 1) + �� (1 )
7 2 14
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty9}
\begin{paste}{CycleIndicatorsXmpPageEmpty9}{CycleIndicatorsXmpPagePatch9}
\pastebutton{CycleIndicatorsXmpPageEmpty9}{\showpaste}
\tab{5}\spadcommand{dihedral 7}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch10}
\begin{paste}{CycleIndicatorsXmpPageFull10}{CycleIndicatorsXmpPageEmpty10}
\pastebutton{CycleIndicatorsXmpPageFull10}{\hidepaste}
\tab{5}\spadcommand{graphs 5}
\indentrel{3}\begin{verbatim}
(9)
1 1 2 1 2 1 3 1 4 2
� (6 3 1) + � (5 ) + � (4 2) + � (3 1) + � (2 1 )
6 5 4 6 8
+
1 3 4 1 10
�� (2 1 ) + ��� (1 )
12 120
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty10}
\begin{paste}{CycleIndicatorsXmpPageEmpty10}{CycleIndicatorsXmpPagePatch10}
\pastebutton{CycleIndicatorsXmpPageEmpty10}{\showpaste}
\tab{5}\spadcommand{graphs 5}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch11}
\begin{paste}{CycleIndicatorsXmpPageFull11}{CycleIndicatorsXmpPageEmpty11}
\pastebutton{CycleIndicatorsXmpPageFull11}{\hidepaste}
\tab{5}\spadcommand{cap(complete 2**2, complete 2*complete 1**2)}
\indentrel{3}\begin{verbatim}
(10) 4
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty11}
\begin{paste}{CycleIndicatorsXmpPageEmpty11}{CycleIndicatorsXmpPagePatch11}
\pastebutton{CycleIndicatorsXmpPageEmpty11}{\showpaste}
\tab{5}\spadcommand{cap(complete 2**2, complete 2*complete 1**2)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch12}
\begin{paste}{CycleIndicatorsXmpPageFull12}{CycleIndicatorsXmpPageEmpty12}
\pastebutton{CycleIndicatorsXmpPageFull12}{\hidepaste}
\tab{5}\spadcommand{cap(elementary 2**2, complete 2*complete 1**2)}
\indentrel{3}\begin{verbatim}
(11) 2
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty12}
\begin{paste}{CycleIndicatorsXmpPageEmpty12}{CycleIndicatorsXmpPagePatch12}
\pastebutton{CycleIndicatorsXmpPageEmpty12}{\showpaste}
\tab{5}\spadcommand{cap(elementary 2**2, complete 2*complete 1**2)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch13}
\begin{paste}{CycleIndicatorsXmpPageFull13}{CycleIndicatorsXmpPageEmpty13}
\pastebutton{CycleIndicatorsXmpPageFull13}{\hidepaste}
\tab{5}\spadcommand{cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)}
\indentrel{3}\begin{verbatim}
(12) 24
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty13}
\begin{paste}{CycleIndicatorsXmpPageEmpty13}{CycleIndicatorsXmpPagePatch13}
\pastebutton{CycleIndicatorsXmpPageEmpty13}{\showpaste}
\tab{5}\spadcommand{cap(complete 3*complete 2*complete 1,complete 2**2*complete 1**2)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch14}
\begin{paste}{CycleIndicatorsXmpPageFull14}{CycleIndicatorsXmpPageEmpty14}
\pastebutton{CycleIndicatorsXmpPageFull14}{\hidepaste}
\tab{5}\spadcommand{cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)}
\indentrel{3}\begin{verbatim}
(13) 8
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty14}
\begin{paste}{CycleIndicatorsXmpPageEmpty14}{CycleIndicatorsXmpPagePatch14}
\pastebutton{CycleIndicatorsXmpPageEmpty14}{\showpaste}
\tab{5}\spadcommand{cap(elementary 3*elementary 2*elementary 1,complete 2**2*complete 1**2)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch15}
