From ae3725b1b6208264518fbcd4d7adadd68978d26f Mon Sep 17 00:00:00 2001
From: dos-reis <gdr@axiomatics.org>
Date: Sun, 4 Apr 2010 17:20:33 +0000
Subject: 	* algebra/boolean.spad.pamphlet (BooleanLogic): New. 
 (PropositionalLogic): Extend it. 	* algebra/aggcat.spad.pamphlet
 (BitAggregate): Likewise. 	* algebra/si.spad.pamphlet (SingleInteger):
 Assert membership to 	BooleanLogic.

---
 src/algebra/strap/SINT.lsp | 431 ++++++++++++++++++++++++---------------------
 1 file changed, 226 insertions(+), 205 deletions(-)

(limited to 'src/algebra/strap')

diff --git a/src/algebra/strap/SINT.lsp b/src/algebra/strap/SINT.lsp
index 840a7fcf..fc221547 100644
--- a/src/algebra/strap/SINT.lsp
+++ b/src/algebra/strap/SINT.lsp
@@ -90,190 +90,200 @@
 (PUT '|SINT;And;3$;21| '|SPADreplace| 'LOGAND) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;Or;3$;22|)) 
+                |SINT;and;3$;22|)) 
 
-(PUT '|SINT;Or;3$;22| '|SPADreplace| 'LOGIOR) 
+(PUT '|SINT;and;3$;22| '|SPADreplace| 'LOGAND) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;xor;3$;23|)) 
+                |SINT;Or;3$;23|)) 
 
-(PUT '|SINT;xor;3$;23| '|SPADreplace| 'LOGXOR) 
+(PUT '|SINT;Or;3$;23| '|SPADreplace| 'LOGIOR) 
+
+(DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
+                |SINT;or;3$;24|)) 
+
+(PUT '|SINT;or;3$;24| '|SPADreplace| 'LOGIOR) 
+
+(DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
+                |SINT;xor;3$;25|)) 
+
+(PUT '|SINT;xor;3$;25| '|SPADreplace| 'LOGXOR) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Boolean|)
-                |SINT;<;2$B;24|)) 
+                |SINT;<;2$B;26|)) 
 
-(PUT '|SINT;<;2$B;24| '|SPADreplace| 'QSLESSP) 
+(PUT '|SINT;<;2$B;26| '|SPADreplace| 'QSLESSP) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Boolean|)
-                |SINT;>;2$B;25|)) 
+                |SINT;>;2$B;27|)) 
 
-(PUT '|SINT;>;2$B;25| '|SPADreplace| 'QSGREATERP) 
+(PUT '|SINT;>;2$B;27| '|SPADreplace| 'QSGREATERP) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Boolean|)
-                |SINT;<=;2$B;26|)) 
+                |SINT;<=;2$B;28|)) 
 
-(PUT '|SINT;<=;2$B;26| '|SPADreplace|
+(PUT '|SINT;<=;2$B;28| '|SPADreplace|
      '(XLAM (|x| |y|) (NOT (> |x| |y|)))) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Boolean|)
-                |SINT;>=;2$B;27|)) 
+                |SINT;>=;2$B;29|)) 
 
-(PUT '|SINT;>=;2$B;27| '|SPADreplace| '>=) 
+(PUT '|SINT;>=;2$B;29| '|SPADreplace| '>=) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|)
-                |SINT;inc;2$;28|)) 
+                |SINT;inc;2$;30|)) 
 
-(PUT '|SINT;inc;2$;28| '|SPADreplace| 'QSADD1) 
+(PUT '|SINT;inc;2$;30| '|SPADreplace| 'QSADD1) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|)
-                |SINT;dec;2$;29|)) 
+                |SINT;dec;2$;31|)) 
 
-(PUT '|SINT;dec;2$;29| '|SPADreplace| 'QSSUB1) 
+(PUT '|SINT;dec;2$;31| '|SPADreplace| 'QSSUB1) 
 
-(DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) |SINT;-;2$;30|)) 
+(DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|) |SINT;-;2$;32|)) 
 
-(PUT '|SINT;-;2$;30| '|SPADreplace| 'QSMINUS) 
+(PUT '|SINT;-;2$;32| '|SPADreplace| 'QSMINUS) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;+;3$;31|)) 
+                |SINT;+;3$;33|)) 
 
-(PUT '|SINT;+;3$;31| '|SPADreplace| 'QSPLUS) 
+(PUT '|SINT;+;3$;33| '|SPADreplace| 'QSPLUS) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;-;3$;32|)) 
+                |SINT;-;3$;34|)) 
 
-(PUT '|SINT;-;3$;32| '|SPADreplace| 'QSDIFFERENCE) 
+(PUT '|SINT;-;3$;34| '|SPADreplace| 'QSDIFFERENCE) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;*;3$;33|)) 
+                |SINT;*;3$;35|)) 
 
-(PUT '|SINT;*;3$;33| '|SPADreplace| 'QSTIMES) 
+(PUT '|SINT;*;3$;35| '|SPADreplace| 'QSTIMES) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| (|%IntegerSection| 0) |%Shell|)
                     |%Short|)
-                |SINT;**;$Nni$;34|)) 
+                |SINT;**;$Nni$;36|)) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;quo;3$;35|)) 
+                |SINT;quo;3$;37|)) 
 
-(PUT '|SINT;quo;3$;35| '|SPADreplace| 'QSQUOTIENT) 
+(PUT '|SINT;quo;3$;37| '|SPADreplace| 'QSQUOTIENT) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;rem;3$;36|)) 
+                |SINT;rem;3$;38|)) 
 
