1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
|
\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>>
@
|
