(/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| $) (COND ((SPADCALL |y| (|getShellEntry| $ 8)) NIL) ((SPADCALL |x| (|getShellEntry| $ 8)) T) ('T (< (SPADCALL |x| (|getShellEntry| $ 12)) (SPADCALL |y| (|getShellEntry| $ 12)))))) (DEFUN |EUCDOM-;quo;3S;2| (|x| |y| $) (CAR (SPADCALL |x| |y| (|getShellEntry| $ 16)))) (DEFUN |EUCDOM-;rem;3S;3| (|x| |y| $) (CDR (SPADCALL |x| |y| (|getShellEntry| $ 16)))) (DEFUN |EUCDOM-;exquo;2SU;4| (|x| |y| $) (PROG (|qr|) (RETURN (SEQ (COND ((SPADCALL |x| (|getShellEntry| $ 8)) (CONS 0 (|spadConstant| $ 19))) ((SPADCALL |y| (|getShellEntry| $ 8)) (CONS 1 "failed")) ('T (SEQ (LETT |qr| (SPADCALL |x| |y| (|getShellEntry| $ 16)) |EUCDOM-;exquo;2SU;4|) (EXIT (COND ((SPADCALL (CDR |qr|) (|getShellEntry| $ 8)) (CONS 0 (CAR |qr|))) ('T (CONS 1 "failed"))))))))))) (DEFUN |EUCDOM-;gcd;3S;5| (|x| |y| $) (PROG (|#G13| |#G14|) (RETURN (SEQ (LETT |x| (SPADCALL |x| (|getShellEntry| $ 22)) |EUCDOM-;gcd;3S;5|) (LETT |y| (SPADCALL |y| (|getShellEntry| $ 22)) |EUCDOM-;gcd;3S;5|) (SEQ G190 (COND ((NULL (NOT (SPADCALL |y| (|getShellEntry| $ 8)))) (GO G191))) (SEQ (LETT |#G13| |y| |EUCDOM-;gcd;3S;5|) (LETT |#G14| (SPADCALL |x| |y| (|getShellEntry| $ 24)) |EUCDOM-;gcd;3S;5|) (LETT |x| |#G13| |EUCDOM-;gcd;3S;5|) (LETT |y| |#G14| |EUCDOM-;gcd;3S;5|) (EXIT (LETT |y| (SPADCALL |y| (|getShellEntry| $ 22)) |EUCDOM-;gcd;3S;5|))) NIL (GO G190) G191 (EXIT NIL)) (EXIT |x|))))) (DEFUN |EUCDOM-;unitNormalizeIdealElt| (|s| $) (PROG (|#G16| |u| |c| |a|) (RETURN (SEQ (LETT |#G16| (SPADCALL (QVELT |s| 2) (|getShellEntry| $ 27)) |EUCDOM-;unitNormalizeIdealElt|) (LETT |u| (QVELT |#G16| 0) |EUCDOM-;unitNormalizeIdealElt|) (LETT |c| (QVELT |#G16| 1) |EUCDOM-;unitNormalizeIdealElt|) (LETT |a| (QVELT |#G16| 2) |EUCDOM-;unitNormalizeIdealElt|) |#G16| (EXIT (COND ((SPADCALL |a| (|getShellEntry| $ 28)) |s|) ('T (VECTOR (SPADCALL |a| (QVELT |s| 0) (|getShellEntry| $ 29)) (SPADCALL |a| (QVELT |s| 1) (|getShellEntry| $ 29)) |c|)))))))) (DEFUN |EUCDOM-;extendedEuclidean;2SR;7| (|x| |y| $) (PROG (|s3| |s2| |qr| |s1|) (RETURN (SEQ (LETT |s1| (|EUCDOM-;unitNormalizeIdealElt| (VECTOR (|spadConstant| $ 30) (|spadConstant| $ 19) |x|) $) |EUCDOM-;extendedEuclidean;2SR;7|) (LETT |s2| (|EUCDOM-;unitNormalizeIdealElt| (VECTOR (|spadConstant| $ 19) (|spadConstant| $ 