-(PUT '|SINT;rem;3$;36| '|SPADreplace| 'QSREMAINDER) 
+(PUT '|SINT;rem;3$;38| '|SPADreplace| 'QSREMAINDER) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Pair|)
-                |SINT;divide;2$R;37|)) 
+                |SINT;divide;2$R;39|)) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;gcd;3$;38|)) 
+                |SINT;gcd;3$;40|)) 
 
-(PUT '|SINT;gcd;3$;38| '|SPADreplace| 'GCD) 
+(PUT '|SINT;gcd;3$;40| '|SPADreplace| 'GCD) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|)
-                |SINT;abs;2$;39|)) 
+                |SINT;abs;2$;41|)) 
 
-(PUT '|SINT;abs;2$;39| '|SPADreplace| 'QSABSVAL) 
+(PUT '|SINT;abs;2$;41| '|SPADreplace| 'QSABSVAL) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|)
-                |SINT;odd?;$B;40|)) 
+                |SINT;odd?;$B;42|)) 
 
-(PUT '|SINT;odd?;$B;40| '|SPADreplace| 'QSODDP) 
+(PUT '|SINT;odd?;$B;42| '|SPADreplace| 'QSODDP) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|)
-                |SINT;zero?;$B;41|)) 
+                |SINT;zero?;$B;43|)) 
 
-(PUT '|SINT;zero?;$B;41| '|SPADreplace| 'QSZEROP) 
+(PUT '|SINT;zero?;$B;43| '|SPADreplace| 'QSZEROP) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|)
-                |SINT;one?;$B;42|)) 
+                |SINT;one?;$B;44|)) 
 
-(PUT '|SINT;one?;$B;42| '|SPADreplace| '(XLAM (|x|) (EQL |x| 1))) 
+(PUT '|SINT;one?;$B;44| '|SPADreplace| '(XLAM (|x|) (EQL |x| 1))) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;max;3$;43|)) 
+                |SINT;max;3$;45|)) 
 
-(PUT '|SINT;max;3$;43| '|SPADreplace| 'QSMAX) 
+(PUT '|SINT;max;3$;45| '|SPADreplace| 'QSMAX) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;min;3$;44|)) 
+                |SINT;min;3$;46|)) 
 
-(PUT '|SINT;min;3$;44| '|SPADreplace| 'QSMIN) 
+(PUT '|SINT;min;3$;46| '|SPADreplace| 'QSMIN) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|)
-                |SINT;hash;2$;45|)) 
+                |SINT;hash;2$;47|)) 
 
-(PUT '|SINT;hash;2$;45| '|SPADreplace| 'HASHEQ) 
+(PUT '|SINT;hash;2$;47| '|SPADreplace| 'HASHEQ) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|)
-                |SINT;length;2$;46|)) 
+                |SINT;length;2$;48|)) 
 
-(PUT '|SINT;length;2$;46| '|SPADreplace| 'INTEGER-LENGTH) 
+(PUT '|SINT;length;2$;48| '|SPADreplace| 'INTEGER-LENGTH) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;shift;3$;47|)) 
+                |SINT;shift;3$;49|)) 
 
-(PUT '|SINT;shift;3$;47| '|SPADreplace| 'QSLEFTSHIFT) 
+(PUT '|SINT;shift;3$;49| '|SPADreplace| 'QSLEFTSHIFT) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Short| |%Shell|)
                     |%Short|)
-                |SINT;mulmod;4$;48|)) 
+                |SINT;mulmod;4$;50|)) 
 
-(PUT '|SINT;mulmod;4$;48| '|SPADreplace| 'QSMULTMOD) 
+(PUT '|SINT;mulmod;4$;50| '|SPADreplace| 'QSMULTMOD) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Short| |%Shell|)
                     |%Short|)
-                |SINT;addmod;4$;49|)) 
+                |SINT;addmod;4$;51|)) 
 
-(PUT '|SINT;addmod;4$;49| '|SPADreplace| 'QSADDMOD) 
+(PUT '|SINT;addmod;4$;51| '|SPADreplace| 'QSADDMOD) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Short| |%Shell|)
                     |%Short|)
-                |SINT;submod;4$;50|)) 
+                |SINT;submod;4$;52|)) 
 
-(PUT '|SINT;submod;4$;50| '|SPADreplace| 'QSDIFMOD) 
+(PUT '|SINT;submod;4$;52| '|SPADreplace| 'QSDIFMOD) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Boolean|)
-                |SINT;negative?;$B;51|)) 
+                |SINT;negative?;$B;53|)) 
 
-(PUT '|SINT;negative?;$B;51| '|SPADreplace| 'QSMINUSP) 
+(PUT '|SINT;negative?;$B;53| '|SPADreplace| 'QSMINUSP) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Shell|) (|%IntegerSection| 0))
-                |SINT;size;Nni;52|)) 
+                |SINT;size;Nni;54|)) 
 
-(PUT '|SINT;size;Nni;52| '|SPADreplace|
+(PUT '|SINT;size;Nni;54| '|SPADreplace|
      '(XLAM NIL (+ (- |$ShortMaximum| |$ShortMinimum|) 1))) 
 
 (DECLAIM (FTYPE (FUNCTION ((|%IntegerSection| 1) |%Shell|) |%Short|)
-                |SINT;index;Pi$;53|)) 
+                |SINT;index;Pi$;55|)) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) (|%IntegerSection| 1))
-                |SINT;lookup;$Pi;54|)) 
+                |SINT;lookup;$Pi;56|)) 
 
