diff --git a/books/bookvol10.2.pamphlet b/books/bookvol10.2.pamphlet index 0b3b925..11a9259 100644 --- a/books/bookvol10.2.pamphlet +++ b/books/bookvol10.2.pamphlet @@ -386,7 +386,7 @@ digraph pic { \pageto{TranscendentalFunctionCategory}{TRANFUN} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llllll} \cross{AHYP}{acosh} & @@ -462,7 +462,7 @@ intermediate test to check that the argument has a reciprocal values. \pageto{TranscendentalFunctionCategory}{TRANFUN} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llllll} \cross{ATRIG}{acos} & @@ -717,7 +717,7 @@ digraph pic { \pageto{SetCategory}{SETCAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{ll} \cross{BASTYPE}{?=?} & @@ -796,7 +796,7 @@ digraph pic { \pageto{SetCategory}{SETCAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \cross{KOERCE}{coerce} @@ -865,7 +865,7 @@ digraph pic { \pageto{IntegerNumberSystem}{INS} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{CFCAT}{binomial} & @@ -946,7 +946,7 @@ digraph pic { \pageto{RealNumberSystem}{RNS} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \cross{KONVERT}{convert} @@ -1066,7 +1066,7 @@ digraph pic { \pageto{TranscendentalFunctionCategory}{TRANFUN} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{ELEMFUN}{?**?} & @@ -1139,7 +1139,7 @@ digraph pic { \pageto{UnivariatePolynomialCategory}{UPOLYC}\hfill \pagefrom{Category}{CATEGORY}\hfill -{\bf Exports:} +{\bf Exports:}\\ \cross{ELTAB}{?.?} @@ -1225,7 +1225,7 @@ intermediate test to check that the argument has a reciprocal values. \pageto{TranscendentalFunctionCategory}{TRANFUN} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llllll} \cross{HYPCAT}{cosh} & @@ -1318,7 +1318,7 @@ digraph pic { \pageto{PolynomialCategory}{POLYCAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{l} \cross{IEVALAB}{eval} @@ -1423,7 +1423,7 @@ digraph pic { \pageto{StringCategory}{STRICAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{l} \cross{OM}{OMwrite} @@ -1500,7 +1500,7 @@ digraph pic { \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PTRANFN}{acosIfCan} & @@ -1695,7 +1695,7 @@ digraph pic { \pageto{QuotientFieldCategory}{QFCAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{l} \cross{PATAB}{convert} @@ -1776,7 +1776,7 @@ digraph pic { \pageto{LiouvillianFunctionCategory}{LFCAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{l} \cross{PRIMCAT}{integral} @@ -1845,7 +1845,7 @@ digraph pic { \pageto{UnivariateTaylorSeriesCategory}{UTSCAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{RADCAT}{nthRoot} & @@ -1939,7 +1939,7 @@ digraph pic { \pageto{XFreeAlgebra}{XFALG} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{RETRACT}{coerce} & @@ -2070,7 +2070,7 @@ digraph pic { \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SPFCAT}{abs} & @@ -2177,7 +2177,7 @@ intermediate test to check that the argument has a reciprocal values. \pageto{TranscendentalFunctionCategory}{TRANFUN} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llllll} \cross{TRIGCAT}{cos} & @@ -2322,7 +2322,7 @@ digraph pic { \item {\bf nil} \end{itemize} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llllll} \cross{AGG}{empty?} & @@ -2438,7 +2438,7 @@ digraph pic { \pagefrom{CombinatorialFunctionCategory}{CFCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{COMBOPC}{binomial} & @@ -2535,7 +2535,7 @@ digraph pic { \pageto{IndexedAggregate}{IXAGG} \pagefrom{Eltable}{ELTAB} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ELTAGG}{elt} & @@ -2660,7 +2660,7 @@ digraph pic { \pageto{PolynomialCategory}{POLYCAT} \pagefrom{InnerEvalable}{IEVALAB} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{l} \cross{EVALAB}{eval} @@ -2769,7 +2769,7 @@ digraph pic { \pagefrom{CoercibleTo}{KOERCE} \pagefrom{Type}{TYPE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{ll} \cross{FORTCAT}{coerce} & @@ -2867,7 +2867,7 @@ digraph pic { \pageto{UnivariateSkewPolynomialCategory}{OREPCAT} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{FRETRCT}{coerce} & @@ -2993,7 +2993,7 @@ digraph pic { \item {\bf nil} \end{itemize} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FPATMAB}{coerce} & @@ -3106,7 +3106,7 @@ digraph pic { \pageto{BitAggregate}{BTAGG} \pagefrom{BasicType}{BASTYPE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LOGIC}{?$/\backslash{}$?} @@ -3191,7 +3191,7 @@ digraph pic { \pagefrom{CoercibleTo}{KOERCE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{PPCURVE}{coerce} & @@ -3288,7 +3288,7 @@ digraph pic { \pagefrom{CoercibleTo}{KOERCE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PSCURVE}{coerce} & @@ -3393,7 +3393,7 @@ digraph pic { \pageto{RealNumberSystem}{RNS} \pagefrom{ConvertibleTo}{KONVERT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{l} \cross{REAL}{convert} @@ -3472,7 +3472,7 @@ digraph pic { \pageto{SegmentExpansionCategory}{SEGXCAT} \pagefrom{Type}{TYPE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SEGCAT}{BY} & @@ -3611,7 +3611,7 @@ digraph pic { \pagefrom{BasicType}{BASTYPE} \pagefrom{CoercibleTo}{KOERCE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SETCAT}{coerce} & @@ -3727,7 +3727,7 @@ reciprocal values. \pagefrom{HyperbolicFunctionCategory}{HYPCAT} \pagefrom{TrigonometricFunctionCategory}{TRIGCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{TRANFUN}{?**?} & @@ -3920,7 +3920,7 @@ digraph pic { \pageto{FunctionSpace}{FS} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ABELSG}{coerce} & @@ -4038,7 +4038,7 @@ digraph pic { \pagefrom{FortranProgramCategory}{FORTCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{FORTFN}{coerce} & @@ -4185,7 +4185,7 @@ digraph pic { \pagefrom{FortranProgramCategory}{FORTCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{ll} \cross{FMC}{coerce} & @@ -4284,7 +4284,7 @@ digraph pic { \pagefrom{FortranProgramCategory}{FORTCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{FMFUN}{coerce} & @@ -4432,7 +4432,7 @@ digraph pic { \pagefrom{FortranProgramCategory}{FORTCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \end{tabular} @@ -4529,7 +4529,7 @@ digraph pic { \pagefrom{FortranProgramCategory}{FORTCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{FVFUN}{coerce} & @@ -4680,7 +4680,7 @@ digraph pic { \pageto{QuotientFieldCategory}{QFCAT} \pagefrom{Category}{CATEGORY} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{FEVALAB}{eval} & @@ -4814,7 +4814,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FILECAT}{close!