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aldor
#pile
#include "axiom"
+++
+++  Quotients
+++ 
define Quotient(Obj:Category):Category == with
    Quotient:  (A:Obj,B:Obj) -> (A->B) -> (Quo:Obj,A->Quo,(X:Obj)->(A->X)->(Quo->X))
    /:(A:Obj,B:Obj) -> ((A->B)->Obj)
    default
        (A:Obj)/(B:Obj):((A->B)->Obj) ==
            F(f:A->B):Obj == 
                (Q:Obj,insert:A->Q,quo:(X:Obj)->(A->X)->(Q->X)) == Quotient(A,B)(f)
                Q add
            F
+++ +++ Subobjects (the dual of Quotients) +++ define Subobject(Obj:Category):Category == with Subobject: (A:Obj,B:Obj) -> (B->A) -> (Sub:Obj,Sub->A,(X:Obj)->(X->A)->(X->Sub)) \:(A:Obj,B:Obj) -> ((B->A)->Obj) default (A:Obj)\(B:Obj):(B->A)->Obj == F(f:(B->A)): Obj == (S:Obj,include:S->A,sub:(X:Obj)->(X->A)->(X->S)) == Subobject(A,B)(f) S add F
aldor
   Compiling FriCAS source code from file 
      /var/zope2/var/LatexWiki/subobjects.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 ./subobjects.lsp
   Issuing )library command for subobjects
   Reading /var/zope2/var/LatexWiki/subobjects.asy
   Quotient is now explicitly exposed in frame initial 
   Quotient will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/subobjects
   Subobject is now explicitly exposed in frame initial 
   Subobject will be automatically loaded when needed from 
      /var/zope2/var/LatexWiki/subobjects
>> 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




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