aboutsummaryrefslogtreecommitdiff
path: root/src/algebra/si.spad.pamphlet
diff options
context:
space:
mode:
Diffstat (limited to 'src/algebra/si.spad.pamphlet')
-rw-r--r--src/algebra/si.spad.pamphlet855
1 files changed, 0 insertions, 855 deletions
diff --git a/src/algebra/si.spad.pamphlet b/src/algebra/si.spad.pamphlet
index e078bbb9..65253830 100644
--- a/src/algebra/si.spad.pamphlet
+++ b/src/algebra/si.spad.pamphlet
@@ -162,395 +162,7 @@ IntegerNumberSystem(): Category ==
z := mulmod(z, z, p)
@
-\section{INS.lsp BOOTSTRAP}
-{\bf INS} depends on itself. We need to break this cycle to build
-the algebra. So we keep a cached copy of the translated {\bf INS}
-category which we can write into the {\bf MID} directory. We compile
-the lisp code and copy the {\bf INS.o} file to the {\bf OUT} directory.
-This is eventually forcibly replaced by a recompiled version.
-<<INS.lsp BOOTSTRAP>>=
-(/VERSIONCHECK 2)
-
-(DEFPARAMETER |IntegerNumberSystem;AL| 'NIL)
-
-(DEFUN |IntegerNumberSystem| ()
- (LET (#:G1403)
- (COND
- (|IntegerNumberSystem;AL|)
- (T (SETQ |IntegerNumberSystem;AL| (|IntegerNumberSystem;|))))))
-
-(DEFUN |IntegerNumberSystem;| ()
- (PROG (#0=#:G1401)
- (RETURN
- (PROG1 (LETT #0#
- (|sublisV|
- (PAIR '(#1=#:G1395 #2=#:G1396 #3=#:G1397
- #4=#:G1398 #5=#:G1399 #6=#:G1400)
- (LIST '(|Integer|) '(|Integer|)
- '(|Integer|) '(|InputForm|)
- '(|Pattern| (|Integer|))
- '(|Integer|)))
- (|Join| (|UniqueFactorizationDomain|)
- (|EuclideanDomain|)
- (|OrderedIntegralDomain|)
- (|DifferentialRing|)
- (|ConvertibleTo| '#1#)
- (|RetractableTo| '#2#)
- (|LinearlyExplicitRingOver| '#3#)
- (|ConvertibleTo| '#4#)
- (|ConvertibleTo| '#5#)
- (|PatternMatchable| '#6#)
- (|CombinatorialFunctionCategory|)
- (|RealConstant|) (|CharacteristicZero|)
- (|StepThrough|)
- (|mkCategory| '|domain|
- '(((|odd?| ((|Boolean|) $)) T)
- ((|even?| ((|Boolean|) $)) T)
- ((|base| ($)) T)
- ((|length| ($ $)) T)
- ((|shift| ($ $ $)) T)
- ((|bit?| ((|Boolean|) $ $)) T)
- ((|positiveRemainder| ($ $ $)) T)
- ((|symmetricRemainder| ($ $ $)) T)
- ((|rational?| ((|Boolean|) $)) T)
- ((|rational|
- ((|Fraction| (|Integer|)) $))
- T)
- ((|rationalIfCan|
- ((|Union|
- (|Fraction| (|Integer|))
- "failed")
- $))
- T)
- ((|random| ($)) T)
- ((|random| ($ $)) T)
- ((|hash| ($ $)) T)
- ((|copy| ($ $)) T)
- ((|inc| ($ $)) T)
- ((|dec| ($ $)) T)
- ((|mask| ($ $)) T)
- ((|addmod| ($ $ $ $)) T)
- ((|submod| ($ $ $ $)) T)
- ((|mulmod| ($ $ $ $)) T)
- ((|powmod| ($ $ $ $)) T)
- ((|invmod| ($ $ $)) T))
- '((|multiplicativeValuation| T)
- (|canonicalUnitNormal| T))
- '((|Fraction| (|Integer|))
- (|Boolean|))
- NIL)))
- |IntegerNumberSystem|)
- (SETELT #0# 0 '(|IntegerNumberSystem|))))))
-
-(MAKEPROP '|IntegerNumberSystem| 'NILADIC T)
-@
-\section{INS-.lsp BOOTSTRAP}
-{\bf INS-} depends on {\bf INS}. We need to break this cycle to build
-the algebra. So we keep a cached copy of the translated {\bf INS-}
-category which we can write into the {\bf MID} directory. We compile
-the lisp code and copy the {\bf INS-.o} file to the {\bf OUT} directory.
-This is eventually forcibly replaced by a recompiled version.