\begin{paste}{CycleIndicatorsXmpPageFull15}{CycleIndicatorsXmpPageEmpty15}
\pastebutton{CycleIndicatorsXmpPageFull15}{\hidepaste}
\tab{5}\spadcommand{cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)}
\indentrel{3}\begin{verbatim}
(14) 8
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty15}
\begin{paste}{CycleIndicatorsXmpPageEmpty15}{CycleIndicatorsXmpPagePatch15}
\pastebutton{CycleIndicatorsXmpPageEmpty15}{\showpaste}
\tab{5}\spadcommand{cap(complete 3*complete 2*complete 1,elementary 2**2*elementary 1**2)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch16}
\begin{paste}{CycleIndicatorsXmpPageFull16}{CycleIndicatorsXmpPageEmpty16}
\pastebutton{CycleIndicatorsXmpPageFull16}{\hidepaste}
\tab{5}\spadcommand{eval(cup(complete 3*complete 2*complete 1, cup(complete 2**2*complete 1**2,complete 2**3)))}
\indentrel{3}\begin{verbatim}
(15) 1500
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty16}
\begin{paste}{CycleIndicatorsXmpPageEmpty16}{CycleIndicatorsXmpPagePatch16}
\pastebutton{CycleIndicatorsXmpPageEmpty16}{\showpaste}
\tab{5}\spadcommand{eval(cup(complete 3*complete 2*complete 1, cup(complete 2**2*complete 1**2,complete 2**3)))}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch17}
\begin{paste}{CycleIndicatorsXmpPageFull17}{CycleIndicatorsXmpPageEmpty17}
\pastebutton{CycleIndicatorsXmpPageFull17}{\hidepaste}
\tab{5}\spadcommand{square:=dihedral 4}
\indentrel{3}\begin{verbatim}
1 3 2 1 2 1 4
(16) � (4) + � (2 ) + � (2 1 ) + � (1 )
4 8 4 8
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty17}
\begin{paste}{CycleIndicatorsXmpPageEmpty17}{CycleIndicatorsXmpPagePatch17}
\pastebutton{CycleIndicatorsXmpPageEmpty17}{\showpaste}
\tab{5}\spadcommand{square:=dihedral 4}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch18}
\begin{paste}{CycleIndicatorsXmpPageFull18}{CycleIndicatorsXmpPageEmpty18}
\pastebutton{CycleIndicatorsXmpPageFull18}{\hidepaste}
\tab{5}\spadcommand{cap(complete 2**2,square)}
\indentrel{3}\begin{verbatim}
(17) 2
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty18}
\begin{paste}{CycleIndicatorsXmpPageEmpty18}{CycleIndicatorsXmpPagePatch18}
\pastebutton{CycleIndicatorsXmpPageEmpty18}{\showpaste}
\tab{5}\spadcommand{cap(complete 2**2,square)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch19}
\begin{paste}{CycleIndicatorsXmpPageFull19}{CycleIndicatorsXmpPageEmpty19}
\pastebutton{CycleIndicatorsXmpPageFull19}{\hidepaste}
\tab{5}\spadcommand{cap(complete 3*complete 2**2,dihedral 7)}
\indentrel{3}\begin{verbatim}
(18) 18
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty19}
\begin{paste}{CycleIndicatorsXmpPageEmpty19}{CycleIndicatorsXmpPagePatch19}
\pastebutton{CycleIndicatorsXmpPageEmpty19}{\showpaste}
\tab{5}\spadcommand{cap(complete 3*complete 2**2,dihedral 7)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch20}
\begin{paste}{CycleIndicatorsXmpPageFull20}{CycleIndicatorsXmpPageEmpty20}
\pastebutton{CycleIndicatorsXmpPageFull20}{\hidepaste}
\tab{5}\spadcommand{cap(graphs 5,complete 7*complete 3)}
\indentrel{3}\begin{verbatim}
(19) 4
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty20}