-(PUT '|SINT;lookup;$Pi;54| '|SPADreplace|
+(PUT '|SINT;lookup;$Pi;56| '|SPADreplace|
      '(XLAM (|x|) (+ (- |x| |$ShortMinimum|) 1))) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Thing| (|%Vector| *) |%Shell|) |%Pair|)
-                |SINT;reducedSystem;MVR;55|)) 
+                |SINT;reducedSystem;MVR;57|)) 
 
-(PUT '|SINT;reducedSystem;MVR;55| '|SPADreplace| 'CONS) 
+(PUT '|SINT;reducedSystem;MVR;57| '|SPADreplace| 'CONS) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Short| |%Shell|) |%Short|)
-                |SINT;positiveRemainder;3$;56|)) 
+                |SINT;positiveRemainder;3$;58|)) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Integer| |%Shell|) |%Short|)
-                |SINT;coerce;I$;57|)) 
+                |SINT;coerce;I$;59|)) 
 
-(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Short|) |SINT;random;$;58|)) 
+(DECLAIM (FTYPE (FUNCTION (|%Shell|) |%Short|) |SINT;random;$;60|)) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Short|)
-                |SINT;random;2$;59|)) 
+                |SINT;random;2$;61|)) 
 
-(PUT '|SINT;random;2$;59| '|SPADreplace| 'RANDOM) 
+(PUT '|SINT;random;2$;61| '|SPADreplace| 'RANDOM) 
 
 (DECLAIM (FTYPE (FUNCTION (|%Short| |%Shell|) |%Shell|)
-                |SINT;unitNormal;$R;60|)) 
+                |SINT;unitNormal;$R;62|)) 
 
 (DEFUN |SINT;writeOMSingleInt| (|dev| |x| $)
   (SEQ (COND
@@ -368,130 +378,138 @@
   (DECLARE (IGNORE $))
   (LOGAND |x| |y|)) 
 
-(DEFUN |SINT;Or;3$;22| (|x| |y| $)
+(DEFUN |SINT;and;3$;22| (|x| |y| $)
+  (DECLARE (IGNORE $))
+  (LOGAND |x| |y|)) 
+
+(DEFUN |SINT;Or;3$;23| (|x| |y| $)
   (DECLARE (IGNORE $))
   (LOGIOR |x| |y|)) 
 
-(DEFUN |SINT;xor;3$;23| (|x| |y| $)
+(DEFUN |SINT;or;3$;24| (|x| |y| $)
+  (DECLARE (IGNORE $))
+  (LOGIOR |x| |y|)) 
+
+(DEFUN |SINT;xor;3$;25| (|x| |y| $)
   (DECLARE (IGNORE $))
   (LOGXOR |x| |y|)) 
 
-(DEFUN |SINT;<;2$B;24| (|x| |y| $)
+(DEFUN |SINT;<;2$B;26| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSLESSP |x| |y|)) 
 
-(DEFUN |SINT;>;2$B;25| (|x| |y| $)
+(DEFUN |SINT;>;2$B;27| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSGREATERP |x| |y|)) 
 
-(DEFUN |SINT;<=;2$B;26| (|x| |y| $)
+(DEFUN |SINT;<=;2$B;28| (|x| |y| $)
   (DECLARE (IGNORE $))
   (NOT (> |x| |y|))) 
 
-(DEFUN |SINT;>=;2$B;27| (|x| |y| $) (DECLARE (IGNORE $)) (>= |x| |y|)) 
+(DEFUN |SINT;>=;2$B;29| (|x| |y| $) (DECLARE (IGNORE $)) (>= |x| |y|)) 
 
-(DEFUN |SINT;inc;2$;28| (|x| $) (DECLARE (IGNORE $)) (QSADD1 |x|)) 
+(DEFUN |SINT;inc;2$;30| (|x| $) (DECLARE (IGNORE $)) (QSADD1 |x|)) 
 
-(DEFUN |SINT;dec;2$;29| (|x| $) (DECLARE (IGNORE $)) (QSSUB1 |x|)) 
+(DEFUN |SINT;dec;2$;31| (|x| $) (DECLARE (IGNORE $)) (QSSUB1 |x|)) 
 
-(DEFUN |SINT;-;2$;30| (|x| $) (DECLARE (IGNORE $)) (QSMINUS |x|)) 
+(DEFUN |SINT;-;2$;32| (|x| $) (DECLARE (IGNORE $)) (QSMINUS |x|)) 
 
-(DEFUN |SINT;+;3$;31| (|x| |y| $)
+(DEFUN |SINT;+;3$;33| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSPLUS |x| |y|)) 
 
-(DEFUN |SINT;-;3$;32| (|x| |y| $)
+(DEFUN |SINT;-;3$;34| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSDIFFERENCE |x| |y|)) 
 
-(DEFUN |SINT;*;3$;33| (|x| |y| $)
+(DEFUN |SINT;*;3$;35| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSTIMES |x| |y|)) 
 
-(DEFUN |SINT;**;$Nni$;34| (|x| |n| $)
+(DEFUN |SINT;**;$Nni$;36| (|x| |n| $)
   (SPADCALL (EXPT |x| |n|) (|getShellEntry| $ 36))) 
 
-(DEFUN |SINT;quo;3$;35| (|x| |y| $)
+(DEFUN |SINT;quo;3$;37| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSQUOTIENT |x| |y|)) 
 
-(DEFUN |SINT;rem;3$;36| (|x| |y| $)
+(DEFUN |SINT;rem;3$;38| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSREMAINDER |x| |y|)) 
 