-<<INS-.lsp BOOTSTRAP>>=
-
-(/VERSIONCHECK 2)
-
-(PUT '|INS-;characteristic;Nni;1| '|SPADreplace| '(XLAM NIL 0))
-
-(DEFUN |INS-;characteristic;Nni;1| ($) 0)
-
-(DEFUN |INS-;differentiate;2S;2| (|x| $) (|spadConstant| $ 9))
-
-(DEFUN |INS-;even?;SB;3| (|x| $)
- (SPADCALL (SPADCALL |x| (QREFELT $ 12)) (QREFELT $ 13)))
-
-(DEFUN |INS-;positive?;SB;4| (|x| $)
- (SPADCALL (|spadConstant| $ 9) |x| (QREFELT $ 15)))
-
-(PUT '|INS-;copy;2S;5| '|SPADreplace| '(XLAM (|x|) |x|))
-
-(DEFUN |INS-;copy;2S;5| (|x| $) |x|)
-
-(DEFUN |INS-;bit?;2SB;6| (|x| |i| $)
- (SPADCALL (SPADCALL |x| (SPADCALL |i| (QREFELT $ 18)) (QREFELT $ 19))
- (QREFELT $ 12)))
-
-(DEFUN |INS-;mask;2S;7| (|n| $)
- (SPADCALL (SPADCALL (|spadConstant| $ 21) |n| (QREFELT $ 19))
- (QREFELT $ 22)))
-
-(PUT '|INS-;rational?;SB;8| '|SPADreplace| '(XLAM (|x|) 'T))
-
-(DEFUN |INS-;rational?;SB;8| (|x| $) 'T)
-
-(DEFUN |INS-;euclideanSize;SNni;9| (|x| $)
- (PROG (#0=#:G1412 #1=#:G1413)
- (RETURN
- (COND
- ((SPADCALL |x| (|spadConstant| $ 9) (QREFELT $ 25))
- (|error| "euclideanSize called on zero"))
- ((SPADCALL |x| (|spadConstant| $ 9) (QREFELT $ 15))
- (PROG1 (LETT #0# (- (SPADCALL |x| (QREFELT $ 27)))
- |INS-;euclideanSize;SNni;9|)
- (|check-subtype| (>= #0# 0) '(|NonNegativeInteger|) #0#)))
- ('T
- (PROG1 (LETT #1# (SPADCALL |x| (QREFELT $ 27))
- |INS-;euclideanSize;SNni;9|)
- (|check-subtype| (>= #1# 0) '(|NonNegativeInteger|) #1#)))))))
-
-(DEFUN |INS-;convert;SF;10| (|x| $)
- (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 30)))
-
-(DEFUN |INS-;convert;SDf;11| (|x| $)
- (FLOAT (SPADCALL |x| (QREFELT $ 27)) MOST-POSITIVE-LONG-FLOAT))
-
-(DEFUN |INS-;convert;SIf;12| (|x| $)
- (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 35)))
-
-(DEFUN |INS-;retract;SI;13| (|x| $) (SPADCALL |x| (QREFELT $ 27)))
-
-(DEFUN |INS-;convert;SP;14| (|x| $)
- (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 39)))
-
-(DEFUN |INS-;factor;SF;15| (|x| $) (SPADCALL |x| (QREFELT $ 43)))
-
-(DEFUN |INS-;squareFree;SF;16| (|x| $) (SPADCALL |x| (QREFELT $ 46)))
-
-(DEFUN |INS-;prime?;SB;17| (|x| $) (SPADCALL |x| (QREFELT $ 49)))
-
-(DEFUN |INS-;factorial;2S;18| (|x| $) (SPADCALL |x| (QREFELT $ 52)))
-
-(DEFUN |INS-;binomial;3S;19| (|n| |m| $)
- (SPADCALL |n| |m| (QREFELT $ 54)))
-
-(DEFUN |INS-;permutation;3S;20| (|n| |m| $)
- (SPADCALL |n| |m| (QREFELT $ 56)))
-
-(DEFUN |INS-;retractIfCan;SU;21| (|x| $)
- (CONS 0 (SPADCALL |x| (QREFELT $ 27))))
-
-(DEFUN |INS-;init;S;22| ($) (|spadConstant| $ 9))
-
-(DEFUN |INS-;nextItem;SU;23| (|n| $)
- (COND
- ((SPADCALL |n| (QREFELT $ 61)) (CONS 0 (|spadConstant| $ 21)))
- ((SPADCALL (|spadConstant| $ 9) |n| (QREFELT $ 15))
- (CONS 0 (SPADCALL |n| (QREFELT $ 18))))
- ('T (CONS 0 (SPADCALL (|spadConstant| $ 21) |n| (QREFELT $ 62))))))
-
-(DEFUN |INS-;patternMatch;SP2Pmr;24| (|x| |p| |l| $)
- (SPADCALL |x| |p| |l| (QREFELT $ 67)))
-
-(DEFUN |INS-;rational;SF;25| (|x| $)
- (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 71)))
-
-(DEFUN |INS-;rationalIfCan;SU;26| (|x| $)
- (CONS 0 (SPADCALL (SPADCALL |x| (QREFELT $ 27)) (QREFELT $ 71))))
-
-(DEFUN |INS-;symmetricRemainder;3S;27| (|x| |n| $)
- (PROG (|r|)
- (RETURN
- (SEQ (LETT |r| (SPADCALL |x| |n| (QREFELT $ 75))
- |INS-;symmetricRemainder;3S;27|)
- (EXIT (COND
- ((SPADCALL |r| (|spadConstant| $ 9) (QREFELT $ 25))
- |r|)
- ('T
- (SEQ (COND
- ((SPADCALL |n| (|spadConstant| $ 9)
- (QREFELT $ 15))
- (LETT |n| (SPADCALL |n| (QREFELT $ 18))
- |INS-;symmetricRemainder;3S;27|)))
- (EXIT (COND
- ((SPADCALL (|spadConstant| $ 9) |r|
- (QREFELT $ 15))
- (COND
- ((SPADCALL |n|
- (SPADCALL 2 |r| (QREFELT $ 77))
