(/VERSIONCHECK 2) (DEFUN |FFIELDC-;differentiate;2S;1| (|x| $) (|spadConstant| $ 7)) (DEFUN |FFIELDC-;init;S;2| ($) (|spadConstant| $ 7)) (DEFUN |FFIELDC-;nextItem;SU;3| (|a| $) (COND ((SPADCALL (LETT |a| (SPADCALL (+ (SPADCALL |a| (|getShellEntry| $ 11)) 1) (|getShellEntry| $ 12)) |FFIELDC-;nextItem;SU;3|) (|getShellEntry| $ 14)) (CONS 1 "failed")) ('T (CONS 0 |a|)))) (DEFUN |FFIELDC-;order;SOpc;4| (|e| $) (SPADCALL (SPADCALL |e| (|getShellEntry| $ 17)) (|getShellEntry| $ 20))) (DEFUN |FFIELDC-;conditionP;MU;5| (|mat| $) (PROG (|l|) (RETURN (SEQ (LETT |l| (SPADCALL |mat| (|getShellEntry| $ 25)) |FFIELDC-;conditionP;MU;5|) (COND ((OR (NULL |l|) (SPADCALL (ELT $ 14) (|SPADfirst| |l|) (|getShellEntry| $ 27))) (EXIT (CONS 1 "failed")))) (EXIT (CONS 0 (SPADCALL (ELT $ 28) (|SPADfirst| |l|) (|getShellEntry| $ 30)))))))) (DEFUN |FFIELDC-;charthRoot;2S;6| (|x| $) (SPADCALL |x| (QUOTIENT2 (SPADCALL (|getShellEntry| $ 36)) (SPADCALL (|getShellEntry| $ 37))) (|getShellEntry| $ 38))) (DEFUN |FFIELDC-;charthRoot;SU;7| (|x| $) (CONS 0 (SPADCALL |x| (|getShellEntry| $ 28)))) (DEFUN |FFIELDC-;createPrimitiveElement;S;8| ($) (PROG (|sm1| |start| |i| #0=#:G1443 |e| |found|) (RETURN (SEQ (LETT |sm1| (- (SPADCALL (|getShellEntry| $ 36)) 1) |FFIELDC-;createPrimitiveElement;S;8|) (LETT |start| (COND ((SPADCALL (SPADCALL (|getShellEntry| $ 43)) (CONS 1 "polynomial") (|getShellEntry| $ 44)) (SPADCALL (|getShellEntry| $ 37))) ('T 1)) |FFIELDC-;createPrimitiveElement;S;8|) (LETT |found| 'NIL |FFIELDC-;createPrimitiveElement;S;8|) (SEQ (LETT |i| |start| |FFIELDC-;createPrimitiveElement;S;8|) G190 (COND ((NULL (SPADCALL |found| (|getShellEntry| $ 45))) (GO G191))) (SEQ (LETT |e| (SPADCALL (PROG1 (LETT #0# |i| |FFIELDC-;createPrimitiveElement;S;8|) (|check-subtype| (> #0# 0) '(|PositiveInteger|) #0#)) (|getShellEntry| $ 12)) |FFIELDC-;createPrimitiveElement;S;8|) (EXIT (LETT |found| (EQL (SPADCALL |e| (|getShellEntry| $ 17)) |sm1|) |FFIELDC-;createPrimitiveElement;S;8|))) (LETT |i| (+ |i| 1) |FFIELDC-;createPrimitiveElement;S;8|) (GO G190) G191 (EXIT NIL)) (EXIT |e|))))) (DEFUN |FFIELDC-;primitive?;SB;9| (|a| $) (PROG (|explist| |q| |exp| #0=#:G1455 |equalone|) (RETURN (SEQ (COND ((SPADCALL |a| (|getShellEntry| $ 14)) 'NIL) ('T (SEQ (LETT |explist| (SPADCALL (|getShellEntry| $ 49)) |FFIELDC-;primitive?;SB;9|) (LETT |q| (- (SPADCALL (|getShellEntry| $ 36)) 1) |FFIELDC-;primitive?;SB;9|) (LETT |equalone| 'NIL |FFIELDC-;primitive?;SB;9|) (SEQ (LETT |exp| NIL |FFIELDC-;primitive?;SB;9|) (LETT #0# |explist| |FFIELDC-;primitive?;SB;9|) G190 (COND ((OR (ATOM #0#) (PROGN (LETT |exp| (CAR #0#) |FFIELDC-;primitive?;SB;9|) NIL) (NULL (SPADCALL |equalone| (|getShellEntry| $ 45)))) (GO G191))) (SEQ (EXIT (LETT |equalone| (SPADCALL (SPADCALL |a| (QUOTIENT2 |q| (QCAR |exp|)) (|getShellEntry| $ 50)) (|spadConstant| $ 41) (|getShellEntry| $ 51)) |FFIELDC-;primitive?;SB;9|))) (LETT #0# (CDR #0#) |FFIELDC-;primitive?;SB;9|) (GO G190) G191 (EXIT NIL)) (EXIT (SPADCALL |equalone| (|getShellEntry| $ 45)))))))))) (DEFUN |FFIELDC-;order;SPi;10| (|e| $) (PROG (|lof| |rec| #0=#:G1463 |primeDivisor| |j| #1=#:G1464 |a| |goon| |ord|) (RETURN (SEQ (COND ((SPADCALL |e| (|spadConstant| $ 7) (|getShellEntry| $ 51)) (|error| "order(0) is not defined ")) ('T (SEQ (LETT |ord| (- (SPADCALL (|getShellEntry| $ 36)) 1) |FFIELDC-;order;SPi;10|) (LETT |a| 0 |FFIELDC-;order;SPi;10|) (LETT |lof| (SPADCALL (|getShellEntry| $ 49)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |rec| NIL |FFIELDC-;order;SPi;10|) (LETT #0# |lof| |FFIELDC-;order;SPi;10|) G190 (COND ((OR (ATOM #0#) (PROGN (LETT |rec| (CAR #0#) |FFIELDC-;order;SPi;10|) NIL)) (GO G191))) (SEQ (LETT |a| (QUOTIENT2 |ord| (LETT |primeDivisor| (QCAR |rec|) |FFIELDC-;order;SPi;10|)) |FFIELDC-;order;SPi;10|) (LETT |goon| (SPADCALL (SPADCALL |e| |a| (|getShellEntry| $ 50)) (|spadConstant| $ 41) (|getShellEntry| $ 51)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |j| 0 |FFIELDC-;order;SPi;10|) (LETT #1# (- (QCDR |rec|) 2) |FFIELDC-;order;SPi;10|) G190 (COND ((OR (QSGREATERP |j| #1#) (NULL |goon|)) (GO G191))) (SEQ (LETT |ord| |a| |FFIELDC-;order;SPi;10|) (LETT |a| (QUOTIENT2 |ord| |primeDivisor|) |FFIELDC-;order;SPi;10|) (EXIT (LETT |goon| (SPADCALL (SPADCALL |e| |a| (|getShellEntry| $ 50)) (|spadConstant| $ 41) (|getShellEntry| $ 51)) |FFIELDC-;order;SPi;10|))) (LETT |j| (QSADD1 |j|) |FFIELDC-;order;SPi;10|) (GO G190) G191 (EXIT NIL)) (EXIT (COND (|goon| (LETT |ord| |a| |FFIELDC-;order;SPi;10|))))) (LETT #0# (CDR #0#) |FFIELDC-;order;SPi;10|) (GO G190) G191 (EXIT NIL)) (EXIT |ord|)))))))) (DEFUN |FFIELDC-;discreteLog;SNni;11| (|b| $) (PROG (|faclist| |gen| |groupord| |f| #0=#:G1484 |fac| |t| #1=#:G1485 |exp| |exptable| |n| |end| |i| |rho| |found| |disc1| |c| |mult| |disclog| |a|) (RETURN (SEQ (COND ((SPADCALL |b| (|getShellEntry| $ 14)) (|error| "discreteLog: logarithm of zero")) ('T (SEQ (LETT |faclist| (SPADCALL (|getShellEntry| $ 49)) |FFIELDC-;discreteLog;SNni;11|) (LETT |a| |b| |FFIELDC-;discreteLog;SNni;11|) (LETT |gen| (SPADCALL (|getShellEntry| $ 54)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND ((SPADCALL |b| |gen| (|getShellEntry| $ 51)) 1) ('T (SEQ (LETT |disclog| 0 |FFIELDC-;discreteLog;SNni;11|) (LETT |mult| 1 |FFIELDC-;discreteLog;SNni;11|) (LETT |groupord| (- (SPADCALL (|getShellEntry| $ 36)) 1) |FFIELDC-;discreteLog;SNni;11|) (LETT |exp| |groupord| |FFIELDC-;discreteLog;SNni;11|) (SEQ (LETT |f| NIL |FFIELDC-;discreteLog;SNni;11|) (LETT #0# |faclist| |FFIELDC-;discreteLog;SNni;11|) G190 (COND ((OR (ATOM #0#) (PROGN (LETT |f| (CAR #0#) |FFIELDC-;discreteLog;SNni;11|) NIL)) (GO G191))) (SEQ (LETT |fac| (QCAR |f|) |FFIELDC-;discreteLog;SNni;11|) (EXIT (SEQ (LETT |t| 0 |FFIELDC-;discreteLog;SNni;11|) (LETT #1# (- (QCDR |f|) 1) |FFIELDC-;discreteLog;SNni;11|) G190 (COND ((QSGREATERP |t| #1#) (GO G191))) (SEQ (LETT |exp| (QUOTIENT2 |exp| |fac|) |FFIELDC-;discreteLog;SNni;11|) (LETT |exptable| (SPADCALL |fac| (|getShellEntry| $ 56)) |FFIELDC-;discreteLog;SNni;11|) (LETT |n| (SPADCALL |exptable| (|getShellEntry| $ 57)) |FFIELDC-;discreteLog;SNni;11|) (LETT |c| (SPADCALL |a| |exp| (|getShellEntry| $ 50)) |FFIELDC-;discreteLog;SNni;11|) (LETT |end| (QUOTIENT2 (- |fac| 1) |n|) |FFIELDC-;discreteLog;SNni;11|) (LETT |found| 'NIL |FFIELDC-;discreteLog;SNni;11|) (LETT |disc1| 0 |FFIELDC-;discreteLog;SNni;11|) (SEQ (LETT |i| 0 |FFIELDC-;discreteLog;SNni;11|) G190 (COND ((OR (QSGREATERP |i| |end|) (NULL (SPADCALL |found| (|getShellEntry| $ 45)))) (GO G191))) (SEQ (LETT |rho| (SPADCALL (SPADCALL |c| (|getShellEntry| $ 11)) |exptable| (|getShellEntry| $ 59)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND ((QEQCAR |rho| 0) (SEQ (LETT |found| 'T |FFIELDC-;discreteLog;SNni;11|) (EXIT (LETT |disc1| (* (+ (* |n| |i|) (QCDR |rho|)) |mult|) |FFIELDC-;discreteLog;SNni;11|)))) ('T (LETT |c| (SPADCALL |c| (SPADCALL |gen| (* (QUOTIENT2 |groupord| |fac|) (- |n|)) (|getShellEntry| $ 50)) (|getShellEntry| $ 60)) |FFIELDC-;discreteLog;SNni;11|))))) (LETT |i| (QSADD1 |i|) |FFIELDC-;discreteLog;SNni;11|) (GO G190) G191 (EXIT NIL)) (EXIT (COND (|found| (SEQ (LETT |mult| (* |mult| |fac|) |FFIELDC-;discreteLog;SNni;11|) (LETT |disclog| (+ |disclog| |disc1|) |FFIELDC-;discreteLog;SNni;11|) (EXIT (LETT |a| (SPADCALL |a| (SPADCALL |gen| (- |disc1|) (|getShellEntry| $ 50)) (|getShellEntry| $ 60)) |FFIELDC-;discreteLog;SNni;11|)))) ('T (|error| "discreteLog: ?? discrete logarithm"))))) (LETT |t| (QSADD1 |t|) |FFIELDC-;discreteLog;SNni;11|) (GO G190) G191 (EXIT NIL)))) (LETT #0# (CDR #0#) |FFIELDC-;discreteLog;SNni;11|) (GO G190) G191 (EXIT NIL)) (EXIT |disclog|)))))))))))) (DEFUN |FFIELDC-;discreteLog;2SU;12| (|logbase| |b| $) (PROG (|groupord| |faclist| |f| #0=#:G1503 |fac| |primroot| |t| #1=#:G1504 |exp| |rhoHelp| #2=#:G1502 |rho| |disclog| |mult| |a|) (RETURN (SEQ (EXIT (COND ((SPADCALL |b| (|getShellEntry| $ 14)) (SEQ (SPADCALL "discreteLog: logarithm of zero" (|getShellEntry| $ 65)) (EXIT (CONS 1 "failed")))) ((SPADCALL |logbase| (|getShellEntry| $ 14)) (SEQ (SPADCALL "discreteLog: logarithm to base zero" (|getShellEntry| $ 65)) (EXIT (CONS 1 "failed")))) ((SPADCALL |b| |logbase| (|getShellEntry| $ 51)) (CONS 0 1)) ('T (COND ((NULL (ZEROP (REMAINDER2 (LETT |groupord| (SPADCALL |logbase| (|getShellEntry| $ 17)) |FFIELDC-;discreteLog;2SU;12|) (SPADCALL |b| (|getShellEntry| $ 17))))) (SEQ (SPADCALL "discreteLog: second argument not in cyclic group generated by first argument" (|getShellEntry| $ 65)) (EXIT (CONS 1 "failed")))) ('T (SEQ (LETT |faclist| (SPADCALL (SPADCALL |groupord| (|getShellEntry| $ 67)) (|getShellEntry| $ 69)) |FFIELDC-;discreteLog;2SU;12|) (LETT |a| |b| |FFIELDC-;discreteLog;2SU;12|) (LETT |disclog| 0 |FFIELDC-;discreteLog;2SU;12|) (LETT |mult| 1 |FFIELDC-;discreteLog;2SU;12|) (LETT |exp| |groupord| |FFIELDC-;discreteLog;2SU;12|) (SEQ (LETT |f| NIL |FFIELDC-;discreteLog;2SU;12|) (LETT #0# |faclist| |FFIELDC-;discreteLog;2SU;12|) G190 (COND ((OR (ATOM #0#) (PROGN (LETT |f| (CAR #0#) |FFIELDC-;discreteLog;2SU;12|) NIL)) (GO G191))) (SEQ (LETT |fac| (QCAR |f|) |FFIELDC-;discreteLog;2SU;12|) (LETT |primroot| (SPADCALL |logbase| (QUOTIENT2 |groupord| |fac|) (|getShellEntry| $ 50)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (SEQ (LETT |t| 0 |FFIELDC-;discreteLog;2SU;12|) (LETT #1# (- (QCDR |f|) 1) |FFIELDC-;discreteLog;2SU;12|) G190 (COND ((QSGREATERP |t| #1#) (GO G191))) (SEQ (LETT |exp| (QUOTIENT2 |exp| |fac|) |FFIELDC-;discreteLog;2SU;12|) (LETT |rhoHelp| (SPADCALL |primroot| (SPADCALL |a| |exp| (|getShellEntry| $ 50)) |fac| (|getShellEntry| $ 71)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (COND ((QEQCAR |rhoHelp| 1) (PROGN (LETT #2# (CONS 1 "failed") |FFIELDC-;discreteLog;2SU;12|) (GO #2#))) ('T (SEQ (LETT |rho| (SPADCALL (QCDR |rhoHelp|) |mult| (|getShellEntry| $ 72)) |FFIELDC-;discreteLog;2SU;12|) (LETT |disclog| (+ |disclog| |rho|) |FFIELDC-;discreteLog;2SU;12|) (LETT |mult| (* |mult| |fac|) |FFIELDC-;discreteLog;2SU;12|) (EXIT (LETT |a| (SPADCALL |a| (SPADCALL |logbase| (- |rho|) (|getShellEntry| $ 