} & @@ -4962,7 +4962,7 @@ digraph pic { \pageto{OrderedFinite}{ORDFIN} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FINITE}{coerce} @@ -5077,7 +5077,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FNCAT}{coerce} & @@ -5217,7 +5217,7 @@ digraph pic { \pageto{GradedAlgebra}{GRALG} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{GRMOD}{0} & @@ -5367,7 +5367,7 @@ digraph pic { \item {\bf nil} \end{itemize} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{HOAGG}{any?} & @@ -5599,7 +5599,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{IDPC}{coerce} & @@ -5720,7 +5720,7 @@ digraph pic { \pagefrom{PrimitiveFunctionCategory}{PRIMCAT} \pagefrom{TranscendentalFunctionCategory}{TRANFUN} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LFCAT}{Ci} & @@ -5906,7 +5906,7 @@ digraph pic { \pageto{MonadWithUnit}{MONADWU} \pageto{NonAssociativeRng}{NARNG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{MONAD}{coerce} & @@ -6047,7 +6047,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{NUMINT}{coerce} & @@ -6205,7 +6205,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{OPTCAT}{coerce} & @@ -6357,7 +6357,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ODECAT}{coerce} & @@ -6501,7 +6501,7 @@ digraph pic { \pageto{QuotientFieldCategory}{QFCAT} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ORDSET}{coerce} & @@ -6630,7 +6630,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PDECAT}{coerce} & @@ -6793,7 +6793,7 @@ digraph pic { \pageto{RealNumberSystem}{RNS} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PATMAB}{coerce} & @@ -6897,7 +6897,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{RRCC}{allRootsOf} & @@ -7083,7 +7083,7 @@ digraph pic { \pagefrom{SegmentCategory}{SEGCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SEGXCAT}{BY} & @@ -7215,7 +7215,7 @@ operator ``*''. A Semigroup $G(S,*)$ is: \pageto{Rng}{RNG} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SGROUP}{coerce} & @@ -7338,7 +7338,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SEXCAT}{atom?} & @@ -7539,7 +7539,7 @@ digraph pic { \pageto{UnivariatePolynomialCategory}{UPOLYC} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{STEP}{coerce} & @@ -7644,7 +7644,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SPACEC}{check} & @@ -8100,7 +8100,7 @@ digraph pic { \pageto{OrderedAbelianSemiGroup}{OASGP} \pagefrom{AbelianSemiGroup}{ABELSG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ABELMON}{0} & @@ -8242,7 +8242,7 @@ digraph pic { \pageto{StackAggregate}{SKAGG} \pagefrom{HomogeneousAggregate}{HOAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{BGAGG}{any?} & @@ -8415,7 +8415,7 @@ digraph pic { \pagefrom{OrderedSet}{ORDSET} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{CACHESET}{coerce} & @@ -8525,7 +8525,7 @@ digraph pic { \pagefrom{ConvertibleTo}{KONVERT} \pagefrom{HomogeneousAggregate}{HOAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{CLAGG}{any?} & @@ -8784,7 +8784,7 @@ digraph pic { \pagefrom{OrderedSet}{ORDSET} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DVARCAT}{coerce} & @@ -9024,7 +9024,7 @@ digraph pic { \pagefrom{OrderedSet}{ORDSET} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{ES}{belong?} & @@ -9550,7 +9550,7 @@ digraph pic { \pagefrom{GradedModule}{GRMOD} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{GRALG}{0} & @@ -9710,7 +9710,7 @@ digraph pic { \pagefrom{EltableAggregate}{ELTAGG} \pagefrom{HomogeneousAggregate}{HOAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{IXAGG}{any?} & @@ -9989,7 +9989,7 @@ digraph pic { \pageto{NonAssociativeRing}{NASRING} \pagefrom{Monad}{MONAD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{MONADWU}{1} & @@ -10173,7 +10173,7 @@ digraph pic { \pageto{Ring}{RING} \pagefrom{SemiGroup}{SGROUP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{MONOID}{1} & @@ -10327,7 +10327,7 @@ digraph pic { \pagefrom{Finite}{FINITE} \pagefrom{OrderedSet}{ORDSET} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ORDFIN}{coerce} & @@ -10445,7 +10445,7 @@ digraph pic { \pageto{UnaryRecursiveAggregate}{URAGG} \pagefrom{HomogeneousAggregate}{HOAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{RCAGG}{any?} & @@ -10676,7 +10676,7 @@ first column in an array and vice versa. \pageto{MatrixCategory}{MATCAT} \pagefrom{HomogeneousAggregate}{HOAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ARR2CAT}{any?} & @@ -11219,7 +11219,7 @@ digraph pic { \pageto{BinaryTreeCategory}{BTCAT} \pagefrom{RecursiveAggregate}{RCAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{BRAGG}{any?} & @@ -11516,7 +11516,7 @@ digraph pic { \pageto{OrderedCancellationAbelianMonoid}{OCAMON} \pagefrom{AbelianMonoid}{ABELMON} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{CABMON}{0} & @@ -11641,7 +11641,7 @@ digraph pic { \pagefrom{BagAggregate}{BGAGG} \pagefrom{Collection}{CLAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DIOPS}{any?} & @@ -11876,7 +11876,7 @@ digraph pic { \pagefrom{RecursiveAggregate}{RCAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DLAGG}{any?} & @@ -12097,7 +12097,7 @@ digraph pic { \pageto{PermutationCategory}{PERMCAT} \pagefrom{Monoid}{MONOID} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{GROUP}{1} & @@ -12277,7 +12277,7 @@ digraph pic { \pagefrom{Collection}{CLAGG} \pagefrom{IndexedAggregate}{IXAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LNAGG}{any?} & @@ -13778,7 +13778,7 @@ should be put into these packages. \pageto{RectangularMatrixCategory}{RMATCAT} \pageto{SquareMatrixCategory}{SMATCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{MATCAT}{antisymmetric?} & @@ -14792,7 +14792,7 @@ digraph pic { \pagefrom{AbelianMonoid}{ABELMON} \pagefrom{OrderedSet}{ORDSET} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{OASGP}{0} & @@ -14928,7 +14928,7 @@ digraph pic { \pagefrom{Monoid}{MONOID} \pagefrom{OrderedSet}{ORDSET} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ORDMON}{1} & @@ -15074,7 +15074,7 @@ digraph pic { \pagefrom{Collection}{CLAGG} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{PSETCAT}{any?