- (QREFELT $ 15))
- (SPADCALL |r| |n| (QREFELT $ 62)))
- ('T |r|)))
- ((NULL (SPADCALL (|spadConstant| $ 9)
- (SPADCALL
- (SPADCALL 2 |r|
- (QREFELT $ 77))
- |n| (QREFELT $ 78))
- (QREFELT $ 15)))
- (SPADCALL |r| |n| (QREFELT $ 78)))
- ('T |r|)))))))))))
-
-(DEFUN |INS-;invmod;3S;28| (|a| |b| $)
- (PROG (|q| |r| |r1| |c| |c1| |d| |d1|)
- (RETURN
- (SEQ (COND
- ((SPADCALL |a| (QREFELT $ 80))
- (LETT |a| (SPADCALL |a| |b| (QREFELT $ 81))
- |INS-;invmod;3S;28|)))
- (LETT |c| |a| |INS-;invmod;3S;28|)
- (LETT |c1| (|spadConstant| $ 21) |INS-;invmod;3S;28|)
- (LETT |d| |b| |INS-;invmod;3S;28|)
- (LETT |d1| (|spadConstant| $ 9) |INS-;invmod;3S;28|)
- (SEQ G190
- (COND
- ((NULL (SPADCALL (SPADCALL |d| (QREFELT $ 61))
- (QREFELT $ 13)))
- (GO G191)))
- (SEQ (LETT |q| (SPADCALL |c| |d| (QREFELT $ 82))
- |INS-;invmod;3S;28|)
- (LETT |r|
- (SPADCALL |c|
- (SPADCALL |q| |d| (QREFELT $ 83))
- (QREFELT $ 62))
- |INS-;invmod;3S;28|)
- (LETT |r1|
- (SPADCALL |c1|
- (SPADCALL |q| |d1| (QREFELT $ 83))
- (QREFELT $ 62))
- |INS-;invmod;3S;28|)
- (LETT |c| |d| |INS-;invmod;3S;28|)
- (LETT |c1| |d1| |INS-;invmod;3S;28|)
- (LETT |d| |r| |INS-;invmod;3S;28|)
- (EXIT (LETT |d1| |r1| |INS-;invmod;3S;28|)))
- NIL (GO G190) G191 (EXIT NIL))
- (EXIT (COND
- ((SPADCALL |c| (|spadConstant| $ 21) (QREFELT $ 25))
- (COND
- ((SPADCALL |c1| (QREFELT $ 80))
- (SPADCALL |c1| |b| (QREFELT $ 78)))
- ('T |c1|)))
- ('T (|error| "inverse does not exist"))))))))
-
-(DEFUN |INS-;powmod;4S;29| (|x| |n| |p| $)
- (PROG (|y| #0=#:G1470 |z|)
- (RETURN
- (SEQ (EXIT (SEQ (COND
- ((SPADCALL |x| (QREFELT $ 80))
- (LETT |x| (SPADCALL |x| |p| (QREFELT $ 81))
- |INS-;powmod;4S;29|)))
- (EXIT (COND
- ((SPADCALL |x| (QREFELT $ 61))
- (|spadConstant| $ 9))
- ((SPADCALL |n| (QREFELT $ 61))
- (|spadConstant| $ 21))
- ('T
- (SEQ (LETT |y| (|spadConstant| $ 21)
- |INS-;powmod;4S;29|)
- (LETT |z| |x| |INS-;powmod;4S;29|)
- (EXIT
- (SEQ G190 NIL
- (SEQ
- (COND
- ((SPADCALL |n| (QREFELT $ 12))
- (LETT |y|
- (SPADCALL |y| |z| |p|
- (QREFELT $ 85))
- |INS-;powmod;4S;29|)))
- (EXIT
- (COND
- ((SPADCALL
- (LETT |n|
- (SPADCALL |n|
- (SPADCALL
- (|spadConstant| $ 21)
- (QREFELT $ 18))
- (QREFELT $ 19))
- |INS-;powmod;4S;29|)
- (QREFELT $ 61))
- (PROGN
- (LETT #0# |y|
- |INS-;powmod;4S;29|)
- (GO #0#)))
- ('T
- (LETT |z|
- (SPADCALL |z| |z| |p|
- (QREFELT $ 85))
- |INS-;powmod;4S;29|)))))
- NIL (GO G190) G191 (EXIT NIL)))))))))
- #0# (EXIT #0#)))))
-
-(DEFUN |IntegerNumberSystem&| (|#1|)
- (PROG (|dv$1| |dv$| $ |pv$|)
- (RETURN
- (PROGN
- (LETT |dv$1| (|devaluate| |#1|) . #0=(|IntegerNumberSystem&|))
- (LETT |dv$| (LIST '|IntegerNumberSystem&| |dv$1|) . #0#)
- (LETT $ (GETREFV 87) . #0#)
- (QSETREFV $ 0 |dv$|)
- (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
- (|stuffDomainSlots| $)
- (QSETREFV $ 6 |#1|)
- $))))
-
-(MAKEPROP '|IntegerNumberSystem&| '|infovec|
- (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|)
- (|NonNegativeInteger|) |INS-;characteristic;Nni;1|
- (0 . |Zero|) |INS-;differentiate;2S;2| (|Boolean|)
- (4 . |odd?|) (9 . |not|) |INS-;even?;SB;3| (14 . <)
- |INS-;positive?;SB;4| |INS-;copy;2S;5| (20 . -)
- (25 . |shift|) |INS-;bit?;2SB;6| (31 . |One|) (35 . |dec|)
- |INS-;mask;2S;7| |INS-;rational?;SB;8| (40 . =)
- (|Integer|) (46 . |convert|) |INS-;euclideanSize;SNni;9|
- (|Float|) (51 . |coerce|) |INS-;convert;SF;10|
- (|DoubleFloat|) |INS-;convert;SDf;11| (|InputForm|)
- (56 . |convert|) |INS-;convert;SIf;12|
- |INS-;retract;SI;13| (|Pattern| 26) (61 . |coerce|)
- |INS-;convert;SP;14| (|Factored| 6)
- (|IntegerFactorizationPackage| 6) (66 . |factor|)
- (|Factored| $) |INS-;factor;SF;15| (71 . |squareFree|)
- |INS-;squareFree;SF;16| (|IntegerPrimesPackage| 6)
- (76 . |prime?|) |INS-;prime?;SB;17|
- (|IntegerCombinatoricFunctions| 6) (81 . |factorial|)
- |INS-;factorial;2S;18| (86 . |binomial|)
- |INS-;binomial;3S;19| (92 . |permutation|)
- |INS-;permutation;3S;20| (|Union| 26 '"failed")
- |INS-;retractIfCan;SU;21| |INS-;init;S;22| (98 . |zero?|)
- (103 . -) (|Union| $ '"failed") |INS-;nextItem;SU;23|
- (|PatternMatchResult| 26 6)
- (|PatternMatchIntegerNumberSystem| 6)
- (109 . |patternMatch|) (|PatternMatchResult| 26 $)
- |INS-;patternMatch;SP2Pmr;24| (|Fraction| 26)
- (116 . |coerce|) |INS-;rational;SF;25|
- (|Union| 70 '"failed") |INS-;rationalIfCan;SU;26|
- (121 . |rem|) (|PositiveInteger|) (127 . *) (133 . +)
- |INS-;symmetricRemainder;3S;27| (139 . |negative?|)
- (144 . |positiveRemainder|) (150 . |quo|) (156 . *)
- |INS-;invmod;3S;28| (162 . |mulmod|) |INS-;powmod;4S;29|)
- '#(|symmetricRemainder| 169 |squareFree| 175 |retractIfCan|
- 180 |retract| 185 |rationalIfCan| 190 |rational?| 195
- |rational| 200 |prime?| 205 |powmod| 210 |positive?| 217
- |permutation| 222 |patternMatch| 228 |nextItem| 235 |mask|
- 240 |invmod| 245 |init| 251 |factorial| 255 |factor| 260
- |even?| 265 |euclideanSize| 270 |differentiate| 275 |copy|
- 280 |convert| 285 |characteristic| 305 |bit?| 309
- |binomial| 315)
- 'NIL
- (CONS (|makeByteWordVec2| 1 'NIL)
- (CONS '#()
- (CONS '#()
- (|makeByteWordVec2| 86
- '(0 6 0 9 1 6 11 0 12 1 11 0 0 13 2 6
- 11 0 0 15 1 6 0 0 18 2 6 0 0 0 19 0 6
- 0 21 1 6 0 0 22 2 6 11 0 0 25 1 6 26
- 0 27 1 29 0 26 30 1 34 0 26 35 1 38 0
- 26 39 1 42 41 6 43 1 42 41 6 46 1 48
- 11 6 49 1 51 6 6 52 2 51 6 6 6 54 2
- 51 6 6 6 56 1 6 11 0 61 2 6 0 0 0 62
- 3 66 65 6 38 65 67 1 70 0 26 71 2 6 0
- 0 0 75 2 6 0 76 0 77 2 6 0 0 0 78 1 6
- 11 0 80 2 6 0 0 0 81 2 6 0 0 0 82 2 6
- 0 0 0 83 3 6 0 0 0 0 85 2 0 0 0 0 79
- 1 0 44 0 47 1 0 58 0 59 1 0 26 0 37 1
- 0 73 0 74 1 0 11 0 24 1 0 70 0 72 1 0
- 11 0 50 3 0 0 0 0 0 86 1 0 11 0 16 2
- 0 0 0 0 57 3 0 68 0 38 68 69 1 0 63 0
- 64 1 0 0 0 23 2 0 0 0 0 84 0 0 0 60 1
- 0 0 0 53 1 0 44 0 45 1 0 11 0 14 1 0
- 7 0 28 1 0 0 0 10 1 0 0 0 17 1 0 32 0
- 33 1 0 29 0 31 1 0 38 0 40 1 0 34 0
- 36 0 0 7 8 2 0 11 0 0 20 2 0 0 0 0
- 55)))))
- '|lookupComplete|))
-@
\section{domain SINT SingleInteger}
The definition of {\bf one?} has been rewritten
as it relies on calling {\bf ONEP} which is a function specific
@@ -751,473 +363,6 @@ SingleInteger(): Join(IntegerNumberSystem,Logic,OpenMath) with
@
-\section{SINT.lsp BOOTSTRAP}
-
-<<SINT.lsp BOOTSTRAP>>=
-
-(/VERSIONCHECK 2)
-
-(DEFUN |SINT;writeOMSingleInt| (|dev| |x| $)
- (SEQ (COND
- ((QSLESSP |x| 0)
- (SEQ (SPADCALL |dev| (|getShellEntry| $ 9))
- (SPADCALL |dev| "arith1" "unaryminus"
- (|getShellEntry| $ 11))
- (SPADCALL |dev| (QSMINUS |x|) (|getShellEntry| $ 13))
- (EXIT (SPADCALL |dev| (|getShellEntry| $ 14)))))
- ('T (SPADCALL |dev| |x| (|getShellEntry| $ 13))))))
-
-(DEFUN |SINT;OMwrite;$S;2| (|x| $)
- (PROG (|sp| |dev| |s|)
- (RETURN
- (SEQ (LETT |s| "" |SINT;OMwrite;$S;2|)
- (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |SINT;OMwrite;$S;2|)
- (LETT |dev|
- (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 16))
- (|getShellEntry| $ 17))
- |SINT;OMwrite;$S;2|)
- (SPADCALL |dev| (|getShellEntry| $ 18))
- (|SINT;writeOMSingleInt| |dev| |x| $)
- (SPADCALL |dev| (|getShellEntry| $ 19))
- (SPADCALL |dev| (|getShellEntry| $ 20))
- (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |SINT;OMwrite;$S;2|)
- (EXIT |s|)))))
-
-(DEFUN |SINT;OMwrite;$BS;3| (|x| |wholeObj| $)
- (PROG (|sp| |dev| |s|)
