(/VERSIONCHECK 2) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Boolean|) |EUCDOM-;sizeLess?;2SB;1|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |EUCDOM-;quo;3S;2|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |EUCDOM-;rem;3S;3|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Pair|) |EUCDOM-;exquo;2SU;4|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Thing|) |EUCDOM-;gcd;3S;5|)) (DECLAIM (FTYPE (FUNCTION (|%Shell| |%Shell|) |%Shell|) |EUCDOM-;unitNormalizeIdealElt|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Shell|) |%Shell|) |EUCDOM-;extendedEuclidean;2SR;7|)) (DECLAIM (FTYPE (FUNCTION (|%Thing| |%Thing| |%Thing| |%Shell|) |%Pair|) |EUCDOM-;extendedEuclidean;3SU;8|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Shell|) |%Pair|) |EUCDOM-;principalIdeal;LR;9|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Thing| |%Shell|) |%Pair|) |EUCDOM-;expressIdealMember;LSU;10|)) (DECLAIM (FTYPE (FUNCTION (|%List| |%Thing| |%Shell|) |%Pair|) |EUCDOM-;multiEuclidean;LSU;11|)) (DEFUN |EUCDOM-;sizeLess?;2SB;1| (|x| |y| $) (AND (NOT (SPADCALL |y| (|shellEntry| $ 8))) (OR (SPADCALL |x| (|shellEntry| $ 8)) (< (SPADCALL |x| (|shellEntry| $ 12)) (SPADCALL |y| (|shellEntry| $ 12)))))) (DEFUN |EUCDOM-;quo;3S;2| (|x| |y| $) (CAR (SPADCALL |x| |y| (|shellEntry| $ 16)))) (DEFUN |EUCDOM-;rem;3S;3| (|x| |y| $) (CDR (SPADCALL |x| |y| (|shellEntry| $ 16)))) (DEFUN |EUCDOM-;exquo;2SU;4| (|x| |y| $) (COND ((SPADCALL |x| (|shellEntry| $ 8)) (CONS 0 (|spadConstant| $ 19))) ((SPADCALL |y| (|shellEntry| $ 8)) (CONS 1 "failed")) (T (LET ((|qr| (SPADCALL |x| |y| (|shellEntry| $ 16)))) (COND ((SPADCALL (CDR |qr|) (|shellEntry| $ 8)) (CONS 0 (CAR |qr|))) (T (CONS 1 "failed"))))))) (DEFUN |EUCDOM-;gcd;3S;5| (|x| |y| $) (PROG (|#G13| |#G14|) (RETURN (SEQ (SETQ |x| (SPADCALL |x| (|shellEntry| $ 22))) (SETQ |y| (SPADCALL |y| (|shellEntry| $ 22))) (LOOP (COND ((NOT (NOT (SPADCALL |y| (|shellEntry| $ 8)))) (RETURN NIL)) (T (SEQ (LETT |#G13| |y| |EUCDOM-;gcd;3S;5|) (LETT |#G14| (SPADCALL |x| |y| (|shellEntry| $ 24)) |EUCDOM-;gcd;3S;5|) (SETQ |x| |#G13|) (SETQ |y| |#G14|) (EXIT (SETQ |y| (SPADCALL |y| (|shellEntry| $ 22)))))))) (EXIT |x|))))) (DEFUN |EUCDOM-;unitNormalizeIdealElt| (|s| $) (LET* ((|#G16| (SPADCALL (SVREF |s| 2) (|shellEntry| $ 27))) (|u| (SVREF |#G16| 0)) (|c| (SVREF |#G16| 1)) (|a| (SVREF |#G16| 2))) (SEQ |#G16| (EXIT (COND ((SPADCALL |a| (|shellEntry| $ 28)) |s|) (T (VECTOR (SPADCALL |a| (SVREF |s| 0) (|shellEntry| $ 29)) (SPADCALL |a| (SVREF |s| 1) (|shellEntry| $ 29)) |c|))))))) (DEFUN |EUCDOM-;extendedEuclidean;2SR;7| (|x| |y| $) (PROG (|qr| |s3|) (RETURN (LET ((|s1| (|EUCDOM-;unitNormalizeIdealElt| (VECTOR (|spadConstant| $ 30) (|spadConstant| $ 19) |x|) $)) (|s2| (|EUCDOM-;unitNormalizeIdealElt| (VECTOR (|spadConstant| $ 19) (|spadConstant| $ 30) |y|) $))) (COND ((SPADCALL |y| (|shellEntry| $ 8)) |s1|) ((SPADCALL |x| (|shellEntry| $ 8)) |s2|) (T (SEQ (LOOP (COND ((NOT (NOT (SPADCALL (SVREF |s2| 2) (|shellEntry| $ 8)))) (RETURN NIL)) (T (SEQ (LETT |qr| (SPADCALL (SVREF |s1| 2) (SVREF |s2| 2) (|shellEntry| $ 16)) |EUCDOM-;extendedEuclidean;2SR;7|) (LETT |s3| (VECTOR (SPADCALL (SVREF |s1| 0) (SPADCALL (CAR |qr|) (SVREF |s2| 0) (|shellEntry| $ 29)) (|shellEntry| $ 31)) (SPADCALL (SVREF |s1| 1) (SPADCALL (CAR |qr|) (SVREF |s2| 1) (|shellEntry| $ 29)) (|shellEntry| $ 31)) (CDR |qr|)) |EUCDOM-;extendedEuclidean;2SR;7|) (SETQ |s1| |s2|) (EXIT (SETQ |s2| (|EUCDOM-;unitNormalizeIdealElt| |s3| $))))))) (COND ((AND (NOT (SPADCALL (SVREF |s1| 0) (|shellEntry| $ 8))) (NOT (SPADCALL (SVREF |s1| 0) |y| (|shellEntry| $ 32)))) (SEQ (SETQ |qr| (SPADCALL (SVREF |s1| 0) |y| (|shellEntry| $ 16))) (SETF (SVREF |s1| 0) (CDR |qr|)) (SETF (SVREF |s1| 1) (SPADCALL (SVREF |s1| 1) (SPADCALL (CAR |qr|) |x| (|shellEntry| $ 29)) (|shellEntry| $ 33))) (EXIT (SETQ |s1| (|EUCDOM-;unitNormalizeIdealElt| |s1| $)))))) (EXIT |s1|)))))))) (DEFUN |EUCDOM-;extendedEuclidean;3SU;8| (|x| |y| |z| $) (PROG (|qr|) (RETURN (COND ((SPADCALL |z| (|shellEntry| $ 8)) (CONS 0 (CONS (|spadConstant| $ 19) (|spadConstant| $ 19)))) (T (LET* ((|s| (SPADCALL |x| |y| (|shellEntry| $ 36))) (|w| (SPADCALL |z| (SVREF |s| 2) (|shellEntry| $ 37)))) (COND ((EQL (CAR |w|) 1) (CONS 1 "failed")) ((SPADCALL |y| (|shellEntry| $ 8)) (CONS 0 (CONS (SPADCALL (SVREF |s| 0) (CDR |w|) (|shellEntry| $ 29)) (SPADCALL (SVREF |s| 1) (CDR |w|) (|shellEntry| $ 29))))) (T (SEQ (LETT |qr| (SPADCALL (SPADCALL (SVREF |s| 0) (CDR |w|) (|shellEntry| $ 29)) |y| (|shellEntry| $ 16)) |EUCDOM-;extendedEuclidean;3SU;8|) (EXIT (CONS 0 (CONS (CDR |qr|) (SPADCALL (SPADCALL (SVREF |s| 1) (CDR |w|) (|shellEntry| $ 29)) (SPADCALL (CAR |qr|) |x| (|shellEntry| $ 29)) (|shellEntry| $ 33)))))))))))))) (DEFUN |EUCDOM-;principalIdeal;LR;9| (|l| $) (COND ((SPADCALL |l| NIL (|shellEntry| $ 42)) (|error| "empty list passed to principalIdeal")) ((SPADCALL (CDR |l|) NIL (|shellEntry| $ 42)) (LET ((|uca| (SPADCALL (|SPADfirst| |l|) (|shellEntry| $ 27)))) (CONS (LIST (SVREF |uca| 0)) (SVREF |uca| 1)))) ((SPADCALL (CDR (CDR |l|)) NIL (|shellEntry| $ 42)) (LET ((|u| (SPADCALL (|SPADfirst| |l|) (SPADCALL |l| (|shellEntry| $ 45)) (|shellEntry| $ 36)))) (CONS (LIST (SVREF |u| 0) (SVREF |u| 1)) (SVREF |u| 2)))) (T (LET* ((|v| (SPADCALL (CDR |l|) (|shellEntry| $ 48))) (|u| (SPADCALL (|SPADfirst| |l|) (CDR |v|) (|shellEntry| $ 36)))) (CONS (CONS (SVREF |u| 0) (LET ((#0=#:G1494 (CAR |v|)) (#1=#:G1493 NIL)) (LOOP (COND ((ATOM #0#) (RETURN (NREVERSE #1#))) (T (LET ((|vv| (CAR #0#))) (SETQ #1# (CONS (SPADCALL (SVREF |u| 1) |vv| (|shellEntry| $ 29)) #1#))))) (SETQ #0# (CDR #0#))))) (SVREF |u| 2)))))) (DEFUN |EUCDOM-;expressIdealMember;LSU;10| (|l| |z| $) (COND ((SPADCALL |z| (|spadConstant| $ 19) (|shellEntry| $ 51)) (CONS 0 (LET ((#0=#:G1496 |l|) (#1=#:G1495 NIL)) (LOOP (COND ((ATOM #0#) (RETURN (NREVERSE #1#))) (T (LET ((|v| (CAR #0#))) (SETQ #1# (CONS (|spadConstant| $ 19) #1#))))) (SETQ #0# (CDR #0#)))))) (T (LET* ((|pid| (SPADCALL |l| (|shellEntry| $ 48))) (|q| (SPADCALL |z| (CDR |pid|) (|shellEntry| $ 37)))) (COND ((EQL (CAR |q|) 1) (CONS 1 "failed")) (T (CONS 0 (LET ((#2=#:G1498 (CAR |pid|)) (#3=#:G1497 NIL)) (LOOP (COND ((ATOM #2#) (RETURN (NREVERSE #3#))) (T (LET ((|v| (CAR #2#))) (SETQ #3# (CONS (SPADCALL (CDR |q|) |v| (|shellEntry| $ 29)) #3#))))) (SETQ #2# (CDR #2#))))))))))) (DEFUN |EUCDOM-;multiEuclidean;LSU;11| (|l| |z| $) (PROG (|l1| |l2| |u| |v1| |v2|) (RETURN (LET ((|n| (LIST-LENGTH |l|))) (COND ((ZEROP |n|) (|error| "empty list passed to multiEuclidean")) ((EQL |n| 1) (CONS 0 (LIST |z|))) (T (SEQ (LETT |l1| (SPADCALL |l| (|shellEntry| $ 58)) |EUCDOM-;multiEuclidean;LSU;11|) (LETT |l2| (SPADCALL |l1| (TRUNCATE |n| 2) (|shellEntry| $ 61)) |EUCDOM-;multiEuclidean;LSU;11|) (LETT |u| (SPADCALL (LET ((#0=#:G1479 NIL) (#1=#:G1480 T) (#2=#:G1499 |l1|)) (LOOP (COND ((ATOM #2#) (RETURN (COND (#1# (|spadConstant| $ 30)) (T #0#)))) (T (LET ((#3=#:G1372 (CAR #2#))) (LET ((#4=#:G1478 #3#)) (COND (#1# (SETQ #0# #4#)) (T (SETQ #0# (SPADCALL #0# #4# (|shellEntry| $ 29))))) (SETQ #1# NIL))))) (SETQ #2# (CDR #2#)))) (LET ((#5=#:G1482 NIL) (#6=#:G1483 T) (#7=#:G1500 |l2|)) (LOOP (COND ((ATOM #7#) (RETURN (COND (#6# (|spadConstant| $ 30)) (T #5#)))) (T (LET ((#8=#:G1373 (CAR #7#))) (LET ((#9=#:G1481 #8#)) (COND (#6# (SETQ #5# #9#)) (T (SETQ #5# (SPADCALL #5# #9# (|shellEntry| $ 29))))) (SETQ #6# NIL))))) (SETQ #7# (CDR #7#)))) |z| (|shellEntry| $ 62)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((EQL (CAR |u|) 1) (CONS 1 "failed")) (T (SEQ (LETT |v1| (SPADCALL |l1| (CDR (CDR |u|)) (|shellEntry| $ 63)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((EQL (CAR |v1|) 1) (CONS 1 "failed")) (T (SEQ (LETT |v2| (SPADCALL |l2| (CAR (CDR |u|)) (|shellEntry| $ 63)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((EQL (CAR |v2|) 1) (CONS 1 "failed")) (T (CONS 0 (SPADCALL (CDR |v1|) (CDR |v2|) (|shellEntry| $ 64))))))))))))))))))))) (DEFUN |EuclideanDomain&| (|#1|) (LET* ((|dv$1| (|devaluate| |#1|)) (|dv$| (LIST '|EuclideanDomain&| |dv$1|)) ($ (|newShell| 66)) (|pv$| (|buildPredVector| 0 0 NIL))) (SETF (|shellEntry| $ 0) |dv$|) (SETF (|shellEntry| $ 3) |pv$|) (|stuffDomainSlots| $) (SETF (|shellEntry| $ 6) |#1|) $)) (MAKEPROP '|EuclideanDomain&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (|Boolean|) (0 . |zero?|) (5 . |false|) (9 . |true|) (|NonNegativeInteger|) (13 . |euclideanSize|) (18 . <) |EUCDOM-;sizeLess?;2SB;1| (|Record| (|:| |quotient| $) (|:| |remainder| $)) (24 . |divide|) |EUCDOM-;quo;3S;2| |EUCDOM-;rem;3S;3| (30 . |Zero|) (|Union| $ '"failed") |EUCDOM-;exquo;2SU;4| (34 . |unitCanonical|) (39 . |not|) (44 . |rem|) |EUCDOM-;gcd;3S;5| (|Record| (|:| |unit| $) (|:| |canonical| $) (|:| |associate| $)) (50 . |unitNormal|) (55 . |one?|) (60 . *) (66 . |One|) (70 . -) (76 . |sizeLess?|) (82 . +) (|Record| (|:| |coef1| $) (|:| |coef2| $) (|:| |generator| $)) |EUCDOM-;extendedEuclidean;2SR;7| (88 . |extendedEuclidean|) (94 . |exquo|) (|Record| (|:| |coef1| $) (|:| |coef2| $)) (|Union| 38 '"failed") |EUCDOM-;extendedEuclidean;3SU;8| (|List| 6) (100 . =) (106 . |rest|) (111 . |first|) (116 . |second|) (|List| $) (|Record| (|:| |coef| 46) (|:| |generator| $)) (121 . |principalIdeal|) (126 . |cons|) |EUCDOM-;principalIdeal;LR;9| (132 . =) (|Union| 46 '"failed") |EUCDOM-;expressIdealMember;LSU;10| (138 . |#|) (143 . |zero?|) (148 . |One|) (152 . =) (158 . |copy|) (163 . |quo|) (|Integer|) (169 . |split!|) (175 . |extendedEuclidean|) (182 . |multiEuclidean|) (188 . |concat|) |EUCDOM-;multiEuclidean;LSU;11|) '#(|sizeLess?| 194 |rem| 200 |quo| 206 |principalIdeal| 212 |multiEuclidean| 217 |gcd| 223 |extendedEuclidean| 229 |exquo| 242 |expressIdealMember| 248) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() (|makeByteWordVec2| 65 '(1 6 7 0 8 0 7 0 9 0 7 0 10 1 6 11 0 12 2 11 7 0 0 13 2 6 15 0 0 16 0 6 0 19 1 6 0 0 22 1 7 0 0 23 2 6 0 0 0 24 1 6 26 0 27 1 6 7 0 28 2 6 0 0 0 29 0 6 0 30 2 6 0 0 0 31 2 6 7 0 0 32 2 6 0 0 0 33 2 6 34 0 0 36 2 6 20 0 0 37 2 41 7 0 0 42 1 41 0 0 43 1 41 6 0 44 1 41 6 0 45 1 6 47 46 48 2 41 0 6 0 49 2 6 7 0 0 51 1 41 11 0 54 1 11 7 0 55 0 11 0 56 2 11 7 0 0 57 1 41 0 0 58 2 11 0 0 0 59 2 41 0 0 60 61 3 6 39 0 0 0 62 2 6 52 46 0 63 2 41 0 0 0 64 2 0 7 0 0 14 2 0 0 0 0 18 2 0 0 0 0 17 1 0 47 46 50 2 0 52 46 0 65 2 0 0 0 0 25 3 0 39 0 0 0 40 2 0 34 0 0 35 2 0 20 0 0 21 2 0 52 46 0 53))))) '|lookupComplete|))