-(DEFUN |SINT;divide;2$R;37| (|x| |y| $)
+(DEFUN |SINT;divide;2$R;39| (|x| |y| $)
   (CONS (QSQUOTIENT |x| |y|) (QSREMAINDER |x| |y|))) 
 
-(DEFUN |SINT;gcd;3$;38| (|x| |y| $)
+(DEFUN |SINT;gcd;3$;40| (|x| |y| $)
   (DECLARE (IGNORE $))
   (GCD |x| |y|)) 
 
-(DEFUN |SINT;abs;2$;39| (|x| $) (DECLARE (IGNORE $)) (QSABSVAL |x|)) 
+(DEFUN |SINT;abs;2$;41| (|x| $) (DECLARE (IGNORE $)) (QSABSVAL |x|)) 
 
-(DEFUN |SINT;odd?;$B;40| (|x| $) (DECLARE (IGNORE $)) (QSODDP |x|)) 
+(DEFUN |SINT;odd?;$B;42| (|x| $) (DECLARE (IGNORE $)) (QSODDP |x|)) 
 
-(DEFUN |SINT;zero?;$B;41| (|x| $) (DECLARE (IGNORE $)) (QSZEROP |x|)) 
+(DEFUN |SINT;zero?;$B;43| (|x| $) (DECLARE (IGNORE $)) (QSZEROP |x|)) 
 
-(DEFUN |SINT;one?;$B;42| (|x| $) (DECLARE (IGNORE $)) (EQL |x| 1)) 
+(DEFUN |SINT;one?;$B;44| (|x| $) (DECLARE (IGNORE $)) (EQL |x| 1)) 
 
-(DEFUN |SINT;max;3$;43| (|x| |y| $)
+(DEFUN |SINT;max;3$;45| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSMAX |x| |y|)) 
 
-(DEFUN |SINT;min;3$;44| (|x| |y| $)
+(DEFUN |SINT;min;3$;46| (|x| |y| $)
   (DECLARE (IGNORE $))
   (QSMIN |x| |y|)) 
 
-(DEFUN |SINT;hash;2$;45| (|x| $) (DECLARE (IGNORE $)) (HASHEQ |x|)) 
+(DEFUN |SINT;hash;2$;47| (|x| $) (DECLARE (IGNORE $)) (HASHEQ |x|)) 
 
-(DEFUN |SINT;length;2$;46| (|x| $)
+(DEFUN |SINT;length;2$;48| (|x| $)
   (DECLARE (IGNORE $))
   (INTEGER-LENGTH |x|)) 
 
-(DEFUN |SINT;shift;3$;47| (|x| |n| $)
+(DEFUN |SINT;shift;3$;49| (|x| |n| $)
   (DECLARE (IGNORE $))
   (QSLEFTSHIFT |x| |n|)) 
 
-(DEFUN |SINT;mulmod;4$;48| (|a| |b| |p| $)
+(DEFUN |SINT;mulmod;4$;50| (|a| |b| |p| $)
   (DECLARE (IGNORE $))
   (QSMULTMOD |a| |b| |p|)) 
 
-(DEFUN |SINT;addmod;4$;49| (|a| |b| |p| $)
+(DEFUN |SINT;addmod;4$;51| (|a| |b| |p| $)
   (DECLARE (IGNORE $))
   (QSADDMOD |a| |b| |p|)) 
 
-(DEFUN |SINT;submod;4$;50| (|a| |b| |p| $)
+(DEFUN |SINT;submod;4$;52| (|a| |b| |p| $)
   (DECLARE (IGNORE $))
   (QSDIFMOD |a| |b| |p|)) 
 
-(DEFUN |SINT;negative?;$B;51| (|x| $)
+(DEFUN |SINT;negative?;$B;53| (|x| $)
   (DECLARE (IGNORE $))
   (QSMINUSP |x|)) 
 
-(DEFUN |SINT;size;Nni;52| ($)
+(DEFUN |SINT;size;Nni;54| ($)
   (DECLARE (IGNORE $))
   (+ (- |$ShortMaximum| |$ShortMinimum|) 1)) 
 
-(DEFUN |SINT;index;Pi$;53| (|i| $)
-  (PROG (#0=#:G1457)
+(DEFUN |SINT;index;Pi$;55| (|i| $)
+  (PROG (#0=#:G1459)
     (RETURN
       (PROG1 (LETT #0# (- (+ |i| |$ShortMinimum|) 1)
-                   |SINT;index;Pi$;53|)
+                   |SINT;index;Pi$;55|)
         (|check-subtype| (SMINTP #0#) '(|SingleInteger|) #0#))))) 
 
-(DEFUN |SINT;lookup;$Pi;54| (|x| $)
+(DEFUN |SINT;lookup;$Pi;56| (|x| $)
   (DECLARE (IGNORE $))
   (+ (- |x| |$ShortMinimum|) 1)) 
 
-(DEFUN |SINT;reducedSystem;MVR;55| (|m| |v| $)
+(DEFUN |SINT;reducedSystem;MVR;57| (|m| |v| $)
   (DECLARE (IGNORE $))
   (CONS |m| |v|)) 
 
-(DEFUN |SINT;positiveRemainder;3$;56| (|x| |n| $)
+(DEFUN |SINT;positiveRemainder;3$;58| (|x| |n| $)
   (PROG (|r|)
     (RETURN
       (SEQ (LETT |r| (QSREMAINDER |x| |n|)
-                 |SINT;positiveRemainder;3$;56|)
+                 |SINT;positiveRemainder;3$;58|)
            (EXIT (COND
                    ((QSMINUSP |r|)
                     (COND
@@ -499,18 +517,18 @@
                       ('T (QSPLUS |r| |n|))))
                    ('T |r|))))))) 
 
