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 Topics FrontPage SandBox SandboxIsomorphic <-- You are here. This page deals with specification of isomorphic domains. aldor#include "aldor" #include "aldorio" define IsIsomorphicTo(C: Category, T: C): Category == with { coerce: % -> T } -- abelian monoid with a distinguished element. AbelianMonoid1: Category == with { 0: %; 1: %; -- a distinguished element (generator) +: (%, %) -> %; } -- Integers Dom1: AbelianMonoid1 == add { Rep == Integer; import from Rep; 0: % == per 0; 1: % == per 1; (x: %) + (y: %): % == per(rep x + rep y); } -- Even integers Dom2: AbelianMonoid1 == add { Rep == Integer; import from Rep; 0: % == per 0; 1: % == per 2; (x: %) + (y: %): % == per(rep x + rep y); } -- Integers represented as sticks. DomS: AbelianMonoid1 == add { Rep == String; import from Rep; 0: % == per ""; 1: % == per "|"; (x: %) + (y: %): % == per(rep x + rep y); } extend Dom1: IsIsomorphicTo(AbelianMonoid1, Dom2) == add { coerce(x: %): Dom2 == never; } extend Dom2: IsIsomorphicTo(AbelianMonoid1, DomS) == add { coerce(x: %): DomS == never; } extend DomS: IsIsomorphicTo(AbelianMonoid1, Dom1) == add { coerce(x: %): Dom1 == never; } aldor Compiling FriCAS source code from file /var/zope2/var/LatexWiki/5159550970087145340-25px001.as using AXIOM-XL compiler and options -O -Fasy -Fao -Flsp -laxiom -Mno-ALDOR_W_WillObsolete -DAxiom -Y $AXIOM/algebra -I$AXIOM/algebra Use the system command )set compiler args to change these options. Compiling Lisp source code from file ./5159550970087145340-25px001.lsp Issuing )library command for 5159550970087145340-25px001 Reading /var/zope2/var/LatexWiki/5159550970087145340-25px001.asy DomS is now explicitly exposed in frame initial DomS will be automatically loaded when needed from /var/zope2/var/LatexWiki/5159550970087145340-25px001 Dom2 is now explicitly exposed in frame initial Dom2 will be automatically loaded when needed from /var/zope2/var/LatexWiki/5159550970087145340-25px001 Dom1 is now explicitly exposed in frame initial Dom1 will be automatically loaded when needed from /var/zope2/var/LatexWiki/5159550970087145340-25px001 IsIsomorphicTo is now explicitly exposed in frame initial IsIsomorphicTo will be automatically loaded when needed from /var/zope2/var/LatexWiki/5159550970087145340-25px001 AbelianMonoid1 is now explicitly exposed in frame initial AbelianMonoid1 will be automatically loaded when needed from /var/zope2/var/LatexWiki/5159550970087145340-25px001 >> System error: The bounding indices 163 and 162 are bad for a sequence of length 162. See also: The ANSI Standard, Glossary entry for "bounding index designator" The ANSI Standard, writeup for Issue SUBSEQ-OUT-OF-BOUNDS:IS-AN-ERROR Some tasks: Give implementations instead of never. Give a uniform implementation instead of never that works for any Domain DomX.

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