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 Topics FrontPage OldWishList SandBoxCombinat <-- You are here. SandBox SandBoxCombinat <-- You are here. This page demonstrates one of the very early attempts to do something similar to MuPAD combinat's "decomposable objects" in Aldor/Axiom. Meanwhile, we adopted the point of view of species, as shown on SandBoxSpecies \begin{aldor} #include "axiom.as" macro CCC == CombinatorialClassCategory; import from Integer; import from List Integer; import from OutputForm; CombinatorialClassCategory: Category == with { list: Integer -> List %; count: Integer -> Integer; import from NonNegativeInteger; default count(i: Integer): Integer == (#list(i))::Integer; coerce: % -> OutputForm; } Primitive(n: Integer): CombinatorialClassCategory == add { Rep == Integer; count(i: Integer): Integer == if i=n then 1 else 0; list(i: Integer): List % == if i=n then [per 1] else []; coerce(x: %): OutputForm == message(" ") } Epsilon: CombinatorialClassCategory == Primitive(0) add; Atom: CombinatorialClassCategory == Primitive(1) add; UnionClass(S1: CCC, S2: CCC): CCC == add { Rep == Union(s1: S1, s2: S2); count(i: Integer): Integer == count(i)$S1 + count(i)$S2; import from Rep; import from List S1; import from List S2; list(i: Integer): List % == { result: List % := []; for a in list(i)$S1 repeat result := cons(per union a, result); for b in list(i)$S2 repeat result := cons(per union b, result); result; } coerce(x: %): OutputForm == { (rep x) case s1 => ((rep x).s1)::OutputForm; ((rep x).s2)::OutputForm; } } CrossClass(S1: CCC, S2: CCC): with { CombinatorialClassCategory } == add { Rep == Record(t1: S1, t2: S2); count(i: Integer): Integer == { result := 0; for k in 1 .. i-1 repeat { result := result + count(k)$S1 * count(i-k)$S2; } result; } import from Rep; import from List S1; import from List S2; list(i: Integer): List % == { result: List % := []; for k in 1..i-1 repeat { for a in list(k)$S1 repeat { for b in list(i-k)$S2 repeat { result := cons(per record(a, b), result); } } } result; } coerce(x: %): OutputForm == { a := ((rep x).t1)::OutputForm; b := ((rep x).t2)::OutputForm; c: List OutputForm := [a, b]; vconcat [hconcat [hspace 1, message("o")], hconcat [hspace 1, message("/"), hspace 1, message("\")], hconcat [a,hspace 3,b]] } } TreeClass: CombinatorialClassCategory == UnionClass(Atom, CrossClass(TreeClass, TreeClass) ) add; \end{aldor} \begin{axiom} [count(i)$TreeClass for i in 1..7] \end{axiom} \begin{axiom} )set output tex off )set output algebra on (list(5)$TreeClass)::List OutputForm \end{axiom} Some or all expressions may not have rendered properly, because Axiom returned the following error:Error: export FRICAS=/usr/local/lib/fricas/target/x86_64-unknown-linux; export ALDORROOT=/usr/local/aldor/linux/1.1.0; export PATH=$ALDORROOT/bin:$PATH; export HOME=/var/zope2/var/LatexWiki; ulimit -t 600; export LD_LIBRARY_PATH=/usr/local/lib/fricas/target/x86_64-unknown-linux/lib; LANG=en_US.UTF-8 $FRICAS/bin/FRICASsys < /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/6466883624509906992-25px.axm /bin/sh: /usr/local/lib/fricas/target/x86_64-unknown-linux/bin/FRICASsys: not found  Some or all expressions may not have rendered properly, because Latex returned the following error:This is pdfTeXk, Version 3.141592-1.40.3 (Web2C 7.5.6) \write18 enabled. %&-line parsing enabled. entering extended mode (./2289839254627963517-16.0px.tex LaTeX2e <2005/12/01> Babel and hyphenation patterns for english, usenglishmax, dumylang, noh yphenation, arabic, farsi, croatian, ukrainian, russian, bulgarian, czech, slov ak, danish, dutch, finnish, basque, french, german, ngerman, ibycus, greek, mon ogreek, ancientgreek, hungarian, italian, latin, mongolian, norsk, icelandic, i nterlingua, turkish, coptic, romanian, welsh, serbian, slovenian, estonian, esp eranto, uppersorbian, indonesian, polish, portuguese, spanish, catalan, galicia n, swedish, ukenglish, pinyin, loaded. 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LaTeX Warning: Characters dropped after \end{axiom}' on input line 211. [2] (./2289839254627963517-16.0px.aux) ) (see the transcript file for additional information) Output written on 2289839254627963517-16.0px.dvi (2 pages, 3436 bytes). Transcript written on 2289839254627963517-16.0px.log. `

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