- (RETURN
- (SEQ (LETT |s| "" |SINT;OMwrite;$BS;3|)
- (LETT |sp| (OM-STRINGTOSTRINGPTR |s|) |SINT;OMwrite;$BS;3|)
- (LETT |dev|
- (SPADCALL |sp| (SPADCALL (|getShellEntry| $ 16))
- (|getShellEntry| $ 17))
- |SINT;OMwrite;$BS;3|)
- (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 18))))
- (|SINT;writeOMSingleInt| |dev| |x| $)
- (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 19))))
- (SPADCALL |dev| (|getShellEntry| $ 20))
- (LETT |s| (OM-STRINGPTRTOSTRING |sp|) |SINT;OMwrite;$BS;3|)
- (EXIT |s|)))))
-
-(DEFUN |SINT;OMwrite;Omd$V;4| (|dev| |x| $)
- (SEQ (SPADCALL |dev| (|getShellEntry| $ 18))
- (|SINT;writeOMSingleInt| |dev| |x| $)
- (EXIT (SPADCALL |dev| (|getShellEntry| $ 19)))))
-
-(DEFUN |SINT;OMwrite;Omd$BV;5| (|dev| |x| |wholeObj| $)
- (SEQ (COND (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 18))))
- (|SINT;writeOMSingleInt| |dev| |x| $)
- (EXIT (COND
- (|wholeObj| (SPADCALL |dev| (|getShellEntry| $ 19)))))))
-
-(PUT '|SINT;reducedSystem;MM;6| '|SPADreplace| '(XLAM (|m|) |m|))
-
-(DEFUN |SINT;reducedSystem;MM;6| (|m| $) |m|)
-
-(DEFUN |SINT;coerce;$Of;7| (|x| $)
- (SPADCALL |x| (|getShellEntry| $ 30)))
-
-(PUT '|SINT;convert;$I;8| '|SPADreplace| '(XLAM (|x|) |x|))
-
-(DEFUN |SINT;convert;$I;8| (|x| $) |x|)
-
-(DEFUN |SINT;*;I2$;9| (|i| |y| $)
- (QSTIMES (SPADCALL |i| (|getShellEntry| $ 33)) |y|))
-
-(PUT '|SINT;Zero;$;10| '|SPADreplace| '(XLAM NIL 0))
-
-(DEFUN |SINT;Zero;$;10| ($) 0)
-
-(PUT '|SINT;One;$;11| '|SPADreplace| '(XLAM NIL 1))
-
-(DEFUN |SINT;One;$;11| ($) 1)
-
-(PUT '|SINT;base;$;12| '|SPADreplace| '(XLAM NIL 2))
-
-(DEFUN |SINT;base;$;12| ($) 2)
-
-(PUT '|SINT;max;$;13| '|SPADreplace| '(XLAM NIL MOST-POSITIVE-FIXNUM))
-
-(DEFUN |SINT;max;$;13| ($) MOST-POSITIVE-FIXNUM)
-
-(PUT '|SINT;min;$;14| '|SPADreplace| '(XLAM NIL MOST-NEGATIVE-FIXNUM))
-
-(DEFUN |SINT;min;$;14| ($) MOST-NEGATIVE-FIXNUM)
-
-(PUT '|SINT;=;2$B;15| '|SPADreplace| 'EQL)
-
-(DEFUN |SINT;=;2$B;15| (|x| |y| $) (EQL |x| |y|))
-
-(PUT '|SINT;~;2$;16| '|SPADreplace| 'LOGNOT)
-
-(DEFUN |SINT;~;2$;16| (|x| $) (LOGNOT |x|))
-
-(PUT '|SINT;not;2$;17| '|SPADreplace| 'LOGNOT)
-
-(DEFUN |SINT;not;2$;17| (|x| $) (LOGNOT |x|))
-
-(PUT '|SINT;/\\;3$;18| '|SPADreplace| 'LOGAND)
-
-(DEFUN |SINT;/\\;3$;18| (|x| |y| $) (LOGAND |x| |y|))
-
-(PUT '|SINT;\\/;3$;19| '|SPADreplace| 'LOGIOR)
-
-(DEFUN |SINT;\\/;3$;19| (|x| |y| $) (LOGIOR |x| |y|))
-
-(PUT '|SINT;Not;2$;20| '|SPADreplace| 'LOGNOT)
-
-(DEFUN |SINT;Not;2$;20| (|x| $) (LOGNOT |x|))
-
-(PUT '|SINT;And;3$;21| '|SPADreplace| 'LOGAND)
-
-(DEFUN |SINT;And;3$;21| (|x| |y| $) (LOGAND |x| |y|))
-
-(PUT '|SINT;Or;3$;22| '|SPADreplace| 'LOGIOR)
-
-(DEFUN |SINT;Or;3$;22| (|x| |y| $) (LOGIOR |x| |y|))
-
-(PUT '|SINT;xor;3$;23| '|SPADreplace| 'LOGXOR)
-
-(DEFUN |SINT;xor;3$;23| (|x| |y| $) (LOGXOR |x| |y|))
-
-(PUT '|SINT;<;2$B;24| '|SPADreplace| 'QSLESSP)
-
-(DEFUN |SINT;<;2$B;24| (|x| |y| $) (QSLESSP |x| |y|))
-
-(PUT '|SINT;inc;2$;25| '|SPADreplace| 'QSADD1)
-
-(DEFUN |SINT;inc;2$;25| (|x| $) (QSADD1 |x|))
-
-(PUT '|SINT;dec;2$;26| '|SPADreplace| 'QSSUB1)
-
-(DEFUN |SINT;dec;2$;26| (|x| $) (QSSUB1 |x|))
-
-(PUT '|SINT;-;2$;27| '|SPADreplace| 'QSMINUS)
-
-(DEFUN |SINT;-;2$;27| (|x| $) (QSMINUS |x|))
-
-(PUT '|SINT;+;3$;28| '|SPADreplace| 'QSPLUS)
-
-(DEFUN |SINT;+;3$;28| (|x| |y| $) (QSPLUS |x| |y|))
-
-(PUT '|SINT;-;3$;29| '|SPADreplace| 'QSDIFFERENCE)
-
-(DEFUN |SINT;-;3$;29| (|x| |y| $) (QSDIFFERENCE |x| |y|))
-
-(PUT '|SINT;*;3$;30| '|SPADreplace| 'QSTIMES)
-
-(DEFUN |SINT;*;3$;30| (|x| |y| $) (QSTIMES |x| |y|))
-
-(DEFUN |SINT;**;$Nni$;31| (|x| |n| $)