\begin{paste}{CycleIndicatorsXmpPageEmpty20}{CycleIndicatorsXmpPagePatch20}
\pastebutton{CycleIndicatorsXmpPageEmpty20}{\showpaste}
\tab{5}\spadcommand{cap(graphs 5,complete 7*complete 3)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch21}
\begin{paste}{CycleIndicatorsXmpPageFull21}{CycleIndicatorsXmpPageEmpty21}
\pastebutton{CycleIndicatorsXmpPageFull21}{\hidepaste}
\tab{5}\spadcommand{s(x) == powerSum(x)}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty21}
\begin{paste}{CycleIndicatorsXmpPageEmpty21}{CycleIndicatorsXmpPagePatch21}
\pastebutton{CycleIndicatorsXmpPageEmpty21}{\showpaste}
\tab{5}\spadcommand{s(x) == powerSum(x)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch22}
\begin{paste}{CycleIndicatorsXmpPageFull22}{CycleIndicatorsXmpPageEmpty22}
\pastebutton{CycleIndicatorsXmpPageFull22}{\hidepaste}
\tab{5}\spadcommand{cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)}
\indentrel{3}\begin{verbatim}
1 2 1 2 2 3 4 1 8
(21) � (4 ) + � (3 1 ) + � (2 ) + �� (1 )
4 3 8 24
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty22}
\begin{paste}{CycleIndicatorsXmpPageEmpty22}{CycleIndicatorsXmpPagePatch22}
\pastebutton{CycleIndicatorsXmpPageEmpty22}{\showpaste}
\tab{5}\spadcommand{cube:=(1/24)*(s 1**8+9*s 2**4 + 8*s 3**2*s 1**2+6*s 4**2)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch23}
\begin{paste}{CycleIndicatorsXmpPageFull23}{CycleIndicatorsXmpPageEmpty23}
\pastebutton{CycleIndicatorsXmpPageFull23}{\hidepaste}
\tab{5}\spadcommand{cap(complete 4**2,cube)}
\indentrel{3}\begin{verbatim}
(22) 7
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty23}
\begin{paste}{CycleIndicatorsXmpPageEmpty23}{CycleIndicatorsXmpPagePatch23}
\pastebutton{CycleIndicatorsXmpPageEmpty23}{\showpaste}
\tab{5}\spadcommand{cap(complete 4**2,cube)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch24}
\begin{paste}{CycleIndicatorsXmpPageFull24}{CycleIndicatorsXmpPageEmpty24}
\pastebutton{CycleIndicatorsXmpPageFull24}{\hidepaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))}
\indentrel{3}\begin{verbatim}
(23) 7
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty24}
\begin{paste}{CycleIndicatorsXmpPageEmpty24}{CycleIndicatorsXmpPagePatch24}
\pastebutton{CycleIndicatorsXmpPageEmpty24}{\showpaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(elementary 4,elementary 2))}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch25}
\begin{paste}{CycleIndicatorsXmpPageFull25}{CycleIndicatorsXmpPageEmpty25}
\pastebutton{CycleIndicatorsXmpPageFull25}{\hidepaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))}
\indentrel{3}\begin{verbatim}
(24) 17
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty25}
\begin{paste}{CycleIndicatorsXmpPageEmpty25}{CycleIndicatorsXmpPagePatch25}
\pastebutton{CycleIndicatorsXmpPageEmpty25}{\showpaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(elementary 4,complete 2))}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch26}
\begin{paste}{CycleIndicatorsXmpPageFull26}{CycleIndicatorsXmpPageEmpty26}
\pastebutton{CycleIndicatorsXmpPageFull26}{\hidepaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))}
\indentrel{3}\begin{verbatim}
(25) 10
