diff options
author | dos-reis <gdr@axiomatics.org> | 2008-03-14 04:33:31 +0000 |
---|---|---|
committer | dos-reis <gdr@axiomatics.org> | 2008-03-14 04:33:31 +0000 |
commit | bf8029a3f0eb72caa84f6cd31e2f5f784cff5bcc (patch) | |
tree | 64f5135ee043fe87b69769f881d37482b341c672 /src/algebra/ffcat.spad.pamphlet | |
parent | d1ebc50619fe75e940812f84220d087a2f77b3f5 (diff) | |
download | open-axiom-bf8029a3f0eb72caa84f6cd31e2f5f784cff5bcc.tar.gz |
* algebra/catdef.spad.pamphlet: Update cached Lisp translation.
* algebra/sf.spad.pamphlet: Likewise.
* algebra/si.spad.pamphlet: Likewise.
* algebra/fspace.spad.pamphlet: Likewise.
* algebra/ffcat.spad.pamphlet: Likewise.
* algebra/polset.spad.pamphlet: Likewise.
* algebra/fraction.spad.pamphlet: Likewise.
* algebra/triset.spad.pamphlet: Likewise.
* algebra/polycat.spad.pamphlet: Likewise.
Diffstat (limited to 'src/algebra/ffcat.spad.pamphlet')
-rw-r--r-- | src/algebra/ffcat.spad.pamphlet | 651 |
1 files changed, 627 insertions, 24 deletions
diff --git a/src/algebra/ffcat.spad.pamphlet b/src/algebra/ffcat.spad.pamphlet index 9505c555..f8047d80 100644 --- a/src/algebra/ffcat.spad.pamphlet +++ b/src/algebra/ffcat.spad.pamphlet @@ -714,15 +714,65 @@ Note that this code is not included in the generated catdef.spad file. <<FFIELDC.lsp BOOTSTRAP>>= -(|/VERSIONCHECK| 2) +(/VERSIONCHECK 2) -(SETQ |FiniteFieldCategory;AL| (QUOTE NIL)) +(DEFPARAMETER |FiniteFieldCategory;AL| 'NIL) -(DEFUN |FiniteFieldCategory| NIL (LET (#:G83129) (COND (|FiniteFieldCategory;AL|) (T (SETQ |FiniteFieldCategory;AL| (|FiniteFieldCategory;|)))))) +(DEFUN |FiniteFieldCategory| () + (LET (#:G1395) + (COND + (|FiniteFieldCategory;AL|) + (T (SETQ |FiniteFieldCategory;AL| (|FiniteFieldCategory;|)))))) -(DEFUN |FiniteFieldCategory;| NIL (PROG (#1=#:G83127) (RETURN (PROG1 (LETT #1# (|Join| (|FieldOfPrimeCharacteristic|) (|Finite|) (|StepThrough|) (|DifferentialRing|) (|mkCategory| (QUOTE |domain|) (QUOTE (((|charthRoot| (|$| |$|)) T) ((|conditionP| ((|Union| (|Vector| |$|) "failed") (|Matrix| |$|))) T) ((|factorsOfCyclicGroupSize| ((|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|)))))) T) ((|tableForDiscreteLogarithm| ((|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|))) T) ((|createPrimitiveElement| (|$|)) T) ((|primitiveElement| (|$|)) T) ((|primitive?| ((|Boolean|) |$|)) T) ((|discreteLog| ((|NonNegativeInteger|) |$|)) T) ((|order| ((|PositiveInteger|) |$|)) T) ((|representationType| ((|Union| "prime" "polynomial" "normal" "cyclic"))) T))) NIL (QUOTE ((|PositiveInteger|) (|NonNegativeInteger|) (|Boolean|) (|Table| (|PositiveInteger|) (|NonNegativeInteger|)) (|Integer|) (|List| (|Record| (|:| |factor| (|Integer|)) (|:| |exponent| (|Integer|)))) (|Matrix| |$|))) NIL)) |FiniteFieldCategory|) (SETELT #1# 0 (QUOTE (|FiniteFieldCategory|))))))) +(DEFUN |FiniteFieldCategory;| () + (PROG (#0=#:G1393) + (RETURN + (PROG1 (LETT #0# + (|Join| (|FieldOfPrimeCharacteristic|) (|Finite|) + (|StepThrough|) (|DifferentialRing|) + (|mkCategory| '|domain| + '(((|charthRoot| ($ $)) T) + ((|conditionP| + ((|Union| (|Vector| $) "failed") + (|Matrix| $))) + T) + ((|factorsOfCyclicGroupSize| + ((|List| + (|Record| + (|:| |factor| (|Integer|)) + (|:| |exponent| (|Integer|)))))) + T) + ((|tableForDiscreteLogarithm| + ((|Table| (|PositiveInteger|) + (|NonNegativeInteger|)) + (|Integer|))) + T) + ((|createPrimitiveElement| ($)) T) + ((|primitiveElement| ($)) T) + ((|primitive?