-(DEFUN |SINT;coerce;I$;57| (|x| $)
+(DEFUN |SINT;coerce;I$;59| (|x| $)
   (PROG1 |x| (|check-subtype| (SMINTP |x|) '(|SingleInteger|) |x|))) 
 
-(DEFUN |SINT;random;$;58| ($)
+(DEFUN |SINT;random;$;60| ($)
   (SEQ (|setShellEntry| $ 6
            (REMAINDER (TIMES 314159269 (|getShellEntry| $ 6))
                2147483647))
        (EXIT (REMAINDER (|getShellEntry| $ 6) 67108864)))) 
 
-(DEFUN |SINT;random;2$;59| (|n| $) (DECLARE (IGNORE $)) (RANDOM |n|)) 
+(DEFUN |SINT;random;2$;61| (|n| $) (DECLARE (IGNORE $)) (RANDOM |n|)) 
 
-(DEFUN |SINT;unitNormal;$R;60| (|x| $)
+(DEFUN |SINT;unitNormal;$R;62| (|x| $)
   (COND
     ((QSLESSP |x| 0) (VECTOR -1 (QSMINUS |x|) -1))
     ('T (VECTOR 1 |x| 1)))) 
@@ -518,7 +536,7 @@
 (DEFUN |SingleInteger| ()
   (PROG ()
     (RETURN
-      (PROG (#0=#:G1492)
+      (PROG (#0=#:G1494)
         (RETURN
           (COND
             ((LETT #0# (HGET |$ConstructorCache| '|SingleInteger|)
@@ -540,7 +558,7 @@
     (RETURN
       (PROGN
         (LETT |dv$| '(|SingleInteger|) . #0=(|SingleInteger|))
-        (LETT $ (|newShell| 115) . #0#)
+        (LETT $ (|newShell| 117) . #0#)
         (|setShellEntry| $ 0 |dv$|)
         (|setShellEntry| $ 3
             (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
@@ -554,9 +572,9 @@
     (LIST '#(NIL NIL NIL NIL NIL (|Integer|) '|seed|
              (CONS IDENTITY
                    (FUNCALL (|dispatchFunction| |SINT;Zero;$;10|) $))
-             (0 . |Zero|) (|Boolean|) |SINT;<;2$B;24| (|Void|)
+             (0 . |Zero|) (|Boolean|) |SINT;<;2$B;26| (|Void|)
              (|OpenMathDevice|) (4 . |OMputApp|) (|String|)
-             (9 . |OMputSymbol|) |SINT;-;2$;30| |SINT;convert;$I;8|
+             (9 . |OMputSymbol|) |SINT;-;2$;32| |SINT;convert;$I;8|
              (16 . |OMputInteger|) (22 . |OMputEndApp|)
              (|OpenMathEncoding|) (27 . |OMencodingXML|)
              (31 . |OMopenString|) (37 . |OMputObject|)
@@ -565,7 +583,7 @@
              |SINT;OMwrite;Omd$V;4| |SINT;OMwrite;Omd$BV;5|
              (|Matrix| 5) (|Matrix| $) |SINT;reducedSystem;MM;6|
              (|OutputForm|) (52 . |coerce|) |SINT;coerce;$Of;7|
-             (57 . |coerce|) |SINT;*;3$;33| |SINT;*;I2$;9|
+             (57 . |coerce|) |SINT;*;3$;35| |SINT;*;I2$;9|
              (CONS IDENTITY
                    (FUNCALL (|dispatchFunction| |SINT;One;$;11|) $))
              |SINT;base;$;12|
@@ -575,33 +593,34 @@
                    (FUNCALL (|dispatchFunction| |SINT;min;$;14|) $))
              |SINT;=;2$B;15| |SINT;~;2$;16| |SINT;not;2$;17|
              |SINT;/\\;3$;18| |SINT;\\/;3$;19| |SINT;Not;2$;20|
-             |SINT;And;3$;21| |SINT;Or;3$;22| |SINT;xor;3$;23|
-             |SINT;>;2$B;25| (62 . |not|) |SINT;<=;2$B;26|
-             |SINT;>=;2$B;27| |SINT;inc;2$;28| |SINT;dec;2$;29|
-             |SINT;+;3$;31| |SINT;-;3$;32| (|NonNegativeInteger|)
-             |SINT;**;$Nni$;34| |SINT;quo;3$;35| |SINT;rem;3$;36|
+             |SINT;And;3$;21| |SINT;and;3$;22| |SINT;Or;3$;23|
+             |SINT;or;3$;24| |SINT;xor;3$;25| |SINT;>;2$B;27|
+             (62 . |not|) |SINT;<=;2$B;28| |SINT;>=;2$B;29|
+             |SINT;inc;2$;30| |SINT;dec;2$;31| |SINT;+;3$;33|
+             |SINT;-;3$;34| (|NonNegativeInteger|) |SINT;**;$Nni$;36|
+             |SINT;quo;3$;37| |SINT;rem;3$;38|
              (|Record| (|:| |quotient| $) (|:| |remainder| $))
-             |SINT;divide;2$R;37| |SINT;gcd;3$;38| |SINT;abs;2$;39|
-             |SINT;odd?;$B;40| |SINT;zero?;$B;41| (67 . |One|)
-             |SINT;one?;$B;42| |SINT;max;3$;43| |SINT;min;3$;44|
-             (|SingleInteger|) |SINT;hash;2$;45| |SINT;length;2$;46|
-             |SINT;shift;3$;47| |SINT;mulmod;4$;48| |SINT;addmod;4$;49|
-             |SINT;submod;4$;50| |SINT;negative?;$B;51|
-             |SINT;size;Nni;52| (|PositiveInteger|) (71 . +) (77 . -)
-             |SINT;index;Pi$;53| |SINT;lookup;$Pi;54| (|Vector| 5)
-             (|Record| (|:| |mat| 30) (|:| |vec| 88)) (|Vector| $)
-             |SINT;reducedSystem;MVR;55| |SINT;positiveRemainder;3$;56|
-             |SINT;coerce;I$;57| |SINT;random;$;58| |SINT;random;2$;59|
+             |SINT;divide;2$R;39| |SINT;gcd;3$;40| |SINT;abs;2$;41|
+             |SINT;odd?;$B;42| |SINT;zero?;$B;43| (67 . |One|)