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty26}
\begin{paste}{CycleIndicatorsXmpPageEmpty26}{CycleIndicatorsXmpPagePatch26}
\pastebutton{CycleIndicatorsXmpPageEmpty26}{\showpaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(complete 4,elementary 2))}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch27}
\begin{paste}{CycleIndicatorsXmpPageFull27}{CycleIndicatorsXmpPageEmpty27}
\pastebutton{CycleIndicatorsXmpPageFull27}{\hidepaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))}
\indentrel{3}\begin{verbatim}
(26) 23
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty27}
\begin{paste}{CycleIndicatorsXmpPageEmpty27}{CycleIndicatorsXmpPagePatch27}
\pastebutton{CycleIndicatorsXmpPageEmpty27}{\showpaste}
\tab{5}\spadcommand{cap(complete 2**3*complete 1**2,wreath(complete 4,complete 2))}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch28}
\begin{paste}{CycleIndicatorsXmpPageFull28}{CycleIndicatorsXmpPageEmpty28}
\pastebutton{CycleIndicatorsXmpPageFull28}{\hidepaste}
\tab{5}\spadcommand{x: ULS(FRAC INT,'x,0) := 'x\bound{x }}
\indentrel{3}\begin{verbatim}
(27) x
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty28}
\begin{paste}{CycleIndicatorsXmpPageEmpty28}{CycleIndicatorsXmpPagePatch28}
\pastebutton{CycleIndicatorsXmpPageEmpty28}{\showpaste}
\tab{5}\spadcommand{x: ULS(FRAC INT,'x,0) := 'x\bound{x }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch29}
\begin{paste}{CycleIndicatorsXmpPageFull29}{CycleIndicatorsXmpPageEmpty29}
\pastebutton{CycleIndicatorsXmpPageFull29}{\hidepaste}
\tab{5}\spadcommand{ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0)\bound{zodec }}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty29}
\begin{paste}{CycleIndicatorsXmpPageEmpty29}{CycleIndicatorsXmpPagePatch29}
\pastebutton{CycleIndicatorsXmpPageEmpty29}{\showpaste}
\tab{5}\spadcommand{ZeroOrOne: INT -> ULS(FRAC INT, 'x, 0)\bound{zodec }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch30}
\begin{paste}{CycleIndicatorsXmpPageFull30}{CycleIndicatorsXmpPageEmpty30}
\pastebutton{CycleIndicatorsXmpPageFull30}{\hidepaste}
\tab{5}\spadcommand{Integers: INT -> ULS(FRAC INT, 'x, 0)\bound{idec }}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty30}
\begin{paste}{CycleIndicatorsXmpPageEmpty30}{CycleIndicatorsXmpPagePatch30}
\pastebutton{CycleIndicatorsXmpPageEmpty30}{\showpaste}
\tab{5}\spadcommand{Integers: INT -> ULS(FRAC INT, 'x, 0)\bound{idec }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch31}
\begin{paste}{CycleIndicatorsXmpPageFull31}{CycleIndicatorsXmpPageEmpty31}
\pastebutton{CycleIndicatorsXmpPageFull31}{\hidepaste}
\tab{5}\spadcommand{ZeroOrOne n == 1+x**n\free{x zodec }\bound{zo }}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty31}
\begin{paste}{CycleIndicatorsXmpPageEmpty31}{CycleIndicatorsXmpPagePatch31}
\pastebutton{CycleIndicatorsXmpPageEmpty31}{\showpaste}
\tab{5}\spadcommand{ZeroOrOne n == 1+x**n\free{x zodec }\bound{zo }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch32}
\begin{paste}{CycleIndicatorsXmpPageFull32}{CycleIndicatorsXmpPageEmpty32}
\pastebutton{CycleIndicatorsXmpPageFull32}{\hidepaste}
\tab{5}\spadcommand{ZeroOrOne 5\free{zo }}