30) |y|) $) |EUCDOM-;extendedEuclidean;2SR;7|) (EXIT (COND ((SPADCALL |y| (|getShellEntry| $ 8)) |s1|) ((SPADCALL |x| (|getShellEntry| $ 8)) |s2|) ('T (SEQ (SEQ G190 (COND ((NULL (NOT (SPADCALL (QVELT |s2| 2) (|getShellEntry| $ 8)))) (GO G191))) (SEQ (LETT |qr| (SPADCALL (QVELT |s1| 2) (QVELT |s2| 2) (|getShellEntry| $ 16)) |EUCDOM-;extendedEuclidean;2SR;7|) (LETT |s3| (VECTOR (SPADCALL (QVELT |s1| 0) (SPADCALL (CAR |qr|) (QVELT |s2| 0) (|getShellEntry| $ 29)) (|getShellEntry| $ 31)) (SPADCALL (QVELT |s1| 1) (SPADCALL (CAR |qr|) (QVELT |s2| 1) (|getShellEntry| $ 29)) (|getShellEntry| $ 31)) (CDR |qr|)) |EUCDOM-;extendedEuclidean;2SR;7|) (LETT |s1| |s2| |EUCDOM-;extendedEuclidean;2SR;7|) (EXIT (LETT |s2| (|EUCDOM-;unitNormalizeIdealElt| |s3| $) |EUCDOM-;extendedEuclidean;2SR;7|))) NIL (GO G190) G191 (EXIT NIL)) (COND ((NOT (SPADCALL (QVELT |s1| 0) (|getShellEntry| $ 8))) (COND ((NOT (SPADCALL (QVELT |s1| 0) |y| (|getShellEntry| $ 32))) (SEQ (LETT |qr| (SPADCALL (QVELT |s1| 0) |y| (|getShellEntry| $ 16)) |EUCDOM-;extendedEuclidean;2SR;7|) (QSETVELT |s1| 0 (CDR |qr|)) (QSETVELT |s1| 1 (SPADCALL (QVELT |s1| 1) (SPADCALL (CAR |qr|) |x| (|getShellEntry| $ 29)) (|getShellEntry| $ 33))) (EXIT (LETT |s1| (|EUCDOM-;unitNormalizeIdealElt| |s1| $) |EUCDOM-;extendedEuclidean;2SR;7|))))))) (EXIT |s1|))))))))) (DEFUN |EUCDOM-;extendedEuclidean;3SU;8| (|x| |y| |z| $) (PROG (|s| |w| |qr|) (RETURN (SEQ (COND ((SPADCALL |z| (|getShellEntry| $ 8)) (CONS 0 (CONS (|spadConstant| $ 19) (|spadConstant| $ 19)))) ('T (SEQ (LETT |s| (SPADCALL |x| |y| (|getShellEntry| $ 36)) |EUCDOM-;extendedEuclidean;3SU;8|) (LETT |w| (SPADCALL |z| (QVELT |s| 2) (|getShellEntry| $ 37)) |EUCDOM-;extendedEuclidean;3SU;8|) (EXIT (COND ((EQL (CAR |w|) 1) (CONS 1 "failed")) ((SPADCALL |y| (|getShellEntry| $ 8)) (CONS 0 (CONS (SPADCALL (QVELT |s| 0) (CDR |w|) (|getShellEntry| $ 29)) (SPADCALL (QVELT |s| 1) (CDR |w|) (|getShellEntry| $ 29))))) ('T (SEQ (LETT |qr| (SPADCALL (SPADCALL (QVELT |s| 0) (CDR |w|) (|getShellEntry| $ 29)) |y| (|getShellEntry| $ 16)) |EUCDOM-;extendedEuclidean;3SU;8|) (EXIT (CONS 0 (CONS (CDR |qr|) (SPADCALL (SPADCALL (QVELT |s| 1) (CDR |w|) (|getShellEntry| $ 29)) (SPADCALL (CAR |qr|) |x| (|getShellEntry| $ 29)) (|getShellEntry| $ 33)))))))))))))))) (DEFUN |EUCDOM-;principalIdeal;LR;9| (|l| $) (PROG (|uca| |v| |u|) (RETURN (SEQ (COND ((SPADCALL |l| NIL (|getShellEntry| $ 42)) (|error| "empty list passed to principalIdeal")) ((SPADCALL (CDR |l|) NIL (|getShellEntry| $ 42)) (SEQ (LETT |uca| (SPADCALL (|SPADfirst| |l|) (|getShellEntry| $ 27)) |EUCDOM-;principalIdeal;LR;9|) (EXIT (CONS (LIST (QVELT |uca| 0)) (QVELT |uca| 1))))) ((SPADCALL (CDR (CDR |l|)) NIL (|getShellEntry| $ 42)) (SEQ (LETT |u| (SPADCALL (|SPADfirst| |l|) (SPADCALL |l| (|getShellEntry| $ 45)) (|getShellEntry| $ 36)) |EUCDOM-;principalIdeal;LR;9|) (EXIT (CONS (LIST (QVELT |u| 0) (QVELT |u| 1)) (QVELT |u| 2))))) ('T (SEQ (LETT |v| (SPADCALL (CDR |l|) (|getShellEntry| $ 48)) |EUCDOM-;principalIdeal;LR;9|) (LETT |u| (SPADCALL (|SPADfirst| |l|) (CDR |v|) (|getShellEntry| $ 36)) |EUCDOM-;principalIdeal;LR;9|) (EXIT (CONS (CONS (QVELT |u| 0) (LET ((#0=#:G1519 (CAR |v|)) (#1=#:G1518 NIL)) (LOOP (COND ((ATOM #0#) (RETURN (NREVERSE #1#))) (T (LET ((|vv| (CAR #0#))) (SETQ #1# (CONS (SPADCALL (QVELT |u| 1) |vv| (|getShellEntry| $ 29)) #1#))))) (SETQ #0# (CDR #0#))))) (QVELT |u| 2)))))))))) (DEFUN |EUCDOM-;expressIdealMember;LSU;10| (|l| |z| $) (PROG (|pid| |q|) (RETURN (SEQ (COND ((SPADCALL |z| (|spadConstant| $ 19) (|getShellEntry| $ 51)) (CONS 0 (LET ((#0=#:G1521 |l|) (#1=#:G1520 NIL)) (LOOP (COND ((ATOM #0#) (RETURN (NREVERSE #1#))) (T (LET ((|v| (CAR #0#))) (SETQ #1# (CONS (|spadConstant| $ 19) #1#))))) (SETQ #0# (CDR #0#)))))) ('T (SEQ (LETT |pid| (SPADCALL |l| (|getShellEntry| $ 48)) |EUCDOM-;expressIdealMember;LSU;10|) (LETT |q| (SPADCALL |z| (CDR |pid|) (|getShellEntry| $ 37)) |EUCDOM-;expressIdealMember;LSU;10|) (EXIT (COND ((EQL (CAR |q|) 1) (CONS 1 "failed")) ('T (CONS 0 (LET ((#2=#:G1523 (CAR |pid|)) (#3=#:G1522 NIL)) (LOOP (COND ((ATOM #2#) (RETURN (NREVERSE #3#))) (T (LET ((|v| (CAR #2#))) (SETQ #3# (CONS (SPADCALL (CDR |q|) |v| (|getShellEntry| $ 29)) #3#))))) (SETQ #2# (CDR #2#))))))))))))))) (DEFUN |EUCDOM-;multiEuclidean;LSU;11| (|l| |z| $) (PROG (|n| |l1| |l2| #0=#:G1397 #1=#:G1524 #2=#:G1505 #3=#:G1503 #4=#:G1504 #5=#:G1398 #6=#:G1525 #7=#:G1508 #8=#:G1506 #9=#:G1507 |u| |v1| |v2|) (RETURN (SEQ (LETT |n| (LENGTH |l|) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((ZEROP |n|) (|error| "empty list passed to multiEuclidean")) ((EQL |n| 1) (CONS 0 (LIST |z|))) ('T (SEQ (LETT |l1| (SPADCALL |l| (|getShellEntry| $ 58)) |EUCDOM-;multiEuclidean;LSU;11|) (LETT |l2| (SPADCALL |l1| (QUOTIENT2 |n| 2) (|getShellEntry| $ 61)) |EUCDOM-;multiEuclidean;LSU;11|) (LETT |u| (SPADCALL (PROGN (LETT #4# NIL |EUCDOM-;multiEuclidean;LSU;11|) (SEQ (LETT #0# NIL |EUCDOM-;multiEuclidean;LSU;11|) (LETT #1# |l1| |EUCDOM-;multiEuclidean;LSU;11|) G190 (COND ((OR (ATOM #1#) (PROGN (SETQ #0# (CAR #1#)) NIL)) (GO G191))) (SEQ (EXIT (PROGN (LETT #2# #0# |EUCDOM-;multiEuclidean;LSU;11|) (COND (#4# (LETT #3# (SPADCALL #3# #2# (|getShellEntry| $ 29)) |EUCDOM-;multiEuclidean;LSU;11|)) ('T (PROGN (LETT #3# #2# |EUCDOM-;multiEuclidean;LSU;11|) (LETT #4# 'T |EUCDOM-;multiEuclidean;LSU;11|))))))) (SETQ #1# (CDR #1#)) (GO G190) G191 (EXIT NIL)) (COND (#4# #3#) ('T (|spadConstant| $ 30)))) (PROGN (LETT #9# NIL |EUCDOM-;multiEuclidean;LSU;11|) (SEQ (LETT #5# NIL |EUCDOM-;multiEuclidean;LSU;11|) (LETT #6# |l2| |EUCDOM-;multiEuclidean;LSU;11|) G190 (COND ((OR (ATOM #6#) (PROGN (SETQ #5# (CAR #6#)) NIL)) (GO G191))) (SEQ (EXIT (PROGN (LETT #7# #5# |EUCDOM-;multiEuclidean;LSU;11|) (COND (#9# (LETT #8# (SPADCALL #8# #7# (|getShellEntry| $ 29)) |EUCDOM-;multiEuclidean;LSU;11|)) ('T (PROGN (LETT #8# #7# |EUCDOM-;multiEuclidean;LSU;11|) (LETT #9# 'T |EUCDOM-;multiEuclidean;LSU;11|))))))) (SETQ #6# (CDR #6#)) (GO G190) G191 (EXIT NIL)) (COND (#9# #8#) ('T (|spadConstant| $ 30)))) |z| (|getShellEntry| $ 62)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((EQL (CAR |u|) 1) (CONS 1 "failed")) ('T (SEQ (LETT |v1| (SPADCALL |l1| (CDR (CDR |u|)) (|getShellEntry| $ 63)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((EQL (CAR |v1|) 1) (CONS 1 "failed")) ('T (SEQ (LETT |v2| (SPADCALL |l2| (CAR (CDR |u|)) (|getShellEntry| $ 63)) |EUCDOM-;multiEuclidean;LSU;11|) (EXIT (COND ((EQL (CAR |v2|) 1) (CONS 1 "failed")) ('T (CONS 0 (SPADCALL (CDR |v1|) (CDR |v2|) (|getShellEntry| $ 64)))))))))))))))))))))) (DEFUN |EuclideanDomain&| (|#1|) (LET* ((|dv$1| (|devaluate| |#1|)) (|dv$| (LIST '|EuclideanDomain&| |dv$1|)) ($ (|newShell| 66)) (|pv$| (|buildPredVector| 0 0 NIL))) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 |pv$|) (|stuffDomainSlots| $) (|setShellEntry| $ 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|))