} & @@ -15676,7 +15676,7 @@ digraph pic { \pageto{OrderedMultisetAggregate}{OMSAGG} \pagefrom{BagAggregate}{BGAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PRQAGG}{any?} & @@ -15853,7 +15853,7 @@ digraph pic { \pageto{DequeueAggregate}{DQAGG} \pagefrom{BagAggregate}{BGAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{QUAGG}{any?} & @@ -16045,7 +16045,7 @@ digraph pic { \pagefrom{Collection}{CLAGG} \pagefrom{SetCategory}{SETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SETAGG}{any?} & @@ -16333,7 +16333,7 @@ digraph pic { \pageto{DequeueAggregate}{DQAGG} \pagefrom{BagAggregate}{BGAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SKAGG}{any?} & @@ -16526,7 +16526,7 @@ digraph pic { \pageto{StreamAggregate}{STAGG} \pagefrom{RecursiveAggregate}{RCAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{URAGG}{any?} & @@ -17005,7 +17005,7 @@ digraph pic { \pageto{Rng}{RNG} \pagefrom{CancellationAbelianMonoid}{CABMON} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ABELGRP}{0} & @@ -17147,7 +17147,7 @@ digraph pic { \pagefrom{BinaryRecursiveAggregate}{BRAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{BTCAT}{any?} & @@ -17378,7 +17378,7 @@ digraph pic { \pageto{KeyedDictionary}{KDAGG} \pagefrom{DictionaryOperations}{DIOPS} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DIAGG}{any?} & @@ -17607,7 +17607,7 @@ digraph pic { \pagefrom{QueueAggregate}{QUAGG} \pagefrom{StackAggregate}{SKAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DQAGG}{any?} & @@ -17843,7 +17843,7 @@ digraph pic { \pageto{ListAggregate}{LSAGG} \pagefrom{LinearAggregate}{LNAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ELAGG}{any?} & @@ -18143,7 +18143,7 @@ digraph pic { \pagefrom{LinearAggregate}{LNAGG} \pagefrom{OrderedSet}{ORDSET} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FLAGG}{any?} & @@ -18490,7 +18490,7 @@ digraph pic { \pagefrom{CancellationAbelianMonoid}{CABMON} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FAMONC}{0} & @@ -18677,7 +18677,7 @@ digraph pic { \pageto{MultisetAggregate}{MSETAGG} \pagefrom{DictionaryOperations}{DIOPS} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{MDAGG}{any?} & @@ -18885,7 +18885,7 @@ digraph pic { \pagefrom{AbelianMonoid}{ABELMON} \pagefrom{OrderedAbelianSemiGroup}{OASGP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{OAMON}{0} & @@ -18996,7 +18996,7 @@ digraph pic { \pagefrom{Group}{GROUP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PERMCAT}{1} & @@ -19196,7 +19196,7 @@ digraph pic { \pagefrom{LinearAggregate}{LNAGG} \pagefrom{UnaryRecursiveAggregate}{URAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{STAGG}{any?} & @@ -19593,7 +19593,7 @@ digraph pic { \pageto{RegularTriangularSetCategory}{RSETCAT} \pagefrom{PolynomialSetCategory}{PSETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{ll} \cross{TSETCAT}{algebraic?} & @@ -20406,7 +20406,7 @@ digraph pic { \pagefrom{AbelianGroup}{ABELGRP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FDIVCAT}{0} & @@ -20582,7 +20582,7 @@ digraph pic { \pagefrom{Dictionary}{DIAGG} \pagefrom{SetAggregate}{SETAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FSAGG}{any?} & @@ -20911,7 +20911,7 @@ digraph pic { \pageto{TableAggregate}{TBAGG} \pagefrom{Dictionary}{DIAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{KDAGG}{any?} & @@ -21154,7 +21154,7 @@ digraph pic { \pagefrom{StreamAggregate}{STAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LZSTAGG}{any?} & @@ -21979,7 +21979,7 @@ digraph pic { \pageto{Ring}{RING} \pagefrom{AbelianGroup}{ABELGRP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LMODULE}{0} & @@ -22102,7 +22102,7 @@ digraph pic { \pagefrom{ExtensibleLinearAggregate}{ELAGG} \pagefrom{FiniteLinearAggregate}{FLAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{LSAGG}{any?} & @@ -22679,7 +22679,7 @@ digraph pic { \pagefrom{MultiDictionary}{MDAGG} \pagefrom{SetAggregate}{SETAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{MSETAGG}{any?} & @@ -22896,7 +22896,7 @@ digraph pic { \pagefrom{AbelianGroup}{ABELGRP} \pagefrom{Monad}{MONAD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{NARNG}{0} & @@ -23049,7 +23049,7 @@ digraph pic { \pageto{VectorCategory}{VECTCAT} \pagefrom{FiniteLinearAggregate}{FLAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{A1AGG}{any?} & @@ -23547,7 +23547,7 @@ digraph pic { \pagefrom{CancellationAbelianMonoid}{CABMON} \pagefrom{OrderedAbelianMonoid}{OAMON} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{OCAMON}{0} & @@ -23670,7 +23670,7 @@ digraph pic { \pageto{SquareFreeRegularTriangularSetCategory}{SFRTCAT} \pagefrom{TriangularSetCategory}{TSETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{RSETCAT}{algebraicCoefficients?} & @@ -24329,7 +24329,7 @@ digraph pic { \pageto{BiModule}{BMODULE} \pagefrom{AbelianGroup}{ABELGRP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{RMODULE}{0} & @@ -24447,7 +24447,7 @@ Rng is a Ring that does not necessarily have a unit. \pagefrom{AbelianGroup}{ABELGRP} \pagefrom{SemiGroup}{SGROUP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{RNG}{0} & @@ -24586,7 +24586,7 @@ digraph pic { \pagefrom{LeftModule}{LMODULE} \pagefrom{RightModule}{RMODULE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{BMODULE}{0} & @@ -24729,7 +24729,7 @@ digraph pic { \pagefrom{OneDimensionalArrayAggregate}{A1AGG} \pagefrom{OrderedSet}{ORDSET} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{BTAGG}{any?} & @@ -25084,7 +25084,7 @@ digraph pic { \pagefrom{MonadWithUnit}{MONADWU} \pagefrom{NonAssociativeRng}{NARNG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{NASRING}{0} & @@ -25255,7 +25255,7 @@ digraph pic { \pageto{SquareFreeNormalizedTriangularSetCategory}{SNTSCAT} \pagefrom{RegularTriangularSetCategory}{RSETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{ll} \cross{NTSCAT}{algebraic?} & @@ -25608,7 +25608,7 @@ digraph pic { \pagefrom{AbelianGroup}{ABELGRP} \pagefrom{OrderedCancellationAbelianMonoid}{OCAMON} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{OAGROUP}{0} & @@ -25727,7 +25727,7 @@ digraph pic { \pagefrom{DirectProductCategory}{DIRPCAT} \pagefrom{OrderedCancellationAbelianMonoid}{OCAMON} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{OAMONS}{0} & @@ -25863,7 +25863,7 @@ digraph pic { \pagefrom{MultisetAggregate}{MSETAGG} \pagefrom{PriorityQueueAggregate}{PRQAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{OMSAGG}{any?