\indentrel{3}\begin{verbatim}
5
(31) 1 + x
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty32}
\begin{paste}{CycleIndicatorsXmpPageEmpty32}{CycleIndicatorsXmpPagePatch32}
\pastebutton{CycleIndicatorsXmpPageEmpty32}{\showpaste}
\tab{5}\spadcommand{ZeroOrOne 5\free{zo }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch33}
\begin{paste}{CycleIndicatorsXmpPageFull33}{CycleIndicatorsXmpPageEmpty33}
\pastebutton{CycleIndicatorsXmpPageFull33}{\hidepaste}
\tab{5}\spadcommand{Integers n == 1/(1-x**n)\free{x idec }\bound{i }}
\indentrel{3}\begin{verbatim}
Type: Void
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty33}
\begin{paste}{CycleIndicatorsXmpPageEmpty33}{CycleIndicatorsXmpPagePatch33}
\pastebutton{CycleIndicatorsXmpPageEmpty33}{\showpaste}
\tab{5}\spadcommand{Integers n == 1/(1-x**n)\free{x idec }\bound{i }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch34}
\begin{paste}{CycleIndicatorsXmpPageFull34}{CycleIndicatorsXmpPageEmpty34}
\pastebutton{CycleIndicatorsXmpPageFull34}{\hidepaste}
\tab{5}\spadcommand{Integers 5\free{i }}
\indentrel{3}\begin{verbatim}
5 10 11
(33) 1 + x + x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty34}
\begin{paste}{CycleIndicatorsXmpPageEmpty34}{CycleIndicatorsXmpPagePatch34}
\pastebutton{CycleIndicatorsXmpPageEmpty34}{\showpaste}
\tab{5}\spadcommand{Integers 5\free{i }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch35}
\begin{paste}{CycleIndicatorsXmpPageFull35}{CycleIndicatorsXmpPageEmpty35}
\pastebutton{CycleIndicatorsXmpPageFull35}{\hidepaste}
\tab{5}\spadcommand{eval(ZeroOrOne, graphs 5)\free{zo }}
\indentrel{3}\begin{verbatim}
(34)
2 3 4 5 6 7 8 9
1 + x + 2x + 4x + 6x + 6x + 6x + 4x + 2x + x
+
10 11
x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty35}
\begin{paste}{CycleIndicatorsXmpPageEmpty35}{CycleIndicatorsXmpPagePatch35}
\pastebutton{CycleIndicatorsXmpPageEmpty35}{\showpaste}
\tab{5}\spadcommand{eval(ZeroOrOne, graphs 5)\free{zo }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch36}
\begin{paste}{CycleIndicatorsXmpPageFull36}{CycleIndicatorsXmpPageEmpty36}
\pastebutton{CycleIndicatorsXmpPageFull36}{\hidepaste}
\tab{5}\spadcommand{eval(ZeroOrOne,dihedral 8)\free{zo }}
\indentrel{3}\begin{verbatim}
2 3 4 5 6 7 8
(35) 1 + x + 4x + 5x + 8x + 5x + 4x + x + x
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty36}
\begin{paste}{CycleIndicatorsXmpPageEmpty36}{CycleIndicatorsXmpPagePatch36}
\pastebutton{CycleIndicatorsXmpPageEmpty36}{\showpaste}
\tab{5}\spadcommand{eval(ZeroOrOne,dihedral 8)\free{zo }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch37}
\begin{paste}{CycleIndicatorsXmpPageFull37}{CycleIndicatorsXmpPageEmpty37}
\pastebutton{CycleIndicatorsXmpPageFull37}{\hidepaste}
\tab{5}\spadcommand{eval(Integers,complete 4)\free{i }}
\indentrel{3}\begin{verbatim}
(36)
2 3 4 5 6 7 8
1 + x + 2x + 3x + 5x + 6x + 9x + 11x + 15x
+
9 10 11
18x + 23x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty37}
\begin{paste}{CycleIndicatorsXmpPageEmpty37}{CycleIndicatorsXmpPagePatch37}
\pastebutton{CycleIndicatorsXmpPageEmpty37}{\showpaste}
\tab{5}\spadcommand{eval(Integers,complete 4)\free{i }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch38}