- (SPADCALL (EXPT |x| |n|) (|getShellEntry| $ 33)))
-
-(PUT '|SINT;quo;3$;32| '|SPADreplace| 'QSQUOTIENT)
-
-(DEFUN |SINT;quo;3$;32| (|x| |y| $) (QSQUOTIENT |x| |y|))
-
-(PUT '|SINT;rem;3$;33| '|SPADreplace| 'QSREMAINDER)
-
-(DEFUN |SINT;rem;3$;33| (|x| |y| $) (QSREMAINDER |x| |y|))
-
-(DEFUN |SINT;divide;2$R;34| (|x| |y| $)
- (CONS (QSQUOTIENT |x| |y|) (QSREMAINDER |x| |y|)))
-
-(PUT '|SINT;gcd;3$;35| '|SPADreplace| 'GCD)
-
-(DEFUN |SINT;gcd;3$;35| (|x| |y| $) (GCD |x| |y|))
-
-(PUT '|SINT;abs;2$;36| '|SPADreplace| 'QSABSVAL)
-
-(DEFUN |SINT;abs;2$;36| (|x| $) (QSABSVAL |x|))
-
-(PUT '|SINT;odd?;$B;37| '|SPADreplace| 'QSODDP)
-
-(DEFUN |SINT;odd?;$B;37| (|x| $) (QSODDP |x|))
-
-(PUT '|SINT;zero?;$B;38| '|SPADreplace| 'QSZEROP)
-
-(DEFUN |SINT;zero?;$B;38| (|x| $) (QSZEROP |x|))
-
-(PUT '|SINT;one?;$B;39| '|SPADreplace| '(XLAM (|x|) (EQL |x| 1)))
-
-(DEFUN |SINT;one?;$B;39| (|x| $) (EQL |x| 1))
-
-(PUT '|SINT;max;3$;40| '|SPADreplace| 'QSMAX)
-
-(DEFUN |SINT;max;3$;40| (|x| |y| $) (QSMAX |x| |y|))
-
-(PUT '|SINT;min;3$;41| '|SPADreplace| 'QSMIN)
-
-(DEFUN |SINT;min;3$;41| (|x| |y| $) (QSMIN |x| |y|))
-
-(PUT '|SINT;hash;2$;42| '|SPADreplace| 'HASHEQ)
-
-(DEFUN |SINT;hash;2$;42| (|x| $) (HASHEQ |x|))
-
-(PUT '|SINT;length;2$;43| '|SPADreplace| 'INTEGER-LENGTH)
-
-(DEFUN |SINT;length;2$;43| (|x| $) (INTEGER-LENGTH |x|))
-
-(PUT '|SINT;shift;3$;44| '|SPADreplace| 'QSLEFTSHIFT)
-
-(DEFUN |SINT;shift;3$;44| (|x| |n| $) (QSLEFTSHIFT |x| |n|))
-
-(PUT '|SINT;mulmod;4$;45| '|SPADreplace| 'QSMULTMOD)
-
-(DEFUN |SINT;mulmod;4$;45| (|a| |b| |p| $) (QSMULTMOD |a| |b| |p|))
-
-(PUT '|SINT;addmod;4$;46| '|SPADreplace| 'QSADDMOD)
-
-(DEFUN |SINT;addmod;4$;46| (|a| |b| |p| $) (QSADDMOD |a| |b| |p|))
-
-(PUT '|SINT;submod;4$;47| '|SPADreplace| 'QSDIFMOD)
-
-(DEFUN |SINT;submod;4$;47| (|a| |b| |p| $) (QSDIFMOD |a| |b| |p|))
-
-(PUT '|SINT;negative?;$B;48| '|SPADreplace| 'QSMINUSP)
-
-(DEFUN |SINT;negative?;$B;48| (|x| $) (QSMINUSP |x|))
-
-(PUT '|SINT;reducedSystem;MVR;49| '|SPADreplace| 'CONS)
-
-(DEFUN |SINT;reducedSystem;MVR;49| (|m| |v| $) (CONS |m| |v|))
-
-(DEFUN |SINT;positiveRemainder;3$;50| (|x| |n| $)
- (PROG (|r|)
- (RETURN
- (SEQ (LETT |r| (QSREMAINDER |x| |n|)
- |SINT;positiveRemainder;3$;50|)
- (EXIT (COND
- ((QSMINUSP |r|)
- (COND
- ((QSMINUSP |n|) (QSDIFFERENCE |x| |n|))
- ('T (QSPLUS |r| |n|))))
- ('T |r|)))))))
-
-(DEFUN |SINT;coerce;I$;51| (|x| $)
- (SEQ (COND
- ((NULL (< MOST-POSITIVE-FIXNUM |x|))
- (COND ((NULL (< |x| MOST-NEGATIVE-FIXNUM)) (EXIT |x|)))))
- (EXIT (|error| "integer too large to represent in a machine word"))))
-
-(DEFUN |SINT;random;$;52| ($)
- (SEQ (SETELT $ 6
- (REMAINDER (TIMES 314159269 (|getShellEntry| $ 6))
- 2147483647))
- (EXIT (REMAINDER (|getShellEntry| $ 6) 67108864))))
-
-(PUT '|SINT;random;2$;53| '|SPADreplace| 'RANDOM)
-
-(DEFUN |SINT;random;2$;53| (|n| $) (RANDOM |n|))
-
-(DEFUN |SINT;unitNormal;$R;54| (|x| $)
- (COND
- ((QSLESSP |x| 0) (VECTOR -1 (QSMINUS |x|) -1))
- ('T (VECTOR 1 |x| 1))))
-
-(DEFUN |SingleInteger| ()
- (PROG ()
- (RETURN
- (PROG (#0=#:G1486)
- (RETURN
- (COND
- ((LETT #0# (HGET |$ConstructorCache| '|SingleInteger|)
- |SingleInteger|)
- (|CDRwithIncrement| (CDAR #0#)))
- ('T
- (UNWIND-PROTECT
- (PROG1 (CDDAR (HPUT |$ConstructorCache| '|SingleInteger|
- (LIST
- (CONS NIL
- (CONS 1 (|SingleInteger;|))))))
- (LETT #0# T |SingleInteger|))
- (COND
- ((NOT #0#)
- (HREM |$ConstructorCache| '|SingleInteger|)))))))))))
-
-(DEFUN |SingleInteger;| ()
- (PROG (|dv$| $ |pv$|)
- (RETURN
- (PROGN
- (LETT |dv$| '(|SingleInteger|) . #0=(|SingleInteger|))
- (LETT $ (|newShell| 105) . #0#)
- (|setShellEntry| $ 0 |dv$|)
