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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/input/grpthry.input.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input grpthry.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+<<*>>=
+
+-- Input for page PermutationGroupsPage
+)clear all
+
+x : PERM INT := [[1,3,5],[7,11,9]]
+y : PERM INT := [[3,5,7,9]]
+z : PERM INT := [1,3,11]
+g1 : PERMGRPS INT := [ x , y ]
+g2 : PERMGRPS INT := [ x , z ]
+g3 : PERMGRPS INT := [ y , z ]
+order g1
+degree g3
+movedPoints g2
+orbit (g1, 3)
+orbits g3
+member? ( y , g2 )
+)sh PERMGRPS
+
+-- Input for page IrrRepSymPage
+)clear all
+
+ptn9 := partitions 9
+map(dimIrrRepSym, ptn9)
+yt := listYoungTableaus [4,2]; yt :: (LIST TABLEAU I)
+r1 := irrRepSymNat([4,2],[1,2,4,5,3,6])
+r2 := irrRepSymNat([4,2],[3,2,1,5,6,4])
+r3 := irrRepSymNat([4,2],[4,2,1,3,6,5])
+(r3 = r1*r2) :: Boolean
+irrRepSymNat [4,4,1]
+
+-- Input for page REP1Page
+)clear all
+
+permutationRepresentation [2,3,1,4,6,5,11,10,7,8,9]
+gm2 := createGenericMatrix 2
+symmetricTensors (gm2,2)
+gm3 := createGenericMatrix 3
+antisymmetricTensors (gm3,2)
+tensorProduct(gm2,gm2)
+)sh REP1
+
+-- Input for page REP2Page
+)clear all
+
+r0 := irrRepSymNat [2,2,2,1,1]; r28 := meatAxe (r0::(LIST MATRIX PF 2))
+areEquivalent? (r28.1, r28.2)
+meatAxe r28.2
+isAbsolutelyIrreducible? r28.2
+ma := meatAxe r28.1
+isAbsolutelyIrreducible? ma.1
+isAbsolutelyIrreducible? ma.2
+
+-- Input for page PermutationsPage
+)clear all
+
+px : PERM PF 29 := cycles [[1,3,5],[7,11,9]]
+py : PERM PF 29 := cycles [[3,5,7,9]]
+pz : PERM PF 29 := cycle [1,3,11]
+px * pz
+py ** 3
+inv px
+order px
+movedPoints py
+orbit ( pz , 3 )
+eval ( py , 7 )
+)sh PERM
+
+-- Input for page RepA6Page
+)clear all
+
+genA6 : List PERM INT := [cycle [1,2,3],cycle [2,3,4,5,6]]
+pRA6 := permutationRepresentation (genA6,6)
+sp0 := meatAxe (pRA6::(List Matrix PF 2))
+sp1 := meatAxe sp0.1
+isAbsolutelyIrreducible? sp1.2
+d2211 := irrRepSymNat ([2,2,1,1],genA6)
+d2211m2 := (d2211::(List Matrix PF 2)); sp2 := meatAxe d2211m2
+isAbsolutelyIrreducible? sp2.1
+areEquivalent? (sp2.1, sp1.2)
+dA6d16 := tensorProduct(sp2.1,sp1.2); meatAxe dA6d16
+isAbsolutelyIrreducible? dA6d16
+sp3 := meatAxe (dA6d16 :: (List Matrix FF(2,2)))
+isAbsolutelyIrreducible? sp3.1
+isAbsolutelyIrreducible? sp3.2
+areEquivalent? (sp3.1,sp3.2)
+sp0.2
+sp1.2
+sp2.1
+sp3.1
+sp3.2
+dA6d16
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}