\begin{paste}{CycleIndicatorsXmpPageFull38}{CycleIndicatorsXmpPageEmpty38}
\pastebutton{CycleIndicatorsXmpPageFull38}{\hidepaste}
\tab{5}\spadcommand{eval(Integers,elementary 4)\free{i }}
\indentrel{3}\begin{verbatim}
(37)
6 7 8 9 10 11 12 13
x + x + 2x + 3x + 5x + 6x + 9x + 11x
+
14 15 16 17
15x + 18x + 23x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty38}
\begin{paste}{CycleIndicatorsXmpPageEmpty38}{CycleIndicatorsXmpPagePatch38}
\pastebutton{CycleIndicatorsXmpPageEmpty38}{\showpaste}
\tab{5}\spadcommand{eval(Integers,elementary 4)\free{i }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch39}
\begin{paste}{CycleIndicatorsXmpPageFull39}{CycleIndicatorsXmpPageEmpty39}
\pastebutton{CycleIndicatorsXmpPageFull39}{\hidepaste}
\tab{5}\spadcommand{eval(ZeroOrOne,cube)\free{zo }}
\indentrel{3}\begin{verbatim}
2 3 4 5 6 7 8
(38) 1 + x + 3x + 3x + 7x + 3x + 3x + x + x
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty39}
\begin{paste}{CycleIndicatorsXmpPageEmpty39}{CycleIndicatorsXmpPagePatch39}
\pastebutton{CycleIndicatorsXmpPageEmpty39}{\showpaste}
\tab{5}\spadcommand{eval(ZeroOrOne,cube)\free{zo }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch40}
\begin{paste}{CycleIndicatorsXmpPageFull40}{CycleIndicatorsXmpPageEmpty40}
\pastebutton{CycleIndicatorsXmpPageFull40}{\hidepaste}
\tab{5}\spadcommand{eval(Integers,cube)\free{i }}
\indentrel{3}\begin{verbatim}
(39)
2 3 4 5 6 7
1 + x + 4x + 7x + 21x + 37x + 85x + 151x
+
8 9 10 11
292x + 490x + 848x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty40}
\begin{paste}{CycleIndicatorsXmpPageEmpty40}{CycleIndicatorsXmpPagePatch40}
\pastebutton{CycleIndicatorsXmpPageEmpty40}{\showpaste}
\tab{5}\spadcommand{eval(Integers,cube)\free{i }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch41}
\begin{paste}{CycleIndicatorsXmpPageFull41}{CycleIndicatorsXmpPageEmpty41}
\pastebutton{CycleIndicatorsXmpPageFull41}{\hidepaste}
\tab{5}\spadcommand{eval(Integers,graphs 5)\free{i }}
\indentrel{3}\begin{verbatim}
(40)
2 3 4 5 6 7
1 + x + 3x + 7x + 17x + 35x + 76x + 149x
+
8 9 10 11
291x + 539x + 974x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty41}
\begin{paste}{CycleIndicatorsXmpPageEmpty41}{CycleIndicatorsXmpPagePatch41}
\pastebutton{CycleIndicatorsXmpPageEmpty41}{\showpaste}
\tab{5}\spadcommand{eval(Integers,graphs 5)\free{i }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch42}
\begin{paste}{CycleIndicatorsXmpPageFull42}{CycleIndicatorsXmpPageEmpty42}
\pastebutton{CycleIndicatorsXmpPageFull42}{\hidepaste}
\tab{5}\spadcommand{eval(ZeroOrOne ,graphs 15)\free{zo }}
\indentrel{3}\begin{verbatim}
(41)
2 3 4 5 6 7
1 + x + 2x + 5x + 11x + 26x + 68x + 177x
+
8 9 10 11
496x + 1471x + 4583x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty42}
\begin{paste}{CycleIndicatorsXmpPageEmpty42}{CycleIndicatorsXmpPagePatch42}
\pastebutton{CycleIndicatorsXmpPageEmpty42}{\showpaste}
\tab{5}\spadcommand{eval(ZeroOrOne ,graphs 15)\free{zo }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch43}
\begin{paste}{CycleIndicatorsXmpPageFull43}{CycleIndicatorsXmpPageEmpty43}
\pastebutton{CycleIndicatorsXmpPageFull43}{\hidepaste}