- (|setShellEntry| $ 3
- (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#))
- (|haddProp| |$ConstructorCache| '|SingleInteger| NIL
- (CONS 1 $))
- (|stuffDomainSlots| $)
- (|setShellEntry| $ 6 1)
- $))))
-
-(MAKEPROP '|SingleInteger| '|infovec|
- (LIST '#(NIL NIL NIL NIL NIL NIL '|seed| (|Void|)
- (|OpenMathDevice|) (0 . |OMputApp|) (|String|)
- (5 . |OMputSymbol|) (|Integer|) (12 . |OMputInteger|)
- (18 . |OMputEndApp|) (|OpenMathEncoding|)
- (23 . |OMencodingXML|) (27 . |OMopenString|)
- (33 . |OMputObject|) (38 . |OMputEndObject|)
- (43 . |OMclose|) |SINT;OMwrite;$S;2| (|Boolean|)
- |SINT;OMwrite;$BS;3| |SINT;OMwrite;Omd$V;4|
- |SINT;OMwrite;Omd$BV;5| (|Matrix| 12) (|Matrix| $)
- |SINT;reducedSystem;MM;6| (|OutputForm|) (48 . |coerce|)
- |SINT;coerce;$Of;7| |SINT;convert;$I;8| (53 . |coerce|)
- |SINT;*;I2$;9|
- (CONS IDENTITY
- (FUNCALL (|dispatchFunction| |SINT;Zero;$;10|) $))
- (CONS IDENTITY
- (FUNCALL (|dispatchFunction| |SINT;One;$;11|) $))
- |SINT;base;$;12| |SINT;max;$;13| |SINT;min;$;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;24| |SINT;inc;2$;25| |SINT;dec;2$;26|
- |SINT;-;2$;27| |SINT;+;3$;28| |SINT;-;3$;29|
- |SINT;*;3$;30| (|NonNegativeInteger|) |SINT;**;$Nni$;31|
- |SINT;quo;3$;32| |SINT;rem;3$;33|
- (|Record| (|:| |quotient| $) (|:| |remainder| $))
- |SINT;divide;2$R;34| |SINT;gcd;3$;35| |SINT;abs;2$;36|
- |SINT;odd?;$B;37| |SINT;zero?;$B;38| |SINT;one?;$B;39|
- |SINT;max;3$;40| |SINT;min;3$;41| |SINT;hash;2$;42|
- |SINT;length;2$;43| |SINT;shift;3$;44| |SINT;mulmod;4$;45|
- |SINT;addmod;4$;46| |SINT;submod;4$;47|
- |SINT;negative?;$B;48| (|Vector| 12)
- (|Record| (|:| |mat| 26) (|:| |vec| 76)) (|Vector| $)
- |SINT;reducedSystem;MVR;49| |SINT;positiveRemainder;3$;50|
- |SINT;coerce;I$;51| |SINT;random;$;52| |SINT;random;2$;53|
- (|Record| (|:| |unit| $) (|:| |canonical| $)
- (|:| |associate| $))
- |SINT;unitNormal;$R;54| (|Fraction| 12)
- (|Union| 86 '"failed") (|Union| $ '"failed") (|Float|)
- (|DoubleFloat|) (|Pattern| 12) (|PatternMatchResult| 12 $)
- (|InputForm|) (|Union| 12 '"failed") (|List| $)
- (|Record| (|:| |coef| 95) (|:| |generator| $))
- (|Union| 95 '"failed")
- (|Record| (|:| |coef1| $) (|:| |coef2| $)
- (|:| |generator| $))
- (|Record| (|:| |coef1| $) (|:| |coef2| $))
- (|Union| 99 '"failed") (|Factored| $)
- (|SparseUnivariatePolynomial| $) (|PositiveInteger|)
- (|SingleInteger|))
- '#(~= 58 ~ 64 |zero?| 69 |xor| 74 |unitNormal| 80
- |unitCanonical| 85 |unit?| 90 |symmetricRemainder| 95
- |subtractIfCan| 101 |submod| 107 |squareFreePart| 114
- |squareFree| 119 |sizeLess?| 124 |sign| 130 |shift| 135
- |sample| 141 |retractIfCan| 145 |retract| 150 |rem| 155
- |reducedSystem| 161 |recip| 172 |rationalIfCan| 177
- |rational?| 182 |rational| 187 |random| 192 |quo| 201
- |principalIdeal| 207 |prime?| 212 |powmod| 217
- |positiveRemainder| 224 |positive?| 230 |permutation| 235
- |patternMatch| 241 |one?| 248 |odd?| 253 |not| 258
- |nextItem| 263 |negative?| 268 |multiEuclidean| 273
- |mulmod| 279 |min| 286 |max| 296 |mask| 306 |length| 311
- |lcm| 316 |latex| 327 |invmod| 332 |init| 338 |inc| 342
- |hash| 347 |gcdPolynomial| 357 |gcd| 363 |factorial| 374
- |factor| 379 |extendedEuclidean| 384 |exquo| 397
- |expressIdealMember| 403 |even?| 409 |euclideanSize| 414
- |divide| 419 |differentiate| 425 |dec| 436 |copy| 441
- |convert| 446 |coerce| 471 |characteristic| 491 |bit?| 495
- |binomial| 501 |base| 507 |associates?| 511 |addmod| 517
- |abs| 524 ^ 529 |\\/| 541 |Zero| 547 |Or| 551 |One| 557
- |OMwrite| 561 |Not| 585 D 590 |And| 601 >= 607 > 613 = 619
