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Diffstat (limited to 'src/input/grpthry.input.pamphlet')
-rw-r--r-- | src/input/grpthry.input.pamphlet | 109 |
1 files changed, 109 insertions, 0 deletions
diff --git a/src/input/grpthry.input.pamphlet b/src/input/grpthry.input.pamphlet new file mode 100644 index 00000000..fc6728c8 --- /dev/null +++ b/src/input/grpthry.input.pamphlet @@ -0,0 +1,109 @@ +\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} |