\tab{5}\spadcommand{cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)}
\indentrel{3}\begin{verbatim}
(42) 49958972383320
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty43}
\begin{paste}{CycleIndicatorsXmpPageEmpty43}{CycleIndicatorsXmpPagePatch43}
\pastebutton{CycleIndicatorsXmpPageEmpty43}{\showpaste}
\tab{5}\spadcommand{cap(dihedral 30,complete 7*complete 8*complete 5*complete 10)}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch44}
\begin{paste}{CycleIndicatorsXmpPageFull44}{CycleIndicatorsXmpPageEmpty44}
\pastebutton{CycleIndicatorsXmpPageFull44}{\hidepaste}
\tab{5}\spadcommand{sf3221:= SFunction [3,2,2,1]\bound{sf3221 }}
\indentrel{3}\begin{verbatim}
(43)
1 1 2 1 2 1
�� (6 2) - �� (6 1 ) - �� (4 ) + �� (4 3 1)
12 12 16 12
+
1 4 1 2 1 2 2 1 2
�� (4 1 ) - �� (3 2) + �� (3 1 ) - �� (3 2 1)
24 36 36 24
+
1 3 1 5 1 4 1 3 2
- �� (3 2 1 ) - �� (3 1 ) - ��� (2 ) + �� (2 1 )
36 72 192 48
+
1 2 4 1 6 1 8
�� (2 1 ) - ��� (2 1 ) + ��� (1 )
96 144 576
Type: SymmetricPolynomial Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty44}
\begin{paste}{CycleIndicatorsXmpPageEmpty44}{CycleIndicatorsXmpPagePatch44}
\pastebutton{CycleIndicatorsXmpPageEmpty44}{\showpaste}
\tab{5}\spadcommand{sf3221:= SFunction [3,2,2,1]\bound{sf3221 }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch45}
\begin{paste}{CycleIndicatorsXmpPageFull45}{CycleIndicatorsXmpPageEmpty45}
\pastebutton{CycleIndicatorsXmpPageFull45}{\hidepaste}
\tab{5}\spadcommand{cap(sf3221,complete 2**4)\free{sf3221 }}
\indentrel{3}\begin{verbatim}
(44) 3
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty45}
\begin{paste}{CycleIndicatorsXmpPageEmpty45}{CycleIndicatorsXmpPagePatch45}
\pastebutton{CycleIndicatorsXmpPageEmpty45}{\showpaste}
\tab{5}\spadcommand{cap(sf3221,complete 2**4)\free{sf3221 }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch46}
\begin{paste}{CycleIndicatorsXmpPageFull46}{CycleIndicatorsXmpPageEmpty46}
\pastebutton{CycleIndicatorsXmpPageFull46}{\hidepaste}
\tab{5}\spadcommand{cap(sf3221, powerSum 1**8)\free{sf3221 }}
\indentrel{3}\begin{verbatim}
(45) 70
Type: Fraction Integer
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty46}
\begin{paste}{CycleIndicatorsXmpPageEmpty46}{CycleIndicatorsXmpPagePatch46}
\pastebutton{CycleIndicatorsXmpPageEmpty46}{\showpaste}
\tab{5}\spadcommand{cap(sf3221, powerSum 1**8)\free{sf3221 }}
\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPagePatch47}
\begin{paste}{CycleIndicatorsXmpPageFull47}{CycleIndicatorsXmpPageEmpty47}
\pastebutton{CycleIndicatorsXmpPageFull47}{\hidepaste}
\tab{5}\spadcommand{eval(Integers, sf3221)\free{i sf3221 }}
\indentrel{3}\begin{verbatim}
(46)
9 10 11 12 13 14 15
x + 3x + 7x + 14x + 27x + 47x + 79x
+
16 17 18 19 20
126x + 196x + 294x + 432x + O(x )
Type: UnivariateLaurentSeries(Fraction Integer,x,0)
\end{verbatim}
\indentrel{-3}\end{paste}\end{patch}
\begin{patch}{CycleIndicatorsXmpPageEmpty47}
\begin{paste}{CycleIndicatorsXmpPageEmpty47}{CycleIndicatorsXmpPagePatch47}
\pastebutton{CycleIndicatorsXmpPageEmpty47}{\showpaste}
\tab{5}\spadcommand{eval(Integers, sf3221)\free{i sf3221 }}
\end{paste}\end{patch}