50)) (|getShellEntry| $ 60)) |FFIELDC-;discreteLog;2SU;12|))))))) (LETT |t| (QSADD1 |t|) |FFIELDC-;discreteLog;2SU;12|) (GO G190) G191 (EXIT NIL)))) (LETT #0# (CDR #0#) |FFIELDC-;discreteLog;2SU;12|) (GO G190) G191 (EXIT NIL)) (EXIT (CONS 0 |disclog|)))))))) #2# (EXIT #2#))))) (DEFUN |FFIELDC-;squareFreePolynomial| (|f| $) (SPADCALL |f| (|getShellEntry| $ 77))) (DEFUN |FFIELDC-;factorPolynomial| (|f| $) (SPADCALL |f| (|getShellEntry| $ 79))) (DEFUN |FFIELDC-;factorSquareFreePolynomial| (|f| $) (PROG (|flist| |u| #0=#:G1517 #1=#:G1514 #2=#:G1512 #3=#:G1513) (RETURN (SEQ (COND ((SPADCALL |f| (|spadConstant| $ 80) (|getShellEntry| $ 81)) (|spadConstant| $ 82)) ('T (SEQ (LETT |flist| (SPADCALL |f| 'T (|getShellEntry| $ 86)) |FFIELDC-;factorSquareFreePolynomial|) (EXIT (SPADCALL (SPADCALL (QCAR |flist|) (|getShellEntry| $ 87)) (PROGN (LETT #3# NIL |FFIELDC-;factorSquareFreePolynomial|) (SEQ (LETT |u| NIL |FFIELDC-;factorSquareFreePolynomial|) (LETT #0# (QCDR |flist|) |FFIELDC-;factorSquareFreePolynomial|) G190 (COND ((OR (ATOM #0#) (PROGN (LETT |u| (CAR #0#) |FFIELDC-;factorSquareFreePolynomial|) NIL)) (GO G191))) (SEQ (EXIT (PROGN (LETT #1# (SPADCALL (QCAR |u|) (QCDR |u|) (|getShellEntry| $ 88)) |FFIELDC-;factorSquareFreePolynomial|) (COND (#3# (LETT #2# (SPADCALL #2# #1# (|getShellEntry| $ 89)) |FFIELDC-;factorSquareFreePolynomial|)) ('T (PROGN (LETT #2# #1# |FFIELDC-;factorSquareFreePolynomial|) (LETT #3# 'T |FFIELDC-;factorSquareFreePolynomial|))))))) (LETT #0# (CDR #0#) |FFIELDC-;factorSquareFreePolynomial|) (GO G190) G191 (EXIT NIL)) (COND (#3# #2#) ('T (|spadConstant| $ 90)))) (|getShellEntry| $ 91)))))))))) (DEFUN |FFIELDC-;gcdPolynomial;3Sup;16| (|f| |g| $) (SPADCALL |f| |g| (|getShellEntry| $ 93))) (DEFUN |FiniteFieldCategory&| (|#1|) (PROG (|dv$1| |dv$| $ |pv$|) (RETURN (PROGN (LETT |dv$1| (|devaluate| |#1|) . #0=(|FiniteFieldCategory&|)) (LETT |dv$| (LIST '|FiniteFieldCategory&| |dv$1|) . #0#) (LETT $ (|newShell| 96) . #0#) (|setShellEntry| $ 0 |dv$|) (|setShellEntry| $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) (|stuffDomainSlots| $) (|setShellEntry| $ 6 |#1|) $)))) (MAKEPROP '|FiniteFieldCategory&| '|infovec| (LIST '#(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . |Zero|) |FFIELDC-;differentiate;2S;1| |FFIELDC-;init;S;2| (|PositiveInteger|) (4 . |lookup|) (9 . |index|) (|Boolean|) (14 . |zero?|) (|Union| $ '"failed") |FFIELDC-;nextItem;SU;3| (19 . |order|) (|Integer|) (|OnePointCompletion| 10) (24 . |coerce|) |FFIELDC-;order;SOpc;4| (|Vector| 6) (|List| 22) (|Matrix| 6) (29 . |nullSpace|) (|Mapping| 13 6) (34 . |every?