} & @@ -26136,7 +26136,7 @@ digraph pic { \pagefrom{Monoid}{MONOID} \pagefrom{Rng}{RNG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{RING}{1} & @@ -26307,7 +26307,7 @@ digraph pic { \pageto{SquareFreeNormalizedTriangularSetCategory}{SNTSCAT} \pagefrom{RegularTriangularSetCategory}{RSETCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{ll} \cross{SFRTCAT}{algebraic?} & @@ -26654,7 +26654,7 @@ digraph pic { \pageto{StringCategory}{STRICAT} \pagefrom{OneDimensionalArrayAggregate}{A1AGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{SRAGG}{any?} & @@ -27069,7 +27069,7 @@ digraph pic { \pagefrom{IndexedAggregate}{IXAGG} \pagefrom{KeyedDictionary}{KDAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{TBAGG}{any?} & @@ -27517,7 +27517,7 @@ digraph pic { \pageto{PointCategory}{PTCAT} \pagefrom{OneDimensionalArrayAggregate}{A1AGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{VECTCAT}{any?} & @@ -27860,7 +27860,7 @@ digraph pic { \pagefrom{ListAggregate}{LSAGG} \pagefrom{TableAggregate}{TBAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{ALAGG}{any?} & @@ -28379,7 +28379,7 @@ digraph pic { \pageto{QuotientFieldCategory}{QFCAT} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{CHARNZ}{1} & @@ -28535,7 +28535,7 @@ digraph pic { \pageto{RealNumberSystem}{RNS} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{CHARZ}{1} & @@ -28685,7 +28685,7 @@ Commutative Rings are a subset of IntegralDomains. \pagefrom{BiModule}{BMODULE} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{COMRING}{1} & @@ -28852,7 +28852,7 @@ digraph pic { \pageto{UnivariatePolynomialCategory}{UPOLYC} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DIFRING}{1} & @@ -29032,7 +29032,7 @@ digraph pic { \pagefrom{BiModule}{BMODULE} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ENTIRER}{1} & @@ -29195,7 +29195,7 @@ digraph pic { \pagefrom{BiModule}{BMODULE} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{FMCAT}{0} & @@ -29413,7 +29413,7 @@ digraph pic { \pagefrom{LeftModule}{LMODULE} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LALG}{0} & @@ -29557,7 +29557,7 @@ digraph pic { \pageto{MonogenicAlgebra}{MONOGEN} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LINEXP}{0} & @@ -29724,7 +29724,7 @@ digraph pic { \pageto{VectorSpace}{VSPACE} \pagefrom{BiModule}{BMODULE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{MODULE}{0} & @@ -29864,7 +29864,7 @@ digraph pic { \pagefrom{OrderedAbelianGroup}{OAGROUP} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ORDRING}{1} & @@ -30068,7 +30068,7 @@ digraph pic { \pageto{PolynomialCategory}{POLYCAT} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PDRING}{1} & @@ -30284,7 +30284,7 @@ digraph pic { \pagefrom{VectorCategory}{VECTCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PTCAT}{any?} & @@ -30586,7 +30586,7 @@ The RectangularMatrix domain is matrices of fixed dimension. \pagefrom{HomogeneousAggregate}{HOAGG} \pagefrom{MatrixCategory}{MATCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{RMATCAT}{0} & @@ -30956,7 +30956,7 @@ digraph pic { \pagefrom{NormalizedTriangularSetCategory}{NTSCAT} \pagefrom{SquareFreeRegularTriangularSetCategory}{SFRTCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{ll} \cross{SNTSCAT}{algebraic?} & @@ -31277,7 +31277,7 @@ digraph pic { \pagefrom{SetCategory}{SETCAT} \pagefrom{StringAggregate}{SRAGG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{STRICAT}{any?} & @@ -31621,7 +31621,7 @@ digraph pic { \pagefrom{FullyRetractableTo}{FRETRCT} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{OREPCAT}{0} & @@ -32116,7 +32116,7 @@ digraph pic { \pagefrom{BiModule}{BMODULE} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{XALG}{0} & @@ -32300,7 +32300,7 @@ digraph pic { \pagefrom{Module}{MODULE} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{ALGEBRA}{1} & @@ -32510,7 +32510,7 @@ digraph pic { \pagefrom{PartialDifferentialRing}{PDRING} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DIFEXT}{1} & @@ -32743,7 +32743,7 @@ digraph pic { \pageto{SquareMatrixCategory}{SMATCAT} \pagefrom{LinearlyExplicitRingOver}{LINEXP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FLINEXP}{1} & @@ -32927,7 +32927,7 @@ digraph pic { \pageto{FreeLieAlgebra}{FLALG} \pagefrom{Module}{MODULE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{LIECAT}{0} & @@ -33076,7 +33076,7 @@ digraph pic { \pagefrom{Eltable}{ELTAB} \pagefrom{UnivariateSkewPolynomialCategory}{OREPCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{LODOCAT}{0} & @@ -33408,7 +33408,7 @@ digraph pic { \pagefrom{Module}{MODULE} \pagefrom{NonAssociativeRng}{NARNG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{NAALG}{0} & @@ -33582,7 +33582,7 @@ digraph pic { \pageto{ExtensionField}{XF} \pagefrom{Module}{MODULE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{VSPACE}{0} & @@ -33726,7 +33726,7 @@ digraph pic { \pagefrom{Ring}{RING} \pagefrom{XAlgebra}{XALG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{XFALG}{0} & @@ -34052,7 +34052,7 @@ digraph pic { \pagefrom{OrderedRing}{ORDRING} \pagefrom{OrderedAbelianMonoidSup}{OAMONS} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DIRPCAT}{0} & @@ -34528,7 +34528,7 @@ digraph pic { \pagefrom{Algebra}{ALGEBRA} \pagefrom{EntireRing}{ENTIRER} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DIVRING}{1} & @@ -34726,7 +34726,7 @@ digraph pic { \pageto{FramedNonAssociativeAlgebra}{FRNAALG} \pagefrom{NonAssociativeAlgebra}{NAALG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FINAALG}{0} & @@ -35627,7 +35627,7 @@ digraph pic { \pagefrom{LieAlgebra}{LIECAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FLALG}{0} & @@ -35850,7 +35850,7 @@ Integral Domains are a subset of Unique Factorization domains. \pagefrom{CommutativeRing}{COMRING} \pagefrom{EntireRing}{ENTIRER} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{INTDOM}{0} & @@ -36074,7 +36074,7 @@ digraph pic { \pagefrom{BiModule}{BMODULE} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{MLO}{0} & @@ -36309,7 +36309,7 @@ digraph pic { \pagefrom{FullyEvalableOver}{FEVALAB} \pagefrom{FullyRetractableTo}{FRETRCT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{OC}{0} & @@ -36799,7 +36799,7 @@ digraph pic { \pagefrom{FullyLinearlyExplicitRingOver}{FLINEXP} \pagefrom{FullyRetractableTo}{FRETRCT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{QUATCAT}{0} & @@ -37268,7 +37268,7 @@ The SquareMatrix domain is for square matrices of fixed dimension. \pagefrom{MatrixCategory}{MATCAT} \pagefrom{RectangularMatrixCategory}{RMATCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{SMATCAT}{0} & @@ -37774,7 +37774,7 @@ digraph pic { \pagefrom{XFreeAlgebra}{XFALG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{XPOLYC}{0} & @@ -38033,7 +38033,7 @@ digraph pic { \pagefrom{BiModule}{BMODULE} \pagefrom{Ring}{RING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{AMR}{0} & @@ -38326,7 +38326,7 @@ digraph pic { \pagefrom{OrderedSet}{ORDSET} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FMTC}{0} & @@ -38544,7 +38544,7 @@ digraph pic { \pagefrom{FiniteRankNonAssociativeAlgebra}{FINAALG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FRNAALG}{0} & @@ -39145,7 +39145,7 @@ digraph pic { \pageto{UnivariatePolynomialCategory}{UPOLYC} \pagefrom{IntegralDomain}{INTDOM} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{GCDDOM}{0} & @@ -39372,7 +39372,7 @@ digraph pic { \pagefrom{QuotientFieldCategory}{QFCAT} \pagefrom{OrderedRing}{ORDRING} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{OINTDOM}{1} & @@ -39567,7 +39567,7 @@ digraph pic { \pagefrom{AbelianMonoidRing}{AMR} \pagefrom{FullyRetractableTo}{FRETRCT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FAMR}{0} & @@ -39945,7 +39945,7 @@ digraph pic { \pagefrom{RetractableTo}{RETRACT} \pagefrom{TranscendentalFunctionCategory}{TRANFUN} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{INTCAT}{0} & @@ -40294,7 +40294,7 @@ digraph pic { \pageto{UnivariatePowerSeriesCategory}{UPSCAT} \pagefrom{AbelianMonoidRing}{AMR} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PSCAT}{0} & @@ -40578,7 +40578,7 @@ Principal Ideal Domains are a subset of Euclidean Domains. \pageto{EuclideanDomain}{EUCDOM} \pagefrom{GcdDomain}{GCDDOM} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{PID}{0} & @@ -40777,7 +40777,7 @@ Unique Factorization Domains are a subset of Principal Ideal Domains. \pageto{PolynomialFactorizationExplicit}{PFECAT} \pagefrom{GcdDomain}{GCDDOM} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{UFD}{0} & @@ -40992,7 +40992,7 @@ Euclidean Domains are a subset of Fields. \pageto{QuotientFieldCategory}{QFCAT} \pagefrom{PrincipalIdealDomain}{PID} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{EUCDOM}{1} & @@ -41323,7 +41323,7 @@ digraph pic { \pagefrom{PartialDifferentialRing}{PDRING} \pagefrom{PowerSeriesCategory}{PSCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{MTSCAT}{0} & @@ -41677,7 +41677,7 @@ digraph pic { \pageto{UnivariatePolynomialCategory}{UPOLYC} \pagefrom{UniqueFactorizationDomain}{UFD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{PFECAT}{0} & @@ -41952,7 +41952,7 @@ digraph pic { \pageto{UnivariateTaylorSeriesCategory}{UTSCAT} \pagefrom{PowerSeriesCategory}{PSCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{UPSCAT}{0} & @@ -42355,6 +42355,7 @@ digraph pic { Euclidean Domains are a subset of Fields. \pagefrom{EuclideanDomain}{EUCDOM} +\pageto{PseudoAlgebraicClosureOfPerfectFieldCategory}{PACPERC} {\bf See:} @@ -42373,7 +42374,7 @@ Euclidean Domains are a subset of Fields. \pagefrom{EuclideanDomain}{EUCDOM} \pagefrom{UniqueFactorizationDomain}{UFD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FIELD}{0} & @@ -42625,7 +42626,7 @@ digraph pic { \pagefrom{StepThrough}{STEP} \pagefrom{UniqueFactorizationDomain}{UFD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{INS}{0} & @@ -43131,7 +43132,7 @@ digraph pic { \pagefrom{CharacteristicZero}{CHARZ} \pagefrom{EuclideanDomain}{EUCDOM} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{PADICCT}{0} & @@ -43398,7 +43399,7 @@ digraph pic { \pagefrom{PolynomialFactorizationExplicit}{PFECAT} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{POLYCAT}{0} & @@ -44306,7 +44307,7 @@ digraph pic { \pagefrom{TranscendentalFunctionCategory}{TRANFUN} \pagefrom{UnivariatePowerSeriesCategory}{UPSCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{UTSCAT}{0} & @@ -45183,7 +45184,7 @@ o )show AlgebraicallyClosedField \pagefrom{Field}{FIELD} \pagefrom{RadicalCategory}{RADCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{ACF}{0} & @@ -45596,7 +45597,7 @@ digraph pic { \pagefrom{PolynomialCategory}{POLYCAT} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{DPOLCAT}{0} & @@ -46308,7 +46309,7 @@ digraph pic { \pagefrom{CharacteristicNonZero}{CHARNZ} \pagefrom{Field}{FIELD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{FPC}{0} & @@ -46555,7 +46556,7 @@ digraph pic { \pagefrom{CharacteristicZero}{CHARZ} \pagefrom{Field}{FIELD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{FINRALG}{0} & @@ -46834,7 +46835,7 @@ digraph pic { \pagefrom{Ring}{RING} \pagefrom{SemiGroup}{SGROUP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{FS}{0} & @@ -48147,12 +48148,9 @@ o )show PseudoAlgebraicClosureOfPerfectFieldCategory @ -\pagefrom{DivisionRing}{DIVRING} \pagefrom{Field}{FIELD} -\pagefrom{EuclideanDomain}{EUCDOM} -\pagefrom{UniqueFactorizationDomain}{UFD} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{PACPERC}{0} & \cross{PACPERC}{1} & @@ -48350,7 +48348,7 @@ These exports come from \refto{DivisionRing}(): ++ Any algebraic operations defined for several elements ++ are only defined if all of the concerned elements are comming from ++ a set of related tour extensions. -PseudoAlgebraicClosureOfPerfectFieldCategory : Category == Field with +PseudoAlgebraicClosureOfPerfectFieldCategory() : Category == Field with definingPolynomial: () -> SUP(%) definingPolynomial: % -> SUP % @@ -48434,7 +48432,7 @@ digraph pic { \pagefrom{RetractableTo}{RETRACT} \pagefrom{StepThrough}{STEP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{QFCAT}{0} & @@ -48995,7 +48993,7 @@ digraph pic { \pagefrom{OrderedRing}{ORDRING} \pagefrom{RadicalCategory}{RADCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{RCFIELD}{0} & @@ -49451,7 +49449,7 @@ digraph pic { \pagefrom{RealConstant}{REAL} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{RNS}{0} & @@ -49791,7 +49789,7 @@ digraph pic { \pagefrom{PolynomialCategory}{POLYCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{RPOLCAT}{0} & @@ -51574,7 +51572,7 @@ digraph pic { \pagefrom{TranscendentalFunctionCategory}{TRANFUN} \pagefrom{UnivariatePowerSeriesCategory}{UPSCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{ULSCAT}{0} & @@ -52056,7 +52054,7 @@ digraph pic { \pagefrom{RadicalCategory}{RADCAT} \pagefrom{UnivariatePowerSeriesCategory}{UPSCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{UPXSCAT}{0} & @@ -52528,7 +52526,7 @@ digraph pic { \pagefrom{PolynomialFactorizationExplicit}{PFECAT} \pagefrom{StepThrough}{STEP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{UPOLYC}{0} & @@ -53506,7 +53504,7 @@ digraph pic { \pagefrom{AlgebraicallyClosedField}{ACF} \pagefrom{FunctionSpace}{FS} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{ACFS}{0} & @@ -54086,7 +54084,7 @@ digraph pic { \pagefrom{RetractableTo}{RETRACT} \pagefrom{VectorSpace}{VSPACE} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{XF}{0} & @@ -54413,7 +54411,7 @@ digraph pic { \pagefrom{Finite}{FINITE} \pagefrom{StepThrough}{STEP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{FFIELDC}{0} & @@ -54912,7 +54910,7 @@ digraph pic { \pagefrom{RealNumberSystem}{RNS} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{FPS}{0} & @@ -55294,7 +55292,7 @@ digraph pic { \pageto{MonogenicAlgebra}{MONOGEN} \pagefrom{FiniteRankAlgebra}{FINRALG} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FRAMALG}{0} & @@ -55553,6 +55551,370 @@ digraph pic { @ %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +\pagehead{PseudoAlgebraicClosureOfFiniteFieldCategory}{PACFFC} +\pagepic{ps/v102pseudoalgebraicclosureoffinitefieldcategory.ps}{PACFFC}{0.50} +<>= +)set break resume +)sys rm -f PseudoAlgebraicClosureOfFiniteFieldCategory.output +)spool PseudoAlgebraicClosureOfFiniteFieldCategory.output +)set message test on +)set message auto off +)clear all + +--S 1 of 1 +)show PseudoAlgebraicClosureOfFiniteFieldCategory +--R PseudoAlgebraicClosureOfFiniteFieldCategory is a category constructor +--R Abbreviation for PseudoAlgebraicClosureOfFiniteFieldCategory is PACFFC +--R This constructor is exposed in this frame. +--R Issue )edit bookvol10.2.pamphlet to see algebra source code for PACFFC +--R +--R------------------------------- Operations -------------------------------- +--R ?*? : (Fraction Integer,%) -> % ?*? : (%,Fraction Integer) -> % +--R ?*? : (%,%) -> % ?*? : (Integer,%) -> % +--R ?*? : (PositiveInteger,%) -> % ?**? : (%,Integer) -> % +--R ?**? : (%,PositiveInteger) -> % ?+? : (%,%) -> % +--R ?-? : (%,%) -> % -? : % -> % +--R ?/? : (%,%) -> % ?=? : (%,%) -> Boolean +--R D : % -> % D : (%,NonNegativeInteger) -> % +--R 1 : () -> % 0 : () -> % +--R ?^? : (%,Integer) -> % ?^? : (%,PositiveInteger) -> % +--R associates? : (%,%) -> Boolean charthRoot : % -> % +--R coerce : Fraction Integer -> % coerce : % -> % +--R coerce : Integer -> % coerce : % -> OutputForm +--R conjugate : % -> % createPrimitiveElement : () -> % +--R definingPolynomial : () -> SUP % definingPolynomial : % -> SUP % +--R differentiate : % -> % extDegree : % -> PI +--R factor : % -> Factored % fullOutput : % -> OutputForm +--R gcd : List % -> % gcd : (%,%) -> % +--R ground? : % -> Boolean hash : % -> SingleInteger +--R index : PositiveInteger -> % init : () -> % +--R inv : % -> % latex : % -> String +--R lcm : List % -> % lcm : (%,%) -> % +--R lift : % -> SUP % lift : (%,%) -> SUP % +--R lookup : % -> PositiveInteger maxTower : List % -> % +--R newElement : (SUP %,Symbol) -> % one? : % -> Boolean +--R order : % -> PositiveInteger previousTower : % -> % +--R prime? : % -> Boolean primeFrobenius : % -> % +--R primitive? : % -> Boolean primitiveElement : () -> % +--R ?quo? : (%,%) -> % random : () -> % +--R recip : % -> Union(%,"failed") reduce : SUP % -> % +--R ?rem? : (%,%) -> % sample : () -> % +--R setTower! : % -> Void size : () -> NonNegativeInteger +--R sizeLess? : (%,%) -> Boolean squareFree : % -> Factored % +--R squareFreePart : % -> % unit? : % -> Boolean +--R unitCanonical : % -> % vectorise : (%,%) -> Vector % +--R zero? : % -> Boolean ?~=? : (%,%) -> Boolean +--R ?*? : (NonNegativeInteger,%) -> % +--R ?**? : (%,NonNegativeInteger) -> % +--R ?^? : (%,NonNegativeInteger) -> % +--R characteristic : () -> NonNegativeInteger +--R charthRoot : % -> Union(%,"failed") +--R conditionP : Matrix % -> Union(Vector %,"failed") +--R differentiate : (%,NonNegativeInteger) -> % +--R discreteLog : % -> NonNegativeInteger +--R discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") +--R distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List % +--R divide : (%,%) -> Record(quotient: %,remainder: %) +--R euclideanSize : % -> NonNegativeInteger +--R expressIdealMember : (List %,%) -> Union(List %,"failed") +--R exquo : (%,%) -> Union(%,"failed") +--R extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") +--R extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) +--R factorsOfCyclicGroupSize : () -> List Record(factor: Integer,exponent: Integer) +--R gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % +--R multiEuclidean : (List %,%) -> Union(List %,"failed") +--R newElement : (SUP %,%,Symbol) -> % +--R nextItem : % -> Union(%,"failed") +--R order : % -> OnePointCompletion PositiveInteger +--R primeFrobenius : (%,NonNegativeInteger) -> % +--R principalIdeal : List % -> Record(coef: List %,generator: %) +--R representationType : () -> Union("prime",polynomial,normal,cyclic) +--R subtractIfCan : (%,%) -> Union(%,"failed") +--R tableForDiscreteLogarithm : Integer -> Table(PositiveInteger,NonNegativeInteger) +--R unitNormal : % -> Record(unit: %,canonical: %,associate: %) +--R +--E 1 + +)spool +)lisp (bye) +@ +<>= +==================================================================== +PseudoAlgebraicClosureOfFiniteFieldCategory examples +==================================================================== + +See Also: +o )show PseudoAlgebraicClosureOfFiniteFieldCategory + +@ + +\pagefrom{FieldOfPrimeCharacteristic}{FPC} +\pagefrom{PseudoAlgebraicClosureOfPerfectFieldCategory}{PACPERC} + +{\bf Exports:}\\ +\begin{tabular}{lll} +\cross{PACFFC}{0} & +\cross{PACFFC}{1} & +\cross{PACFFC}{associates?