+             |SINT;one?;$B;44| |SINT;max;3$;45| |SINT;min;3$;46|
+             (|SingleInteger|) |SINT;hash;2$;47| |SINT;length;2$;48|
+             |SINT;shift;3$;49| |SINT;mulmod;4$;50| |SINT;addmod;4$;51|
+             |SINT;submod;4$;52| |SINT;negative?;$B;53|
+             |SINT;size;Nni;54| (|PositiveInteger|) (71 . +) (77 . -)
+             |SINT;index;Pi$;55| |SINT;lookup;$Pi;56| (|Vector| 5)
+             (|Record| (|:| |mat| 30) (|:| |vec| 90)) (|Vector| $)
+             |SINT;reducedSystem;MVR;57| |SINT;positiveRemainder;3$;58|
+             |SINT;coerce;I$;59| |SINT;random;$;60| |SINT;random;2$;61|
              (|Record| (|:| |unit| $) (|:| |canonical| $)
                  (|:| |associate| $))
-             |SINT;unitNormal;$R;60| (|Fraction| 5)
-             (|Union| 98 '"failed") (|DoubleFloat|)
-             (|Union| $ '"failed") (|Float|) (|PatternMatchResult| 5 $)
-             (|Pattern| 5) (|InputForm|) (|Union| 5 '"failed")
-             (|List| $) (|Union| 107 '"failed")
-             (|Record| (|:| |coef| 107) (|:| |generator| $))
+             |SINT;unitNormal;$R;62| (|Fraction| 5)
+             (|Union| 100 '"failed") (|Union| $ '"failed") (|Float|)
+             (|DoubleFloat|) (|Pattern| 5) (|PatternMatchResult| 5 $)
+             (|InputForm|) (|Union| 5 '"failed") (|List| $)
+             (|Union| 109 '"failed")
+             (|Record| (|:| |coef| 109) (|:| |generator| $))
              (|Record| (|:| |coef1| $) (|:| |coef2| $))
-             (|Union| 110 '"failed")
+             (|Union| 112 '"failed")
              (|Record| (|:| |coef1| $) (|:| |coef2| $)
                  (|:| |generator| $))
              (|Factored| $) (|SparseUnivariatePolynomial| $))
@@ -614,20 +633,20 @@
              206 |rational?| 211 |rational| 216 |random| 221 |quo| 230
              |principalIdeal| 236 |prime?| 241 |powmod| 246
              |positiveRemainder| 253 |positive?| 259 |permutation| 264
-             |patternMatch| 270 |one?| 277 |odd?| 282 |not| 287
-             |nextItem| 292 |negative?| 297 |multiEuclidean| 302
-             |mulmod| 308 |min| 315 |max| 325 |mask| 335 |lookup| 340
-             |length| 345 |lcm| 350 |latex| 361 |invmod| 366 |init| 372
-             |index| 376 |inc| 381 |hash| 386 |gcdPolynomial| 391 |gcd|
-             397 |factorial| 408 |factor| 413 |extendedEuclidean| 418
-             |exquo| 431 |expressIdealMember| 437 |even?| 443
-             |euclideanSize| 448 |divide| 453 |differentiate| 459 |dec|
-             470 |copy| 475 |convert| 480 |coerce| 505 |characteristic|
-             525 |bit?| 529 |binomial| 535 |before?| 541 |base| 547
-             |associates?| 551 |addmod| 557 |abs| 564 |\\/| 569 |Zero|
-             575 |Or| 579 |One| 585 |OMwrite| 589 |Not| 613 D 618 |And|
-             629 >= 635 > 641 = 647 <= 653 < 659 |/\\| 665 - 671 + 682
-             ** 688 * 700)
+             |patternMatch| 270 |or| 277 |one?| 283 |odd?| 288 |not|
+             293 |nextItem| 298 |negative?| 303 |multiEuclidean| 308
+             |mulmod| 314 |min| 321 |max| 331 |mask| 341 |lookup| 346
+             |length| 351 |lcm| 356 |latex| 367 |invmod| 372 |init| 378
+             |index| 382 |inc| 387 |hash| 392 |gcdPolynomial| 397 |gcd|
+             403 |factorial| 414 |factor| 419 |extendedEuclidean| 424
+             |exquo| 437 |expressIdealMember| 443 |even?| 449
+             |euclideanSize| 454 |divide| 459 |differentiate| 465 |dec|
+             476 |copy| 481 |convert| 486 |coerce| 511 |characteristic|
+             531 |bit?| 535 |binomial| 541 |before?| 547 |base| 553
+             |associates?| 557 |and| 563 |addmod| 569 |abs| 576 |\\/|
+             581 |Zero| 587 |Or| 591 |One| 597 |OMwrite| 601 |Not| 625
+             D 630 |And| 641 >= 647 > 653 = 659 <= 665 < 671 |/\\| 677
+             - 683 + 694 ** 700 * 712)
           '((|noetherian| . 0) (|canonicalsClosed| . 0)
             (|canonical| . 0) (|canonicalUnitNormal| . 0)
             (|multiplicativeValuation| . 0) (|noZeroDivisors| . 0)
@@ -636,7 +655,7 @@
           (CONS (|makeByteWordVec2| 1
                     '(0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
                       0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
-                      0 0 0 0))