- <= 625 < 631 |/\\| 637 - 643 + 654 ** 660 * 672)
- '((|noetherian| . 0) (|canonicalsClosed| . 0)
- (|canonical| . 0) (|canonicalUnitNormal| . 0)
- (|multiplicativeValuation| . 0) (|noZeroDivisors| . 0)
- ((|commutative| "*") . 0) (|rightUnitary| . 0)
- (|leftUnitary| . 0) (|unitsKnown| . 0))
- (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))
- (CONS '#(|IntegerNumberSystem&| |EuclideanDomain&|
- |UniqueFactorizationDomain&| NIL NIL
- |GcdDomain&| |IntegralDomain&| |Algebra&| NIL
- NIL |DifferentialRing&| |OrderedRing&| NIL NIL
- |Module&| NIL NIL |Ring&| NIL NIL NIL NIL NIL
- |AbelianGroup&| NIL NIL |AbelianMonoid&|
- |Monoid&| NIL NIL |OrderedSet&|
- |AbelianSemiGroup&| |SemiGroup&| |Logic&| NIL
- |SetCategory&| NIL NIL NIL NIL NIL NIL
- |RetractableTo&| NIL |BasicType&| NIL)
- (CONS '#((|IntegerNumberSystem|)
- (|EuclideanDomain|)
- (|UniqueFactorizationDomain|)
- (|PrincipalIdealDomain|)
- (|OrderedIntegralDomain|) (|GcdDomain|)
- (|IntegralDomain|) (|Algebra| $$)
- (|CharacteristicZero|)
- (|LinearlyExplicitRingOver| 12)
- (|DifferentialRing|) (|OrderedRing|)
- (|CommutativeRing|) (|EntireRing|)
- (|Module| $$) (|OrderedAbelianGroup|)
- (|BiModule| $$ $$) (|Ring|)
- (|OrderedCancellationAbelianMonoid|)
- (|LeftModule| $$) (|Rng|)
- (|RightModule| $$)
- (|OrderedAbelianMonoid|)
- (|AbelianGroup|)
- (|OrderedAbelianSemiGroup|)
- (|CancellationAbelianMonoid|)
- (|AbelianMonoid|) (|Monoid|)
- (|StepThrough|) (|PatternMatchable| 12)
- (|OrderedSet|) (|AbelianSemiGroup|)
- (|SemiGroup|) (|Logic|) (|RealConstant|)
- (|SetCategory|) (|OpenMath|)
- (|ConvertibleTo| 89)
- (|ConvertibleTo| 90)
- (|CombinatorialFunctionCategory|)
- (|ConvertibleTo| 91)
- (|ConvertibleTo| 93)
- (|RetractableTo| 12)
- (|ConvertibleTo| 12) (|BasicType|)
- (|CoercibleTo| 29))
- (|makeByteWordVec2| 104
- '(1 8 7 0 9 3 8 7 0 10 10 11 2 8 7 0 12
- 13 1 8 7 0 14 0 15 0 16 2 8 0 10 15
- 17 1 8 7 0 18 1 8 7 0 19 1 8 7 0 20 1
- 12 29 0 30 1 0 0 12 33 2 0 22 0 0 1 1
- 0 0 0 41 1 0 22 0 65 2 0 0 0 0 48 1 0
- 84 0 85 1 0 0 0 1 1 0 22 0 1 2 0 0 0
- 0 1 2 0 88 0 0 1 3 0 0 0 0 0 74 1 0 0
- 0 1 1 0 101 0 1 2 0 22 0 0 1 1 0 12 0
- 1 2 0 0 0 0 71 0 0 0 1 1 0 94 0 1 1 0
- 12 0 1 2 0 0 0 0 59 1 0 26 27 28 2 0
- 77 27 78 79 1 0 88 0 1 1 0 87 0 1 1 0
- 22 0 1 1 0 86 0 1 1 0 0 0 83 0 0 0 82
- 2 0 0 0 0 58 1 0 96 95 1 1 0 22 0 1 3
- 0 0 0 0 0 1 2 0 0 0 0 80 1 0 22 0 1 2
- 0 0 0 0 1 3 0 92 0 91 92 1 1 0 22 0
- 66 1 0 22 0 64 1 0 0 0 42 1 0 88 0 1
- 1 0 22 0 75 2 0 97 95 0 1 3 0 0 0 0 0
- 72 0 0 0 39 2 0 0 0 0 68 0 0 0 38 2 0
- 0 0 0 67 1 0 0 0 1 1 0 0 0 70 1 0 0
- 95 1 2 0 0 0 0 1 1 0 10 0 1 2 0 0 0 0
- 1 0 0 0 1 1 0 0 0 50 1 0 0 0 69 1 0
- 104 0 1 2 0 102 102 102 1 1 0 0 95 1
- 2 0 0 0 0 62 1 0 0 0 1 1 0 101 0 1 2
- 0 98 0 0 1 3 0 100 0 0 0 1 2 0 88 0 0
- 1 2 0 97 95 0 1 1 0 22 0 1 1 0 56 0 1
- 2 0 60 0 0 61 1 0 0 0 1 2 0 0 0 56 1
- 1 0 0 0 51 1 0 0 0 1 1 0 89 0 1 1 0
- 90 0 1 1 0 91 0 1 1 0 93 0 1 1 0 12 0
- 32 1 0 0 12 81 1 0 0 0 1 1 0 0 12 81
- 1 0 29 0 31 0 0 56 1 2 0 22 0 0 1 2 0
- 0 0 0 1 0 0 0 37 2 0 22 0 0 1 3 0 0 0
- 0 0 73 1 0 0 0 63 2 0 0 0 56 1 2 0 0
- 0 103 1 2 0 0 0 0 44 0 0 0 35 2 0 0 0
- 0 47 0 0 0 36 3 0 7 8 0 22 25 2 0 10
- 0 22 23 2 0 7 8 0 24 1 0 10 0 21 1 0
- 0 0 45 1 0 0 0 1 2 0 0 0 56 1 2 0 0 0
- 0 46 2 0 22 0 0 1 2 0 22 0 0 1 2 0 22
- 0 0 40 2 0 22 0 0 1 2 0 22 0 0 49 2 0
- 0 0 0 43 1 0 0 0 52 2 0 0 0 0 54 2 0
- 0 0 0 53 2 0 0 0 56 57 2 0 0 0 103 1
- 2 0 0 0 0 55 2 0 0 12 0 34 2 0 0 56 0
- 1 2 0 0 103 0 1)))))
- '|lookupComplete|))
-
-(MAKEPROP '|SingleInteger| 'NILADIC T)
-@
\section{License}
generated by cgit v1.2.3 (git 2.39.1) at 2024-09-17 07:02:38 +0000