|) (40 . |charthRoot|) (|Mapping| 6 6) (45 . |map|) (|Vector| $) (|Union| 31 '"failed") (|Matrix| $) |FFIELDC-;conditionP;MU;5| (|NonNegativeInteger|) (51 . |size|) (55 . |characteristic|) (59 . **) |FFIELDC-;charthRoot;2S;6| |FFIELDC-;charthRoot;SU;7| (65 . |One|) (|Union| '"prime" '"polynomial" '"normal" '"cyclic") (69 . |representationType|) (73 . =) (79 . |not|) |FFIELDC-;createPrimitiveElement;S;8| (|Record| (|:| |factor| 18) (|:| |exponent| 18)) (|List| 47) (84 . |factorsOfCyclicGroupSize|) (88 . **) (94 . =) |FFIELDC-;primitive?;SB;9| |FFIELDC-;order;SPi;10| (100 . |primitiveElement|) (|Table| 10 35) (104 . |tableForDiscreteLogarithm|) (109 . |#|) (|Union| 35 '"failed") (114 . |search|) (120 . *) |FFIELDC-;discreteLog;SNni;11| (|Void|) (|String|) (|OutputForm|) (126 . |messagePrint|) (|Factored| $) (131 . |factor|) (|Factored| 18) (136 . |factors|) (|DiscreteLogarithmPackage| 6) (141 . |shanksDiscLogAlgorithm|) (148 . *) |FFIELDC-;discreteLog;2SU;12| (|SparseUnivariatePolynomial| 6) (|Factored| 74) (|UnivariatePolynomialSquareFree| 6 74) (154 . |squareFree|) (|DistinctDegreeFactorize| 6 74) (159 . |factor|) (164 . |Zero|) (168 . =) (174 . |Zero|) (|Record| (|:| |irr| 74) (|:| |pow| 18)) (|List| 83) (|Record| (|:| |cont| 6) (|:| |factors| 84)) (178 . |distdfact|) (184 . |coerce|) (189 . |primeFactor|) (195 . *) (201 . |One|) (205 . *) (|EuclideanDomain&| 74) (211 . |gcd|) (|SparseUnivariatePolynomial| $) |FFIELDC-;gcdPolynomial;3Sup;16|) '#(|primitive?| 217 |order| 222 |nextItem| 232 |init| 237 |gcdPolynomial| 241 |discreteLog| 247 |differentiate| 258 |createPrimitiveElement| 263 |conditionP| 267 |charthRoot| 272) 'NIL (CONS (|makeByteWordVec2| 1 'NIL) (CONS '#() (CONS '#() (|makeByteWordVec2| 95 '(0 6 0 7 1 6 10 0 11 1 6 0 10 12 1 6 13 0 14 1 6 10 0 17 1 19 0 18 20 1 24 23 0 25 2 22 13 26 0 27 1 6 0 0 28 2 22 0 29 0 30 0 6 35 36 0 6 35 37 2 6 0 0 35 38 0 6 0 41 0 6 42 43 2 42 13 0 0 44 1 13 0 0 45 0 6 48 49 2 6 0 0 18 50 2 6 13 0 0 51 0 6 0 54 1 6 55 18 56 1 55 35 0 57 2 55 58 10 0 59 2 6 0 0 0 60 1 64 62 63 65 1 18 66 0 67 1 68 48 0 69 3 70 58 6 6 35 71 2 18 0 35 0 72 1 76 75 74 77 1 78 75 74 79 0 74 0 80 2 74 13 0 0 81 0 75 0 82 2 78 85 74 13 86 1 74 0 6 87 2 75 0 74 18 88 2 75 0 0 0 89 0 75 0 90 2 75 0 74 0 91 2 92 0 0 0 93 1 0 13 0 52 1 0 10 0 53 1 0 19 0 21 1 0 15 0 16 0 0 0 9 2 0 94 94 94 95 1 0 35 0 61 2 0 58 0 0 73 1 0 0 0 8 0 0 0 46 1 0 32 33 34 1 0 0 0 39 1 0 15 0 40))))) '|lookupComplete|)) (SETQ |$CategoryFrame| (|put| '|FiniteFieldCategory&| '|isFunctor| '(((|order| ((|PositiveInteger|) $)) T (ELT $ 53)) ((|discreteLog| ((|NonNegativeInteger|) $)) T (ELT $ 61)) ((|primitive?