| ((|Boolean|) $)) T) + ((|discreteLog| + ((|NonNegativeInteger|) $)) + T) + ((|order| ((|PositiveInteger|) $)) T) + ((|representationType| + ((|Union| "prime" "polynomial" + "normal" "cyclic"))) + T)) + NIL + '((|PositiveInteger|) + (|NonNegativeInteger|) (|Boolean|) + (|Table| (|PositiveInteger|) + (|NonNegativeInteger|)) + (|Integer|) + (|List| (|Record| + (|:| |factor| (|Integer|)) + (|:| |exponent| (|Integer|)))) + (|Matrix| $)) + NIL)) + |FiniteFieldCategory|) + (SETELT #0# 0 '(|FiniteFieldCategory|)))))) -(MAKEPROP (QUOTE |FiniteFieldCategory|) (QUOTE NILADIC) T) +(MAKEPROP '|FiniteFieldCategory| 'NILADIC T) @ \section{FFIELDC-.lsp BOOTSTRAP} {\bf FFIELDC-} depends on {\bf FFIELDC}. We need to break this cycle to build @@ -735,43 +785,596 @@ Note that this code is not included in the generated catdef.spad file. <<FFIELDC-.lsp BOOTSTRAP>>= -(|/VERSIONCHECK| 2) +(/VERSIONCHECK 2) -(DEFUN |FFIELDC-;differentiate;2S;1| (|x| |$|) (|spadConstant| |$| 7)) +(DEFUN |FFIELDC-;differentiate;2S;1| (|x| $) (|spadConstant| $ 7)) -(DEFUN |FFIELDC-;init;S;2| (|$|) (|spadConstant| |$| 7)) +(DEFUN |FFIELDC-;init;S;2| ($) (|spadConstant| $ 7)) -(DEFUN |FFIELDC-;nextItem;SU;3| (|a| |$|) (COND ((SPADCALL (LETT |a| (SPADCALL (|+| (SPADCALL |a| (QREFELT |$| 11)) 1) (QREFELT |$| 12)) |FFIELDC-;nextItem;SU;3|) (QREFELT |$| 14)) (CONS 1 "failed")) ((QUOTE T) (CONS 0 |a|)))) +(DEFUN |FFIELDC-;nextItem;SU;3| (|a| $) + (COND + ((SPADCALL + (LETT |a| + (SPADCALL (+ (SPADCALL |a| (QREFELT $ 11)) 1) + (QREFELT $ 12)) + |FFIELDC-;nextItem;SU;3|) + (QREFELT $ 14)) + (CONS 1 "failed")) + ('T (CONS 0 |a|)))) -(DEFUN |FFIELDC-;order;SOpc;4| (|e| |$|) (SPADCALL (SPADCALL |e| (QREFELT |$| 17)) (QREFELT |$| 20))) +(DEFUN |FFIELDC-;order;SOpc;4| (|e| $) + (SPADCALL (SPADCALL |e| (QREFELT $ 17)) (QREFELT $ 20))) -(DEFUN |FFIELDC-;conditionP;MU;5| (|mat| |$|) (PROG (|l|) (RETURN (SEQ (LETT |l| (SPADCALL |mat| (QREFELT |$| 24)) |FFIELDC-;conditionP;MU;5|) (COND ((OR (NULL |l|) (SPADCALL (ELT |$| 14) (|SPADfirst| |l|) (QREFELT |$| 27))) (EXIT (CONS 1 "failed")))) (EXIT (CONS 0 (SPADCALL (ELT |$| 28) (|SPADfirst| |l|) (QREFELT |$| 30)))))))) +(DEFUN |FFIELDC-;conditionP;MU;5| (|mat| $) + (PROG (|l|) + (RETURN + (SEQ (LETT |l| (SPADCALL |mat| (QREFELT $ 24)) + |FFIELDC-;conditionP;MU;5|) + (COND + ((OR (NULL |l|) + (SPADCALL (ELT $ 14) (|SPADfirst| |l|) + (QREFELT $ 27))) + (EXIT (CONS 1 "failed")))) + (EXIT (CONS 0 + (SPADCALL (ELT $ 28) (|SPADfirst| |l|) + (QREFELT $ 30)))))))) -(DEFUN |FFIELDC-;charthRoot;2S;6| (|x| |$|) (SPADCALL |x| (QUOTIENT2 (SPADCALL (QREFELT |$| 35)) (SPADCALL (QREFELT |$| 36))) (QREFELT |$| 37))) +(DEFUN |FFIELDC-;charthRoot;2S;6| (|x| $) + (SPADCALL |x| + (QUOTIENT2 (SPADCALL (QREFELT $ 35)) (SPADCALL (QREFELT $ 36))) + (QREFELT $ 37))) -(DEFUN |FFIELDC-;charthRoot;SU;7| (|x| |$|) (CONS 0 (SPADCALL |x| (QREFELT |$| 28)))) +(DEFUN |FFIELDC-;charthRoot;SU;7| (|x| $) + (CONS 0 (SPADCALL |x| (QREFELT $ 28)))) -(DEFUN |FFIELDC-;createPrimitiveElement;S;8| (|$|) (PROG (|sm1| |start| |i| #1=#:G83175 |e| |found|) (RETURN (SEQ (LETT |sm1| (|-| (SPADCALL (QREFELT |$| 35)) 1) |FFIELDC-;createPrimitiveElement;S;8|) (LETT |start| (COND ((SPADCALL (SPADCALL (QREFELT |$| 42)) (CONS 1 "polynomial") (QREFELT |$| 43)) (SPADCALL (QREFELT |$| 36))) ((QUOTE T) 1)) |FFIELDC-;createPrimitiveElement;S;8|) (LETT |found| (QUOTE NIL) |FFIELDC-;createPrimitiveElement;S;8|) (SEQ (LETT |i| |start| |FFIELDC-;createPrimitiveElement;S;8|) G190 (COND ((NULL (COND (|found| (QUOTE NIL)) ((QUOTE T) (QUOTE T)))) (GO G191))) (SEQ (LETT |e| (SPADCALL (PROG1 (LETT #1# |i| |FFIELDC-;createPrimitiveElement;S;8|) (|check-subtype| (|>| #1# 