From 84db9d8c5349cb8b3e7e2d102867e53e610d7ef2 Mon Sep 17 00:00:00 2001 From: dos-reis Date: Sat, 16 Aug 2008 06:00:35 +0000 Subject: * algebra/strap: New. Sequester cached Lisp translation of algebra bootstrap domains here. --- src/algebra/ffcat.spad.pamphlet | 696 ---------------------------------------- 1 file changed, 696 deletions(-) (limited to 'src/algebra/ffcat.spad.pamphlet') diff --git a/src/algebra/ffcat.spad.pamphlet b/src/algebra/ffcat.spad.pamphlet index fea2d28a..c87c4c12 100644 --- a/src/algebra/ffcat.spad.pamphlet +++ b/src/algebra/ffcat.spad.pamphlet @@ -704,703 +704,7 @@ generated by first argument")$OutputForm gcd(f,g)$EuclideanDomain_&(FP) @ -\section{FFIELDC.lsp BOOTSTRAP} -{\bf FFIELDC} depends on a chain of files. We need to break this cycle to build -the algebra. So we keep a cached copy of the translated {\bf FFIELDC} -category which we can write into the {\bf MID} directory. We compile -the lisp code and copy the {\bf FFIELDC.o} file to the {\bf OUT} directory. -This is eventually forcibly replaced by a recompiled version. -Note that this code is not included in the generated catdef.spad file. - -<>= - -(/VERSIONCHECK 2) - -(DEFPARAMETER |FiniteFieldCategory;AL| 'NIL) - -(DEFUN |FiniteFieldCategory| () - (LET (#:G1395) - (COND - (|FiniteFieldCategory;AL|) - (T (SETQ |FiniteFieldCategory;AL| (|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 '|FiniteFieldCategory| 'NILADIC T) -@ -\section{FFIELDC-.lsp BOOTSTRAP} -{\bf FFIELDC-} depends on {\bf FFIELDC}. We need to break this cycle to build -the algebra. So we keep a cached copy of the translated {\bf FFIELDC-} -category which we can write into the {\bf MID} directory. We compile -the lisp code and copy the {\bf FFIELDC-.o} file to the {\bf OUT} directory. -This is eventually forcibly replaced by a recompiled version. - -Note that this code is not included in the generated catdef.spad file. - -<>= - -(/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=#:G1441 |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=#:G1453 |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=#:G1461 |primeDivisor| |j| #1=#:G1462 |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=#:G1482 |fac| |t| #1=#:G1483 - |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=#:G1501 |fac| |primroot| |t| - #1=#:G1502 |exp| |rhoHelp| #2=#:G1500 |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| - (* (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|) - (|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| $ 76))) - -(DEFUN |FFIELDC-;factorPolynomial| (|f| $) - (SPADCALL |f| (|getShellEntry| $ 78))) - -(DEFUN |FFIELDC-;factorSquareFreePolynomial| (|f| $) - (PROG (|flist| |u| #0=#:G1515 #1=#:G1512 #2=#:G1510 #3=#:G1511) - (RETURN - (SEQ (COND - ((SPADCALL |f| (|spadConstant| $ 79) - (|getShellEntry| $ 80)) - (|spadConstant| $ 81)) - ('T - (SEQ (LETT |flist| - (SPADCALL |f| 'T (|getShellEntry| $ 85)) - |FFIELDC-;factorSquareFreePolynomial|) - (EXIT (SPADCALL - (SPADCALL (QCAR |flist|) - (|getShellEntry| $ 86)) - (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| $ 87)) - |FFIELDC-;factorSquareFreePolynomial|) - (COND - (#3# - (LETT #2# - (SPADCALL #2# #1# - (|getShellEntry| $ 88)) - |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| $ 89)))) - (|getShellEntry| $ 90)))))))))) - -(DEFUN |FFIELDC-;gcdPolynomial;3Sup;16| (|f| |g| $) - (SPADCALL |f| |g| (|getShellEntry| $ 92))) - -(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| 95) . #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|) - |FFIELDC-;discreteLog;2SU;12| - (|SparseUnivariatePolynomial| 6) (|Factored| 73) - (|UnivariatePolynomialSquareFree| 6 73) - (148 . |squareFree|) (|DistinctDegreeFactorize| 6 73) - (153 . |factor|) (158 . |Zero|) (162 . =) (168 . |Zero|) - (|Record| (|:| |irr| 73) (|:| |pow| 18)) (|List| 82) - (|Record| (|:| |cont| 6) (|:| |factors| 83)) - (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| 94 - '(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 1 75 - 74 73 76 1 77 74 73 78 0 73 0 79 2 73 - 13 0 0 80 0 74 0 81 2 77 84 73 13 85 - 1 73 0 6 86 2 74 0 73 18 87 2 74 0 0 - 0 88 0 74 0 89 2 74 0 73 0 90 2 91 0 - 0 0 92 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 93 93 93 - 94 1 0 35 0 61 2 0 58 0 0 72 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|)) -@ \section{package FFSLPE FiniteFieldSolveLinearPolynomialEquation} <>= )abbrev package FFSLPE FiniteFieldSolveLinearPolynomialEquation -- cgit v1.2.3