+                      0 0 0 0 0 0))
                 (CONS '#(|IntegerNumberSystem&| |EuclideanDomain&|
                          |UniqueFactorizationDomain&| NIL NIL
                          |GcdDomain&| |IntegralDomain&| |Algebra&| NIL
@@ -645,9 +664,9 @@
                          |AbelianGroup&| NIL NIL NIL NIL NIL
                          |AbelianMonoid&| |Monoid&| NIL NIL NIL
                          |OrderedSet&| NIL NIL |AbelianSemiGroup&|
-                         |SemiGroup&| NIL |Logic&| NIL |RetractableTo&|
-                         |SetCategory&| NIL NIL NIL NIL NIL NIL NIL NIL
-                         NIL |BasicType&| NIL)
+                         |SemiGroup&| NIL |Logic&| NIL NIL
+                         |RetractableTo&| |SetCategory&| NIL NIL NIL
+                         NIL NIL NIL NIL NIL NIL NIL |BasicType&| NIL)
                       (CONS '#((|IntegerNumberSystem|)
                                (|EuclideanDomain|)
                                (|UniqueFactorizationDomain|)
@@ -675,61 +694,63 @@
                                (|RightLinearSet| $$)
                                (|AbelianSemiGroup|) (|SemiGroup|)
                                (|LeftLinearSet| 5) (|Logic|)
-                               (|RealConstant|) (|RetractableTo| 5)
-                               (|SetCategory|) (|OpenMath|)
-                               (|ConvertibleTo| 102)
-                               (|ConvertibleTo| 100)
-                               (|CombinatorialFunctionCategory|)
+                               (|BooleanLogic|) (|RealConstant|)
+                               (|RetractableTo| 5) (|SetCategory|)
+                               (|OpenMath|) (|Type|)
+                               (|ConvertibleTo| 103)
                                (|ConvertibleTo| 104)
+                               (|CombinatorialFunctionCategory|)
                                (|ConvertibleTo| 105)
+                               (|ConvertibleTo| 107)
                                (|ConvertibleTo| 5) (|CoercibleFrom| $$)
                                (|CoercibleFrom| 5) (|BasicType|)
                                (|CoercibleTo| 33))
-                            (|makeByteWordVec2| 114
+                            (|makeByteWordVec2| 116
                                 '(0 5 0 8 1 12 11 0 13 3 12 11 0 14 14
                                   15 2 12 11 0 5 18 1 12 11 0 19 0 20 0
                                   21 2 12 0 14 20 22 1 12 11 0 23 1 12
                                   11 0 24 1 12 11 0 25 1 5 33 0 34 1 0
-                                  0 5 36 1 9 0 0 53 0 5 0 70 2 83 0 0 0
-                                  84 2 5 0 0 0 85 2 0 9 0 0 1 1 0 0 0
-                                  44 1 0 9 0 69 2 0 0 0 0 51 1 0 96 0
-                                  97 1 0 0 0 1 1 0 9 0 1 2 0 0 0 0 1 2
-                                  0 101 0 0 1 3 0 0 0 0 0 80 1 0 0 0 1
-                                  1 0 113 0 1 2 0 9 0 0 1 0 0 60 82 1 0
-                                  5 0 1 2 0 0 0 0 77 0 0 0 1 1 0 106 0
-                                  1 1 0 5 0 1 2 0 0 0 0 63 2 0 89 31 90
-                                  91 1 0 30 31 32 1 0 101 0 1 1 0 99 0
-                                  1 1 0 9 0 1 1 0 98 0 1 1 0 0 0 95 0 0
-                                  0 94 2 0 0 0 0 62 1 0 109 107 1 1 0 9
-                                  0 1 3 0 0 0 0 0 1 2 0 0 0 0 92 1 0 9
-                                  0 1 2 0 0 0 0 1 3 0 103 0 104 103 1 1
-                                  0 9 0 71 1 0 9 0 68 1 0 0 0 45 1 0
-                                  101 0 1 1 0 9 0 81 2 0 108 107 0 1 3
-                                  0 0 0 0 0 78 0 0 0 42 2 0 0 0 0 73 0
-                                  0 0 41 2 0 0 0 0 72 1 0 0 0 1 1 0 83
-                                  0 87 1 0 0 0 76 2 0 0 0 0 1 1 0 0 107
-                                  1 1 0 14 0 1 2 0 0 0 0 1 0 0 0 1 1 0
-                                  0 83 86 1 0 0 0 56 1 0 74 0 75 2 0
-                                  114 114 114 1 2 0 0 0 0 66 1 0 0 107
-                                  1 1 0 0 0 1 1 0 113 0 1 3 0 111 0 0 0
-                                  1 2 0 112 0 0 1 2 0 101 0 0 1 2 0 108