0) (QUOTE (|PositiveInteger|)) #1#)) (QREFELT |$| 12)) |FFIELDC-;createPrimitiveElement;S;8|) (EXIT (LETT |found| (EQL (SPADCALL |e| (QREFELT |$| 17)) |sm1|) |FFIELDC-;createPrimitiveElement;S;8|))) (LETT |i| (|+| |i| 1) |FFIELDC-;createPrimitiveElement;S;8|) (GO G190) G191 (EXIT NIL)) (EXIT |e|))))) +(DEFUN |FFIELDC-;createPrimitiveElement;S;8| ($) + (PROG (|sm1| |start| |i| #0=#:G1434 |e| |found|) + (RETURN + (SEQ (LETT |sm1| (- (SPADCALL (QREFELT $ 35)) 1) + |FFIELDC-;createPrimitiveElement;S;8|) + (LETT |start| + (COND + ((SPADCALL (SPADCALL (QREFELT $ 42)) + (CONS 1 "polynomial") (QREFELT $ 43)) + (SPADCALL (QREFELT $ 36))) + ('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| (QREFELT $ 44))) (GO G191))) + (SEQ (LETT |e| + (SPADCALL + (PROG1 (LETT #0# |i| + |FFIELDC-;createPrimitiveElement;S;8|) + (|check-subtype| (> #0# 0) + '(|PositiveInteger|) #0#)) + (QREFELT $ 12)) + |FFIELDC-;createPrimitiveElement;S;8|) + (EXIT (LETT |found| + (EQL (SPADCALL |e| (QREFELT $ 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| |$|) (PROG (|explist| |q| |exp| #1=#:G83187 |equalone|) (RETURN (SEQ (COND ((SPADCALL |a| (QREFELT |$| 14)) (QUOTE NIL)) ((QUOTE T) (SEQ (LETT |explist| (SPADCALL (QREFELT |$| 47)) |FFIELDC-;primitive?;SB;9|) (LETT |q| (|-| (SPADCALL (QREFELT |$| 35)) 1) |FFIELDC-;primitive?;SB;9|) (LETT |equalone| (QUOTE NIL) |FFIELDC-;primitive?;SB;9|) (SEQ (LETT |exp| NIL |FFIELDC-;primitive?;SB;9|) (LETT #1# |explist| |FFIELDC-;primitive?;SB;9|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |exp| (CAR #1#) |FFIELDC-;primitive?;SB;9|) NIL) (NULL (COND (|equalone| (QUOTE NIL)) ((QUOTE T) (QUOTE T))))) (GO G191))) (SEQ (EXIT (LETT |equalone| (SPADCALL (SPADCALL |a| (QUOTIENT2 |q| (QCAR |exp|)) (QREFELT |$| 48)) (QREFELT |$| 49)) |FFIELDC-;primitive?;SB;9|))) (LETT #1# (CDR #1#) |FFIELDC-;primitive?;SB;9|) (GO G190) G191 (EXIT NIL)) (EXIT (COND (|equalone| (QUOTE NIL)) ((QUOTE T) (QUOTE T))))))))))) +(DEFUN |FFIELDC-;primitive?;SB;9| (|a| $) + (PROG (|explist| |q| |exp| #0=#:G1446 |equalone|) + (RETURN + (SEQ (COND + ((SPADCALL |a| (QREFELT $ 14)) 'NIL) + ('T + (SEQ (LETT |explist| (SPADCALL (QREFELT $ 48)) + |FFIELDC-;primitive?;SB;9|) + (LETT |q| (- (SPADCALL (QREFELT $ 35)) 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| + (QREFELT $ 44)))) + (GO G191))) + (SEQ (EXIT (LETT |equalone| + (SPADCALL + (SPADCALL |a| + (QUOTIENT2 |q| (QCAR |exp|)) + (QREFELT $ 49)) + (|spadConstant| $ 40) + (QREFELT $ 50)) + |FFIELDC-;primitive?;SB;9|))) + (LETT #0# (CDR #0#) |FFIELDC-;primitive?;SB;9|) + (GO G190) G191 (EXIT NIL)) + (EXIT (SPADCALL |equalone| (QREFELT $ 44)))))))))) -(DEFUN |FFIELDC-;order;SPi;10| (|e| |$|) (PROG (|lof| |rec| #1=#:G83195 |primeDivisor| |j| #2=#:G83196 |a| |goon| |ord|) (RETURN (SEQ (COND ((SPADCALL |e| (|spadConstant| |$| 7) (QREFELT |$| 51)) (|error| "order(0) is not defined ")) ((QUOTE T) (SEQ (LETT |ord| (|-| (SPADCALL (QREFELT |$| 35)) 1) |FFIELDC-;order;SPi;10|) (LETT |a| 0 |FFIELDC-;order;SPi;10|) (LETT |lof| (SPADCALL (QREFELT |$| 47)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |rec| NIL |FFIELDC-;order;SPi;10|) (LETT #1# |lof| |FFIELDC-;order;SPi;10|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |rec| (CAR #1#) |FFIELDC-;order;SPi;10|) NIL)) (GO G191))) (SEQ (LETT |a| (QUOTIENT2 |ord| (LETT |primeDivisor| (QCAR |rec|) |FFIELDC-;order;SPi;10|)) |FFIELDC-;order;SPi;10|) (LETT |goon| (SPADCALL (SPADCALL |e| |a| (QREFELT |$| 48)) (QREFELT |$| 49)) |FFIELDC-;order;SPi;10|) (SEQ (LETT |j| 0 |FFIELDC-;order;SPi;10|) (LETT #2# (|-| (QCDR |rec|) 2) |FFIELDC-;order;SPi;10|) G190 (COND ((OR (QSGREATERP |j| #2#) (NULL |goon|)) (GO G191))) (SEQ (LETT |ord| |a| |FFIELDC-;order;SPi;10|) (LETT |a| (QUOTIENT2 |ord| |primeDivisor|) |FFIELDC-;order;SPi;10|) (EXIT (LETT |goon| (SPADCALL (SPADCALL |e| |a| (QREFELT |$| 48)) (QREFELT |$| 49)) |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 #1# (CDR #1#) |FFIELDC-;order;SPi;10|) (GO G190) G191 (EXIT NIL)) (EXIT |ord|)))))))) +(DEFUN |FFIELDC-;order;SPi;10| (|e| $) + (PROG (|lof| |rec| #0=#:G1454 |primeDivisor| |j| #1=#:G1455 |a| + |goon| |ord|) + (RETURN + (SEQ (COND + ((SPADCALL |e| (|spadConstant| $ 7) (QREFELT $ 50)) + (|error| "order(0) is not defined ")) + ('T + (SEQ (LETT |ord| (- (SPADCALL (QREFELT $ 35)) 1) + |FFIELDC-;order;SPi;10|) + (LETT |a| 0 |FFIELDC-;order;SPi;10|) + (LETT |lof| (SPADCALL (QREFELT $ 48)) + |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| (QREFELT $ 49)) + (|spadConstant| $ 40) + (QREFELT $ 50)) + |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| + (QREFELT $ 49)) + (|spadConstant| $ 40) + (QREFELT $ 50)) + |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| |$|) (PROG (|faclist| |gen| |groupord| |f| #1=#:G83216 |fac| |t| #2=#:G83217 |exp| |exptable| |n| |end| |i| |rho| |found| |disc1| |c| |mult| |disclog| |a|) (RETURN (SEQ (COND ((SPADCALL |b| (QREFELT |$| 14)) (|error| "discreteLog: logarithm of zero")) ((QUOTE T) (SEQ (LETT |faclist| (SPADCALL (QREFELT |$| 47)) |FFIELDC-;discreteLog;SNni;11|) (LETT |a| |b| |FFIELDC-;discreteLog;SNni;11|) (LETT |gen| (SPADCALL (QREFELT |$| 53)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND ((SPADCALL |b| |gen| (QREFELT |$| 51)) 1) ((QUOTE T) (SEQ (LETT |disclog| 0 |FFIELDC-;discreteLog;SNni;11|) (LETT |mult| 1 |FFIELDC-;discreteLog;SNni;11|) (LETT |groupord| (|-| (SPADCALL (QREFELT |$| 35)) 1) |FFIELDC-;discreteLog;SNni;11|) (LETT |exp| |groupord| |FFIELDC-;discreteLog;SNni;11|) (SEQ (LETT |f| NIL |FFIELDC-;discreteLog;SNni;11|) (LETT #1# |faclist| |FFIELDC-;discreteLog;SNni;11|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |f| (CAR #1#) |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 #2# (|-| (QCDR |f|) 1) |FFIELDC-;discreteLog;SNni;11|) G190 (COND ((QSGREATERP |t| #2#) (GO G191))) (SEQ (LETT |exp| (QUOTIENT2 |exp| |fac|) |FFIELDC-;discreteLog;SNni;11|) (LETT |exptable| (SPADCALL |fac| (QREFELT |$| 55)) |FFIELDC-;discreteLog;SNni;11|) (LETT |n| (SPADCALL |exptable| (QREFELT |$| 56)) |FFIELDC-;discreteLog;SNni;11|) (LETT |c| (SPADCALL |a| |exp| (QREFELT |$| 48)) |FFIELDC-;discreteLog;SNni;11|) (LETT |end| (QUOTIENT2 (|-| |fac| 1) |n|) |FFIELDC-;discreteLog;SNni;11|) (LETT |found| (QUOTE NIL) |FFIELDC-;discreteLog;SNni;11|) (LETT |disc1| 0 |FFIELDC-;discreteLog;SNni;11|) (SEQ (LETT |i| 0 |FFIELDC-;discreteLog;SNni;11|) G190 (COND ((OR (QSGREATERP |i| |end|) (NULL (COND (|found| (QUOTE NIL)) ((QUOTE T) (QUOTE T))))) (GO G191))) (SEQ (LETT |rho| (SPADCALL (SPADCALL |c| (QREFELT |$| 11)) |exptable| (QREFELT |$| 58)) |FFIELDC-;discreteLog;SNni;11|) (EXIT (COND ((QEQCAR |rho| 0) (SEQ (LETT |found| (QUOTE T) |FFIELDC-;discreteLog;SNni;11|) (EXIT (LETT |disc1| (|*| (|+| (|*| |n| |i|) (QCDR |rho|)) |mult|) |FFIELDC-;discreteLog;SNni;11|)))) ((QUOTE T) (LETT |c| (SPADCALL |c| (SPADCALL |gen| (|*| (QUOTIENT2 |groupord| |fac|) (|-| |n|)) (QREFELT |$| 48)) (QREFELT |$| 59)) |FFIELDC-;discreteLog;SNni;11|))))) (LETT |i| (QSADD1 |i|) |FFIELDC-;discreteLog;SNni;11|) (GO G190) G191 (EXIT NIL)) (EXIT (COND (|found| (SEQ (LETT |mult| (|*| |mult| |fac|) |FFIELDC-;discreteLog;SNni;11|) (LETT |disclog| (|+| |disclog| |disc1|) |FFIELDC-;discreteLog;SNni;11|) (EXIT (LETT |a| (SPADCALL |a| (SPADCALL |gen| (|-| |disc1|) (QREFELT |$| 48)) (QREFELT |$| 59)) |FFIELDC-;discreteLog;SNni;11|)))) ((QUOTE T) (|error| "discreteLog: ?? discrete logarithm"))))) (LETT |t| (QSADD1 |t|) |FFIELDC-;discreteLog;SNni;11|) (GO G190) G191 (EXIT NIL)))) (LETT #1# (CDR #1#) |FFIELDC-;discreteLog;SNni;11|) (GO G190) G191 (EXIT NIL)) (EXIT |disclog|)))))))))))) +(DEFUN |FFIELDC-;discreteLog;SNni;11| (|b| $) + (PROG (|faclist| |gen| |groupord| |f| #0=#:G1475 |fac| |t| #1=#:G1476 + |exp| |exptable| |n| |end| |i| |rho| |found| |disc1| |c| + |mult| |disclog| |a|) + (RETURN + (SEQ (COND + ((SPADCALL |b| (QREFELT $ 14)) + (|error| "discreteLog: logarithm of zero")) + ('T + (SEQ (LETT |faclist| (SPADCALL (QREFELT $ 48)) + |FFIELDC-;discreteLog;SNni;11|) + (LETT |a| |b| |FFIELDC-;discreteLog;SNni;11|) + (LETT |gen| (SPADCALL (QREFELT $ 53)) + |FFIELDC-;discreteLog;SNni;11|) + (EXIT (COND + ((SPADCALL |b| |gen| (QREFELT $ 50)) 1) + ('T + (SEQ (LETT |disclog| 0 + |FFIELDC-;discreteLog;SNni;11|) + (LETT |mult| 1 + |FFIELDC-;discreteLog;SNni;11|) + (LETT |groupord| + (- (SPADCALL (QREFELT $ 35)) 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| + (QREFELT $ 55)) + |FFIELDC-;discreteLog;SNni;11|) + (LETT |n| + (SPADCALL |exptable| + (QREFELT $ 56)) + |FFIELDC-;discreteLog;SNni;11|) + (LETT |c| + (SPADCALL |a| |exp| + (QREFELT $ 49)) + |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| + (QREFELT $ 44)))) + (GO G191))) + (SEQ + (LETT |rho| + (SPADCALL + (SPADCALL |c| + (QREFELT $ 11)) + |exptable| + (QREFELT $ 58)) + |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|)) + (QREFELT $ 49)) + (QREFELT $ 59)) + |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|) + (QREFELT $ 49)) + (QREFELT $ 59)) + |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| |$|) (PROG (|groupord| |faclist| |f| #1=#:G83235 |fac| |primroot| |t| #2=#:G83236 |exp| |rhoHelp| #3=#:G83234 |rho| |disclog| |mult| |a|) (RETURN (SEQ (EXIT (COND ((SPADCALL |b| (QREFELT |$| 14)) (SEQ (SPADCALL "discreteLog: logarithm of zero" (QREFELT |$| 64)) (EXIT (CONS 1 "failed")))) ((SPADCALL |logbase| (QREFELT |$| 14)) (SEQ (SPADCALL "discreteLog: logarithm to base zero" (QREFELT |$| 64)) (EXIT (CONS 1 "failed")))) ((SPADCALL |b| |logbase| (QREFELT |$| 51)) (CONS 0 1)) ((QUOTE T) (COND ((NULL (ZEROP (REMAINDER2 (LETT |groupord| (SPADCALL |logbase| (QREFELT |$| 17)) |FFIELDC-;discreteLog;2SU;12|) (SPADCALL |b| (QREFELT |$| 17))))) (SEQ (SPADCALL "discreteLog: second argument not in cyclic group generated by first argument" (QREFELT |$| 64)) (EXIT (CONS 1 "failed")))) ((QUOTE T) (SEQ (LETT |faclist| (SPADCALL (SPADCALL |groupord| (QREFELT |$| 66)) (QREFELT |$| 68)) |FFIELDC-;discreteLog;2SU;12|) (LETT |a| |b| |FFIELDC-;discreteLog;2SU;12|) (LETT |disclog| 0 |FFIELDC-;discreteLog;2SU;12|) (LETT |mult| 1 |FFIELDC-;discreteLog;2SU;12|) (LETT |exp| |groupord| |FFIELDC-;discreteLog;2SU;12|) (SEQ (LETT |f| NIL |FFIELDC-;discreteLog;2SU;12|) (LETT #1# |faclist| |FFIELDC-;discreteLog;2SU;12|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |f| (CAR #1#) |FFIELDC-;discreteLog;2SU;12|) NIL)) (GO G191))) (SEQ (LETT |fac| (QCAR |f|) |FFIELDC-;discreteLog;2SU;12|) (LETT |primroot| (SPADCALL |logbase| (QUOTIENT2 |groupord| |fac|) (QREFELT |$| 48)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (SEQ (LETT |t| 0 |FFIELDC-;discreteLog;2SU;12|) (LETT #2# (|-| (QCDR |f|) 1) |FFIELDC-;discreteLog;2SU;12|) G190 (COND ((QSGREATERP |t| #2#) (GO G191))) (SEQ (LETT |exp| (QUOTIENT2 |exp| |fac|) |FFIELDC-;discreteLog;2SU;12|) (LETT |rhoHelp| (SPADCALL |primroot| (SPADCALL |a| |exp| (QREFELT |$| 48)) |fac| (QREFELT |$| 70)) |FFIELDC-;discreteLog;2SU;12|) (EXIT (COND ((QEQCAR |rhoHelp| 1) (PROGN (LETT #3# (CONS 1 "failed") |FFIELDC-;discreteLog;2SU;12|) (GO #3#))) ((QUOTE T) (SEQ (LETT |rho| (|*| (QCDR |rhoHelp|) |mult|) |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|) (QREFELT |$| 48)) (QREFELT |$| 59)) |FFIELDC-;discreteLog;2SU;12|))))))) (LETT |t| (QSADD1 |t|) |FFIELDC-;discreteLog;2SU;12|) (GO G190) G191 (EXIT NIL)))) (LETT #1# (CDR #1#) |FFIELDC-;discreteLog;2SU;12|) (GO G190) G191 (EXIT NIL)) (EXIT (CONS 0 |disclog|)))))))) #3# (EXIT #3#))))) +(DEFUN |FFIELDC-;discreteLog;2SU;12| (|logbase| |b| $) + (PROG (|groupord| |faclist| |f| #0=#:G1494 |fac| |primroot| |t| + #1=#:G1495 |exp| |rhoHelp| #2=#:G1493 |rho| |disclog| + |mult| |a|) + (RETURN + (SEQ (EXIT (COND + ((SPADCALL |b| (QREFELT $ 14)) + (SEQ (SPADCALL "discreteLog: logarithm of zero" + (QREFELT $ 64)) + (EXIT (CONS 1 "failed")))) + ((SPADCALL |logbase| (QREFELT $ 14)) + (SEQ (SPADCALL + "discreteLog: logarithm to base zero" + (QREFELT $ 64)) + (EXIT (CONS 1 "failed")))) + ((SPADCALL |b| |logbase| (QREFELT $ 50)) (CONS 0 1)) + ('T + (COND + ((NULL (ZEROP (REMAINDER2 + (LETT |groupord| + (SPADCALL |logbase| + (QREFELT $ 17)) + |FFIELDC-;discreteLog;2SU;12|) + (SPADCALL |b| (QREFELT $ 17))))) + (SEQ (SPADCALL + "discreteLog: second argument not in cyclic group generated by first argument" + (QREFELT $ 64)) + (EXIT (CONS 1 "failed")))) + ('T + (SEQ (LETT |faclist| + (SPADCALL + (SPADCALL |groupord| + (QREFELT $ 66)) + (QREFELT $ 68)) + |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|) + (QREFELT $ 49)) + |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| + (QREFELT $ 49)) + |fac| (QREFELT $ 70)) + |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| + (* (QCDR |rhoHelp|) + |mult|) + |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|) + (QREFELT $ 49)) + (QREFELT $ 59)) + |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| |$|) (SPADCALL |f| (QREFELT |$| 75))) +(DEFUN |FFIELDC-;squareFreePolynomial| (|f| $) + (SPADCALL |f| (QREFELT $ 75))) -(DEFUN |FFIELDC-;factorPolynomial| (|f| |$|) (SPADCALL |f| (QREFELT |$| 77))) +(DEFUN |FFIELDC-;factorPolynomial| (|f| $) + (SPADCALL |f| (QREFELT $ 77))) -(DEFUN |FFIELDC-;factorSquareFreePolynomial| (|f| |$|) (PROG (|flist| |u| #1=#:G83248 #2=#:G83245 #3=#:G83243 #4=#:G83244) (RETURN (SEQ (COND ((SPADCALL |f| (|spadConstant| |$| 78) (QREFELT |$| 79)) (|spadConstant| |$| 80)) ((QUOTE T) (SEQ (LETT |flist| (SPADCALL |f| (QUOTE T) (QREFELT |$| 83)) |FFIELDC-;factorSquareFreePolynomial|) (EXIT (SPADCALL (SPADCALL (QCAR |flist|) (QREFELT |$| 84)) (PROGN (LETT #4# NIL |FFIELDC-;factorSquareFreePolynomial|) (SEQ (LETT |u| NIL |FFIELDC-;factorSquareFreePolynomial|) (LETT #1# (QCDR |flist|) |FFIELDC-;factorSquareFreePolynomial|) G190 (COND ((OR (ATOM #1#) (PROGN (LETT |u| (CAR #1#) |FFIELDC-;factorSquareFreePolynomial|) NIL)) (GO G191))) (SEQ (EXIT (PROGN (LETT #2# (SPADCALL (QCAR |u|) (QCDR |u|) (QREFELT |$| 85)) |FFIELDC-;factorSquareFreePolynomial|) (COND (#4# (LETT #3# (SPADCALL #3# #2# (QREFELT |$| 86)) |FFIELDC-;factorSquareFreePolynomial|)) ((QUOTE T) (PROGN (LETT #3# #2# |FFIELDC-;factorSquareFreePolynomial|) (LETT #4# (QUOTE T) |FFIELDC-;factorSquareFreePolynomial|))))))) (LETT #1# (CDR #1#) |FFIELDC-;factorSquareFreePolynomial|) (GO G190) G191 (EXIT NIL)) (COND (#4# #3#) ((QUOTE T) (|spadConstant| |$| 87)))) (QREFELT |$| 88)))))))))) +(DEFUN |FFIELDC-;factorSquareFreePolynomial| (|f| $) + (PROG (|flist| |u| #0=#:G1507 #1=#:G1504 #2=#:G1502 #3=#:G1503) + (RETURN + (SEQ (COND + ((SPADCALL |f| (|spadConstant| $ 78) (QREFELT $ 79)) + (|spadConstant| $ 80)) + ('T + (SEQ (LETT |flist| (SPADCALL |f| 'T (QREFELT $ 83)) + |FFIELDC-;factorSquareFreePolynomial|) + (EXIT (SPADCALL + (SPADCALL (QCAR |flist|) (QREFELT $ 84)) + (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|) (QREFELT $ 85)) + |FFIELDC-;factorSquareFreePolynomial|) + (COND + (#3# + (LETT #2# + (SPADCALL #2# #1# + (QREFELT $ 86)) + |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| $ 87)))) + (QREFELT $ 88)))))))))) -(DEFUN |FFIELDC-;gcdPolynomial;3Sup;16| (|f| |g| |$|) (SPADCALL |f| |g| (QREFELT |$| 90))) +(DEFUN |FFIELDC-;gcdPolynomial;3Sup;16| (|f| |g| $) + (SPADCALL |f| |g| (QREFELT $ 90))) -(DEFUN |FiniteFieldCategory&| (|#1|) (PROG (|DV$1| |dv$| |$| |pv$|) (RETURN (PROGN (LETT |DV$1| (|devaluate| |#1|) . #1=(|FiniteFieldCategory&|)) (LETT |dv$| (LIST (QUOTE |FiniteFieldCategory&|) |DV$1|) . #1#) (LETT |$| (GETREFV 93) . #1#) (QSETREFV |$| 0 |dv$|) (QSETREFV |$| 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #1#)) (|stuffDomainSlots| |$|) (QSETREFV |$| 6 |#1|) |$|)))) +(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 $ (GETREFV 93) . #0#) + (QSETREFV $ 0 |dv$|) + (QSETREFV $ 3 (LETT |pv$| (|buildPredVector| 0 0 NIL) . #0#)) + (|stuffDomainSlots| $) + (QSETREFV $ 6 |#1|) + $)))) -(MAKEPROP (QUOTE |FiniteFieldCategory&|) (QUOTE |infovec|) (LIST (QUOTE #(NIL NIL NIL NIL NIL NIL (|local| |#1|) (0 . |Zero|) |FFIELDC-;differentiate;2S;1| |FFIELDC-;init;S;2| (|PositiveInteger|) (4 . |lookup|) (9 . |index|) (|Boolean|) (14 . |zero?|) (|Union| |$| (QUOTE "failed")) |FFIELDC-;nextItem;SU;3| (19 . |order|) (|Integer|) (|OnePointCompletion| 10) (24 . |coerce|) |FFIELDC-;order;SOpc;4| (|List| 26) (|Matrix| 6) (29 . |nullSpace|) (|Mapping| 13 6) (|Vector| 6) (34 . |every?|) (40 . |charthRoot|) (|Mapping| 6 6) (45 . |map|) (|Union| (|Vector| |$|) (QUOTE "failed")) (|Matrix| |$|) |FFIELDC-;conditionP;MU;5| (|NonNegativeInteger|) (51 . |size|) (55 . |characteristic|) (59 . |**|) |FFIELDC-;charthRoot;2S;6| |FFIELDC-;charthRoot;SU;7| (65 . |One|) (|Union| (QUOTE "prime") (QUOTE "polynomial") (QUOTE "normal") (QUOTE "cyclic")) (69 . |representationType|) (73 . |=|) |FFIELDC-;createPrimitiveElement;S;8| (|Record| (|:| |factor| 18) (|:| |exponent| 18)) (|List| 45) (79 . |factorsOfCyclicGroupSize|) (83 . |**|) (89 . |one?|) |FFIELDC-;primitive?;SB;9| (94 . |=|) |FFIELDC-;order;SPi;10| (100 . |primitiveElement|) (|Table| 10 34) (104 . |tableForDiscreteLogarithm|) (109 . |#|) (|Union| 34 (QUOTE "failed")) (114 . |search|) (120 . |*|) |FFIELDC-;discreteLog;SNni;11| (|Void|) (|String|) (|OutputForm|) (126 . |messagePrint|) (|Factored| |$|) (131 . |factor|) (|Factored| 18) (136 . |factors|) (|DiscreteLogarithmPackage| 6) (141 . |shanksDiscLogAlgorithm|) |FFIELDC-;discreteLog;2SU;12| (|Factored| 73) (|SparseUnivariatePolynomial| 6) (|UnivariatePolynomialSquareFree| 6 73) (148 . |squareFree|) (|DistinctDegreeFactorize| 6 73) (153 . |factor|) (158 . |Zero|) (162 . |=|) (168 . |Zero|) (|Record| (|:| |irr| 73) (|:| |pow| 18)) (|Record| (|:| |cont| 6) (|:| |factors| (|List| 81))) (172 . |distdfact|) (178 . |coerce|) (183 . |primeFactor|) (189 . |*|) (195 . |One|) (199 . |*|) (|EuclideanDomain&| 73) (205 . |gcd|) (|SparseUnivariatePolynomial| |$|) |FFIELDC-;gcdPolynomial;3Sup;16|)) (QUOTE #(|primitive?