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authordos-reis <gdr@axiomatics.org>2010-04-22 09:22:47 +0000
committerdos-reis <gdr@axiomatics.org>2010-04-22 09:22:47 +0000
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tree6f01dd1af6f448e30729748febd2446523255563 /src/algebra/young.spad.pamphlet
parent9fac9abefef7f727a59b7861317d148352a43d88 (diff)
downloadopen-axiom-308aa20f031e73d86801a36eeda29424e65077b2.tar.gz
* algebra/young.spad.pamphlet: New.
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+\documentclass{article}
+\usepackage{open-axiom}
+
+\author{Gabriel Dos~Reis}
+
+\begin{document}
+
+\begin{abstract}
+\end{abstract}
+
+\tableofcontents
+\eject
+
+
+\section{Young Diagram}
+
+<<domain YDIAGRAM YoungDiagram>>=
+++ Author: Gabriel Dos Reis
+++ Date Last Created: April 17, 2010
+++ Date Last Modified: April 17, 2010
+++ Description:
+++ This domain provides representations of Young diagrams.
+)abbrev domain YDIAGRAM YoungDiagram
+YoungDiagram(): Public == Private where
+ Public == Join(SetCategory,HomotopicTo Partition) with
+ youngDiagram: List PositiveInteger -> %
+ ++ \spad{youngDiagram l} returns an object representing a Young
+ ++ diagram with shape given by the list of integers \spad{l}
+ shape: % -> Partition
+ ++ \spad{shape x} returns the partition shaping \spad{x}.
+ Private == add
+ macro LP == List PositiveInteger
+ Rep == Partition
+ youngDiagram l == per partition l
+ shape x == rep x
+ coerce(x: %): Partition == rep x
+ coerce(p: Partition): % == per p
+ x = y == rep x = rep y
+ coerce(x: %): OutputForm ==
+ b := box empty()$OutputForm
+ pile [blankSeparate [b for i in 1..n] for n in shape(x)::LP]
+@
+
+
+
+\section{License}
+<<license>>=
+--Copyright (C) 2010, Gabriel Dos Reis.
+--All rights reserved.
+--
+--Redistribution and use in source and binary forms, with or without
+--modification, are permitted provided that the following conditions are
+--met:
+--
+-- - Redistributions of source code must retain the above copyright
+-- notice, this list of conditions and the following disclaimer.
+--
+-- - Redistributions in binary form must reproduce the above copyright
+-- notice, this list of conditions and the following disclaimer in
+-- the documentation and/or other materials provided with the
+-- distribution.
+--
+-- - Neither the name of The Numerical Algorithms Group Ltd. nor the
+-- names of its contributors may be used to endorse or promote products
+-- derived from this software without specific prior written permission.
+--
+--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
+--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
+--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
+--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
+--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
+--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
+--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
+--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
+--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
+--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
+--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+@
+
+
+<<*>>=
+<<license>>
+
+<<domain YDIAGRAM YoungDiagram>>
+@