-                                  107 0 1 1 0 9 0 1 1 0 60 0 1 2 0 64 0
-                                  0 65 1 0 0 0 1 2 0 0 0 60 1 1 0 0 0
-                                  57 1 0 0 0 1 1 0 100 0 1 1 0 102 0 1
-                                  1 0 105 0 1 1 0 104 0 1 1 0 5 0 17 1
-                                  0 0 5 93 1 0 0 0 1 1 0 0 5 93 1 0 33
-                                  0 35 0 0 60 1 2 0 9 0 0 1 2 0 0 0 0 1
-                                  2 0 9 0 0 1 0 0 0 40 2 0 9 0 0 1 3 0
-                                  0 0 0 0 79 1 0 0 0 67 2 0 0 0 0 47 0
-                                  0 0 7 2 0 0 0 0 50 0 0 0 39 2 0 11 12
-                                  0 28 3 0 11 12 0 9 29 2 0 14 0 9 27 1
-                                  0 14 0 26 1 0 0 0 48 1 0 0 0 1 2 0 0
-                                  0 60 1 2 0 0 0 0 49 2 0 9 0 0 55 2 0
-                                  9 0 0 52 2 0 9 0 0 43 2 0 9 0 0 54 2
-                                  0 9 0 0 10 2 0 0 0 0 46 2 0 0 0 0 59
-                                  1 0 0 0 16 2 0 0 0 0 58 2 0 0 0 60 61
-                                  2 0 0 0 83 1 2 0 0 0 0 37 2 0 0 5 0
-                                  38 2 0 0 60 0 1 2 0 0 83 0 1)))))
+                                  0 5 36 1 9 0 0 55 0 5 0 72 2 85 0 0 0
+                                  86 2 5 0 0 0 87 2 0 9 0 0 1 1 0 0 0
+                                  44 1 0 9 0 71 2 0 0 0 0 53 1 0 98 0
+                                  99 1 0 0 0 1 1 0 9 0 1 2 0 0 0 0 1 2
+                                  0 102 0 0 1 3 0 0 0 0 0 82 1 0 0 0 1
+                                  1 0 115 0 1 2 0 9 0 0 1 0 0 62 84 1 0
+                                  5 0 1 2 0 0 0 0 79 0 0 0 1 1 0 108 0
+                                  1 1 0 5 0 1 2 0 0 0 0 65 1 0 30 31 32
+                                  2 0 91 31 92 93 1 0 102 0 1 1 0 101 0
+                                  1 1 0 9 0 1 1 0 100 0 1 0 0 0 96 1 0
+                                  0 0 97 2 0 0 0 0 64 1 0 111 109 1 1 0
+                                  9 0 1 3 0 0 0 0 0 1 2 0 0 0 0 94 1 0
+                                  9 0 1 2 0 0 0 0 1 3 0 106 0 105 106 1
+                                  2 0 0 0 0 52 1 0 9 0 73 1 0 9 0 70 1
+                                  0 0 0 45 1 0 102 0 1 1 0 9 0 83 2 0
+                                  110 109 0 1 3 0 0 0 0 0 80 0 0 0 42 2
+                                  0 0 0 0 75 0 0 0 41 2 0 0 0 0 74 1 0
+                                  0 0 1 1 0 85 0 89 1 0 0 0 78 2 0 0 0
+                                  0 1 1 0 0 109 1 1 0 14 0 1 2 0 0 0 0
+                                  1 0 0 0 1 1 0 0 85 88 1 0 0 0 58 1 0
+                                  76 0 77 2 0 116 116 116 1 2 0 0 0 0
+                                  68 1 0 0 109 1 1 0 0 0 1 1 0 115 0 1
+                                  3 0 113 0 0 0 1 2 0 114 0 0 1 2 0 102
+                                  0 0 1 2 0 110 109 0 1 1 0 9 0 1 1 0
+                                  62 0 1 2 0 66 0 0 67 1 0 0 0 1 2 0 0
+                                  0 62 1 1 0 0 0 59 1 0 0 0 1 1 0 103 0
+                                  1 1 0 104 0 1 1 0 105 0 1 1 0 107 0 1
+                                  1 0 5 0 17 1 0 0 5 95 1 0 0 0 1 1 0 0
+                                  5 95 1 0 33 0 35 0 0 62 1 2 0 9 0 0 1
+                                  2 0 0 0 0 1 2 0 9 0 0 1 0 0 0 40 2 0
+                                  9 0 0 1 2 0 0 0 0 50 3 0 0 0 0 0 81 1
+                                  0 0 0 69 2 0 0 0 0 47 0 0 0 7 2 0 0 0
+                                  0 51 0 0 0 39 3 0 11 12 0 9 29 2 0 14
+                                  0 9 27 2 0 11 12 0 28 1 0 14 0 26 1 0
+                                  0 0 48 1 0 0 0 1 2 0 0 0 62 1 2 0 0 0
+                                  0 49 2 0 9 0 0 57 2 0 9 0 0 54 2 0 9
+                                  0 0 43 2 0 9 0 0 56 2 0 9 0 0 10 2 0
+                                  0 0 0 46 2 0 0 0 0 61 1 0 0 0 16 2 0
+                                  0 0 0 60 2 0 0 0 62 63 2 0 0 0 85 1 2
+                                  0 0 0 0 37 2 0 0 5 0 38 2 0 0 62 0 1
+                                  2 0 0 85 0 1)))))
           '|lookupComplete|)) 
 
 (MAKEPROP '|SingleInteger| 'NILADIC T) 
-- 
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