| 211 |order| 216 |nextItem| 226 |init| 231 |gcdPolynomial| 235 |discreteLog| 241 |differentiate| 252 |createPrimitiveElement| 257 |conditionP| 261 |charthRoot| 266)) (QUOTE NIL) (CONS (|makeByteWordVec2| 1 (QUOTE NIL)) (CONS (QUOTE #()) (CONS (QUOTE #()) (|makeByteWordVec2| 92 (QUOTE (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 23 22 0 24 2 26 13 25 0 27 1 6 0 0 28 2 26 0 29 0 30 0 6 34 35 0 6 34 36 2 6 0 0 34 37 0 6 0 40 0 6 41 42 2 41 13 0 0 43 0 6 46 47 2 6 0 0 18 48 1 6 13 0 49 2 6 13 0 0 51 0 6 0 53 1 6 54 18 55 1 54 34 0 56 2 54 57 10 0 58 2 6 0 0 0 59 1 63 61 62 64 1 18 65 0 66 1 67 46 0 68 3 69 57 6 6 34 70 1 74 72 73 75 1 76 72 73 77 0 73 0 78 2 73 13 0 0 79 0 72 0 80 2 76 82 73 13 83 1 73 0 6 84 2 72 0 73 18 85 2 72 0 0 0 86 0 72 0 87 2 72 0 73 0 88 2 89 0 0 0 90 1 0 13 0 50 1 0 10 0 52 1 0 19 0 21 1 0 15 0 16 0 0 0 9 2 0 91 91 91 92 1 0 34 0 60 2 0 57 0 0 71 1 0 0 0 8 0 0 0 44 1 0 31 32 33 1 0 0 0 38 1 0 15 0 39)))))) (QUOTE |lookupComplete|))) +(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| (|List| 26) (|Matrix| 6) + (29 . |nullSpace|) (|Mapping| 13 6) (|Vector| 6) + (34 . |every?|) (40 . |charthRoot|) (|Mapping| 6 6) + (45 . |map|) (|Union| (|Vector| $) '"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| 46) (84 . |factorsOfCyclicGroupSize|) (88 . **) + (94 . =) |FFIELDC-;primitive?;SB;9| + |FFIELDC-;order;SPi;10| (100 . |primitiveElement|) + (|Table| 10 34) (104 . |tableForDiscreteLogarithm|) + (109 . |#|) (|Union| 34 '"failed") (114 . |search|) + (120 . *) |FFIELDC-;discreteLog;SNni;11| (|Void|) + (|String|) (|OutputForm|) (126 . |messagePrint|) + (|Factored| $) (131 . |factor|) (|Factored| 18) + (136 . |factors|) (|DiscreteLogarithmPackage| 6) + (141 . |shanksDiscLogAlgorithm|) + |FFIELDC-;discreteLog;2SU;12| (|Factored| 73) + (|SparseUnivariatePolynomial| 6) + (|UnivariatePolynomialSquareFree| 6 73) + (148 . |squareFree|) (|DistinctDegreeFactorize| 6 73) + (153 . |factor|) (158 . |Zero|) (162 . =) (168 . |Zero|) + (|Record| (|:| |irr| 73) (|:| |pow| 18)) + (|Record| (|:| |cont| 6) (|:| |factors| (|List| 81))) + (172 . |distdfact|) (178 . |coerce|) (183 . |primeFactor|) + (189 . *) (195 . |One|) (199 . *) (|EuclideanDomain&| 73) + (205 . |gcd|) (|SparseUnivariatePolynomial| $) + |FFIELDC-;gcdPolynomial;3Sup;16|) + '#(|primitive?| 211 |order| 216 |nextItem| 226 |init| 231 + |gcdPolynomial| 235 |discreteLog| 241 |differentiate| 252 + |createPrimitiveElement| 257 |conditionP| 261 |charthRoot| + 266) + 'NIL + (CONS (|makeByteWordVec2| 1 'NIL) + (CONS '#() + (CONS '#() + (|makeByteWordVec2| 92 + '(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 23 + 22 0 24 2 26 13 25 0 27 1 6 0 0 28 2 + 26 0 29 0 30 0 6 34 35 0 6 34 36 2 6 + 0 0 34 37 0 6 0 40 0 6 41 42 2 41 13 + 0 0 43 1 13 0 0 44 0 6 47 48 2 6 0 0 + 18 49 2 6 13 0 0 50 0 6 0 53 1 6 54 + 18 55 1 54 34 0 56 2 54 57 10 0 58 2 + 6 0 0 0 59 1 63 61 62 64 1 18 65 0 66 + 1 67 47 0 68 3 69 57 6 6 34 70 1 74 + 72 73 75 1 76 72 73 77 0 73 0 78 2 73 + 13 0 0 79 0 72 0 80 2 76 82 73 13 83 + 1 73 0 6 84 2 72 0 73 18 85 2 72 0 0 + 0 86 0 72 0 87 2 72 0 73 0 88 2 89 0 + 0 0 90 1 0 13 0 51 1 0 10 0 52 1 0 19 + 0 21 1 0 15 0 16 0 0 0 9 2 0 91 91 91 + 92 1 0 34 0 60 2 0 57 0 0 71 1 0 0 0 + 8 0 0 0 45 1 0 31 32 33 1 0 0 0 38 1 + 0 15 0 39))))) + '|lookupComplete|)) @ \section{package FFSLPE FiniteFieldSolveLinearPolynomialEquation} <<package FFSLPE FiniteFieldSolveLinearPolynomialEquation>>= |