| ((|Boolean|) $)) T (ELT $ 52)) ((|createPrimitiveElement| ($)) T (ELT $ 46)) ((|conditionP| ((|Union| (|Vector| $) "failed") (|Matrix| $))) T (ELT $ 34)) ((|charthRoot| ($ $)) T (ELT $ 39)) ((|differentiate| ($ $)) T (ELT $ 8)) ((|differentiate| ($ $ (|NonNegativeInteger|))) T (ELT $ NIL)) ((|init| ($)) T (ELT $ 9)) ((|nextItem| ((|Union| $ "failed") $)) T (ELT $ 16)) ((|discreteLog| ((|Union| (|NonNegativeInteger|) "failed") $ $)) T (ELT $ 73)) ((|order| ((|OnePointCompletion| (|PositiveInteger|)) $)) T (ELT $ 21)) ((|charthRoot| ((|Union| $ "failed") $)) T (ELT $ 40)) ((|gcdPolynomial| ((|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $) (|SparseUnivariatePolynomial| $))) T (ELT $ 95))) (|addModemap| '|FiniteFieldCategory&| '(|FiniteFieldCategory&| |#1|) '((CATEGORY |domain| (SIGNATURE |order| ((|PositiveInteger|) |#1|)) (SIGNATURE |discreteLog| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |primitive?| ((|Boolean|) |#1|)) (SIGNATURE |createPrimitiveElement| (|#1|)) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |discreteLog| ((|Union| (|NonNegativeInteger|) "failed") |#1| |#1|)) (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) |#1|)) (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)))) (|FiniteFieldCategory|)) T '|FiniteFieldCategory&| (|put| '|FiniteFieldCategory&| '|mode| '(|Mapping| (CATEGORY |domain| (SIGNATURE |order| ((|PositiveInteger|) |#1|)) (SIGNATURE |discreteLog| ((|NonNegativeInteger|) |#1|)) (SIGNATURE |primitive?| ((|Boolean|) |#1|)) (SIGNATURE |createPrimitiveElement| (|#1|)) (SIGNATURE |conditionP| ((|Union| (|Vector| |#1|) "failed") (|Matrix| |#1|))) (SIGNATURE |charthRoot| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1|)) (SIGNATURE |differentiate| (|#1| |#1| (|NonNegativeInteger|))) (SIGNATURE |init| (|#1|)) (SIGNATURE |nextItem| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |discreteLog| ((|Union| (|NonNegativeInteger|) "failed") |#1| |#1|)) (SIGNATURE |order| ((|OnePointCompletion| (|PositiveInteger|)) |#1|)) (SIGNATURE |charthRoot| ((|Union| |#1| "failed") |#1|)) (SIGNATURE |gcdPolynomial| ((|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|) (|SparseUnivariatePolynomial| |#1|)))) (|FiniteFieldCategory|)) |$CategoryFrame|))))