} \\ +\cross{PACFFC}{characteristic} & +\cross{PACFFC}{charthRoot} & +\cross{PACFFC}{conditionP} \\ +\cross{PACFFC}{coerce} & +\cross{PACFFC}{conjugate} & +\cross{PACFFC}{createPrimitiveElement} \\ +\cross{PACFFC}{D} & +\cross{PACFFC}{definingPolynomial} & +\cross{PACFFC}{differentiate} \\ +\cross{PACFFC}{discreteLog} & +\cross{PACFFC}{distinguishedRootsOf} & +\cross{PACFFC}{divide} \\ +\cross{PACFFC}{euclideanSize} & +\cross{PACFFC}{extendedEuclidean} & +\cross{PACFFC}{expressIdealMember} \\ +\cross{PACFFC}{exquo} & +\cross{PACFFC}{extDegree} & +\cross{PACFFC}{factor} \\ +\cross{PACFFC}{factorsOfCyclicGroupSize} & +\cross{PACFFC}{fullOutput} & +\cross{PACFFC}{gcd} \\ +\cross{PACFFC}{gcdPolynomial} & +\cross{PACFFC}{ground?} & +\cross{PACFFC}{hash} \\ +\cross{PACFFC}{index} & +\cross{PACFFC}{init} & +\cross{PACFFC}{inv} \\ +\cross{PACFFC}{latex} & +\cross{PACFFC}{lcm} & +\cross{PACFFC}{lift} \\ +\cross{PACFFC}{lookup} & +\cross{PACFFC}{maxTower} & +\cross{PACFFC}{multiEuclidean} \\ +\cross{PACFFC}{newElement} & +\cross{PACFFC}{nextItem} & +\cross{PACFFC}{one?} \\ +\cross{PACFFC}{order} & +\cross{PACFFC}{previousTower} & +\cross{PACFFC}{prime?} \\ +\cross{PACFFC}{primeFrobenius} & +\cross{PACFFC}{primitive?} & +\cross{PACFFC}{primitiveElement} \\ +\cross{PACFFC}{principalIdeal} & +\cross{PACFFC}{?quo?} & +\cross{PACFFC}{random} \\ +\cross{PACFFC}{recip} & +\cross{PACFFC}{reduce} & +\cross{PACFFC}{?rem?} \\ +\cross{PACFFC}{representationType} & +\cross{PACFFC}{sample} & +\cross{PACFFC}{setTower!} \\ +\cross{PACFFC}{size} & +\cross{PACFFC}{sizeLess?} & +\cross{PACFFC}{squareFree} \\ +\cross{PACFFC}{squareFreePart} & +\cross{PACFFC}{subtractIfCan} & +\cross{PACFFC}{tableForDiscreteLogarithm} \\ +\cross{PACFFC}{unit?} & +\cross{PACFFC}{unitCanonical} & +\cross{PACFFC}{unitNormal} \\ +\cross{PACFFC}{vectorise} & +\cross{PACFFC}{zero?} & +\cross{PACFFC}{?*?} \\ +\cross{PACFFC}{?**?} & +\cross{PACFFC}{?+?} & +\cross{PACFFC}{?-?} \\ +\cross{PACFFC}{-?} & +\cross{PACFFC}{?/?} & +\cross{PACFFC}{?=?} \\ +\cross{PACFFC}{?\^{}?} & +\cross{PACFFC}{?\~{}=?} & +\end{tabular} + +{\bf Attributes Exported:} +\begin{itemize} +\item {\bf \cross{PACFFC}{canonicalUnitNormal}} +is true if we can choose a canonical representative for each class +of associate elements, that is {\tt associates?(a,b)} returns true +if and only if {\tt unitCanonical(a) = unitCanonical(b)}. +\item {\bf \cross{PACFFC}{canonicalsClosed}} +is true if\hfill\\ +{\tt unitCanonical(a)*unitCanonical(b) = unitCanonical(a*b)}. +\item {\bf \cross{PACFFC}{noZeroDivisors}} +is true if $x * y \ne 0$ implies both x and y are non-zero. +\item {\bf \cross{PACFFC}{commutative(``*'')}} +is true if it has an operation $"*": (D,D) -> D$ +which is commutative. +\item {\bf \cross{PACFFC}{unitsKnown}} +is true if a monoid (a multiplicative semigroup with a 1) has +unitsKnown means that the operation {\tt recip} can only return +``failed'' if its argument is not a unit. +\item {\bf \cross{PACFFC}{leftUnitary}} +is true if $1 * x = x$ for all x. +\item {\bf \cross{PACFFC}{rightUnitary}} +is true if $x * 1 = x$ for all x. +\end{itemize} + +These exports come from \refto{PseudoAlgebraicClosureOfPerfectFieldCategory}(): +\begin{verbatim} + ?*? : (Fraction Integer,%) -> % + ?*? : (%,Fraction Integer) -> % + ?*? : (%,%) -> % + ?*? : (Integer,%) -> % + ?*? : (PositiveInteger,%) -> % + ?*? : (NonNegativeInteger,%) -> % + ?**? : (%,Integer) -> % + ?**? : (%,PositiveInteger) -> % + ?**? : (%,NonNegativeInteger) -> % + ?+? : (%,%) -> % + ?-? : (%,%) -> % + -? : % -> % + ?/? : (%,%) -> % + ?=? : (%,%) -> Boolean + 1 : () -> % + 0 : () -> % + ?^? : (%,Integer) -> % + ?^? : (%,PositiveInteger) -> % + ?^? : (%,NonNegativeInteger) -> % + ?~=? : (%,%) -> Boolean + associates? : (%,%) -> Boolean + characteristic : () -> NonNegativeInteger + coerce : Fraction Integer -> % + coerce : % -> % + coerce : Integer -> % + coerce : % -> OutputForm + conjugate : % -> % + definingPolynomial : () -> SUP % + definingPolynomial : % -> SUP % + distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List % + divide : (%,%) -> Record(quotient: %,remainder: %) + euclideanSize : % -> NonNegativeInteger + expressIdealMember : (List %,%) -> Union(List %,"failed") + exquo : (%,%) -> Union(%,"failed") + extDegree : % -> PI + extendedEuclidean : (%,%,%) -> Union(Record(coef1: %,coef2: %),"failed") + extendedEuclidean : (%,%) -> Record(coef1: %,coef2: %,generator: %) + factor : % -> Factored % + fullOutput : % -> OutputForm + gcd : List % -> % + gcd : (%,%) -> % + gcdPolynomial : (SparseUnivariatePolynomial %,SparseUnivariatePolynomial %) -> SparseUnivariatePolynomial % + ground? : % -> Boolean + hash : % -> SingleInteger + inv : % -> % + latex : % -> String + lcm : List % -> % + lcm : (%,%) -> % + lift : % -> SUP % + lift : (%,%) -> SUP % + maxTower : List % -> % + multiEuclidean : (List %,%) -> Union(List %,"failed") + newElement : (SUP %,Symbol) -> % + newElement : (SUP %,%,Symbol) -> % + one? : % -> Boolean + previousTower : % -> % + prime? : % -> Boolean + principalIdeal : List % -> Record(coef: List %,generator: %) + ?quo? : (%,%) -> % + recip : % -> Union(%,"failed") + reduce : SUP % -> % + ?rem? : (%,%) -> % + sample : () -> % + setTower! : % -> Void + sizeLess? : (%,%) -> Boolean + squareFree : % -> Factored % + squareFreePart : % -> % + subtractIfCan : (%,%) -> Union(%,"failed") + unit? : % -> Boolean + unitCanonical : % -> % + unitNormal : % -> Record(unit: %,canonical: %,associate: %) + vectorise : (%,%) -> Vector % + zero? : % -> Boolean +\end{verbatim} + +These exports come from \refto{FiniteFieldCategory}(): +\begin{verbatim} + charthRoot : % -> % + charthRoot : % -> Union(%,"failed") + conditionP : Matrix % -> Union(Vector %,"failed") + createPrimitiveElement : () -> % + D : % -> % + D : (%,NonNegativeInteger) -> % + differentiate : % -> % + differentiate : (%,NonNegativeInteger) -> % + discreteLog : % -> NonNegativeInteger + discreteLog : (%,%) -> Union(NonNegativeInteger,"failed") + factorsOfCyclicGroupSize : () -> + List Record(factor: Integer,exponent: Integer) + index : PositiveInteger -> % + init : () -> % + lookup : % -> PositiveInteger + nextItem : % -> Union(%,"failed") + order : % -> OnePointCompletion PositiveInteger + order : % -> PositiveInteger + primeFrobenius : (%,NonNegativeInteger) -> % + primeFrobenius : % -> % + primitive? : % -> Boolean + primitiveElement : () -> % + random : () -> % + representationType : () -> Union("prime",polynomial,normal,cyclic) + size : () -> NonNegativeInteger + tableForDiscreteLogarithm : Integer -> + Table(PositiveInteger,NonNegativeInteger) +\end{verbatim} + +<>= +)abbrev category PACFFC PseudoAlgebraicClosureOfFiniteFieldCategory +-- PseudoAlgebraicClosureOfFiniteFieldCategory +++ Authors: Gaetan Hache +++ Date Created: june 1996 +++ Date Last Updated: +++ References: +++ Description: This category exports the function for the domain +++ PseudoAlgebraicClosureOfFiniteField which implement dynamic extension +++ using the simple notion of tower extensions. +++ A tower extension T of the ground +++ field K is any sequence of field extension (T : K_0, K_1, ..., K_i...,K_n) +++ where K_0 = K and for i =1,2,...,n, K_i is an extension +++ of K_{i-1} of degree > 1 and defined by an irreducible polynomial +++ p(Z) in K_{i-1}. +++ Two towers (T_1: K_01, K_11,...,K_i1,...,K_n1) +++ and (T_2: K_02, K_12,...,K_i2,...,K_n2) +++ are said to be related if T_1 <= T_2 (or T_1 >= T_2), +++ that is if K_i1 = K_i2 for i=1,2,...,n1 +++ (or i=1,2,...,n2). Any algebraic operations defined for several elements +++ are only defined if all of the concerned elements are comming from +++ a set of related tour extensions. +PseudoAlgebraicClosureOfFiniteFieldCategory:Category == + Join(FiniteFieldCategory, PseudoAlgebraicClosureOfPerfectFieldCategory) +@ +<>= +"PACFFC" [color=lightblue,href="bookvol10.2.pdf#nameddest=PACFFC"]; +"PACFFC" -> "PACPERC" + +@ +<>= +"PseudoAlgebraicClosureOfFiniteFieldCategory" + [color=lightblue,href="bookvol10.2.pdf#nameddest=PACFFC"]; +"PseudoAlgebraicClosureOfFiniteFieldCategory" -> "PACPERC" +"PseudoAlgebraicClosureOfFiniteFieldCategory" -> "FFIELDC" + +@ +<>= +digraph pic { + fontsize=10; + bgcolor="#FFFF66"; + node [shape=box, color=white, style=filled]; + +"PseudoAlgebraicClosureOfFiniteFieldCategory" [color=lightblue]; +"PseudoAlgebraicClosureOfFiniteFieldCategory" -> "PACPERC" +"PseudoAlgebraicClosureOfFiniteFieldCategory" -> "FFIELDC" + +"PACPERC" [color=lightblue]; +"FFIELDC" [color=lightblue]; + +} + +@ +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \pagehead{UnivariateLaurentSeriesConstructorCategory}{ULSCCAT} \pagepic{ps/v102univariatelaurentseriesconstructorcategory.ps}{ULSCCAT}{0.50} @@ -55561,7 +55923,7 @@ digraph pic { \pagefrom{RetractableTo}{RETRACT} \pagefrom{UnivariateLaurentSeriesCategory}{ULSCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{ULSCCAT}{0} & @@ -56215,7 +56577,7 @@ digraph pic { \pagefrom{RetractableTo}{RETRACT} \pagefrom{UnivariatePuiseuxSeriesCategory}{UPXSCAT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{llll} \cross{UPXSCCA}{0} & @@ -56680,7 +57042,7 @@ digraph pic { \pagefrom{ExtensionField}{XF} \pagefrom{RetractableTo}{RETRACT} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{FAXF}{0} & @@ -57332,7 +57694,7 @@ digraph pic { \pagefrom{FullyRetractableTo}{FRETRCT} \pagefrom{LinearlyExplicitRingOver}{LINEXP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{MONOGEN}{0} & @@ -57831,7 +58193,7 @@ digraph pic { \pagefrom{Patternable}{PATAB} \pagefrom{FullyLinearlyExplicitRingOver}{FLINEXP} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lll} \cross{COMPCAT}{0} & @@ -58761,7 +59123,7 @@ digraph pic { \pagefrom{MonogenicAlgebra}{MONOGEN} -{\bf Exports:} +{\bf Exports:}\\ \begin{tabular}{lllll} \cross{FFCAT}{0} & @@ -74074,210 +74436,233 @@ Note that this code is not included in the generated catdef.spad file. @ \chapter{Chunk collections} <>= +<> +<> +<> +<> +<> +<> +<> +<> <> <> +<> <> + +<> <> +<> +<> +<> +<> + +<> +<> +<> +<> <> +<> <> +<> +<> +<> <> + +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> + <> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> <> +<> +<> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> +<> +<> +<> + +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> <> +<> <> <> +<> <> <> +<> +<> +<> +<> +<> <> -<> -<> -<> +<> +<> +<> +<> +<> + +<> +<> <> +<> + <> +<> + +<> <> +<> +<> +<> +<> + +<> + +<> +<> +<> +<> +<> +<> +<> <> +<> +<> + +<> +<> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> <> +<> +<> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> <> -<> -<> -<> -<> -<> -<> -<> -<> +<> + +<> <> +<> <> +<> +<> + +<> +<> +<> <> +<> <> +<> +<> +<> +<> +<> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> <> +<> +<> + +<> +<> <> +<> +<> +<> +<> +<> +<> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> +<> +<> +<> <> +<> <> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> -<> +<> +<> +<> + +<> +<> <> + +<> <> +<> <> +<> +<> +<> <> +<> +<> +<> +<> +<> + +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> +<> + +<> +<> +<> +<> +<> +<> +<> + +<> +<> <> -<> -<> -<> -<> -<> -<> -<> <> +<> +<> +<> <> -<> -<> -<> -<> +<> +<> + +<> +<> + +<> +<> +<> @ <>= digraph dotabb { @@ -74368,6 +74753,7 @@ digraph dotabb { <> <> <> +<> <> <> <> @@ -74490,7 +74876,7 @@ digraph dotabb { <> <> <> - +<> } @ <>= @@ -74638,6 +75024,7 @@ digraph dotfull { <> <> <> +<> <> <> <> @@ -74706,6 +75093,7 @@ digraph dotfull { <> <> <> +<> } @ \eject diff --git a/books/bookvol5.pamphlet b/books/bookvol5.pamphlet index b86d067..e0bb2d8 100644 --- a/books/bookvol5.pamphlet +++ b/books/bookvol5.pamphlet @@ -24469,6 +24469,7 @@ otherwise the new algebra won't be loaded by the interpreter when needed. (|PrimitiveFunctionCategory| . PRIMCAT) (|PrincipalIdealDomain| . PID) (|PriorityQueueAggregate| . PRQAGG) + (|PseudoAlgebraicClosureOfFiniteFieldCategory| . PACFFC) (|PseudoAlgebraicClosureOfPerfectFieldCategory| . PACPERC) (|QuaternionCategory| . QUATCAT) (|QueueAggregate| . QUAGG) diff --git a/books/ps/v102pseudoalgebraicclosureoffinitefieldcategory.ps b/books/ps/v102pseudoalgebraicclosureoffinitefieldcategory.ps new file mode 100644 index 0000000..3488f7f --- /dev/null +++ b/books/ps/v102pseudoalgebraicclosureoffinitefieldcategory.ps @@ -0,0 +1,298 @@ +%!PS-Adobe-3.0 EPSF-3.0 +%%Creator: Graphviz version 2.20.2 (Mon Mar 30 10:09:11 UTC 2009) +%%For: (root) root +%%Title: pic +%%Pages: (atend) +%%BoundingBox: (atend) +%%EndComments +save +%%BeginProlog +/DotDict 200 dict def +DotDict begin + +/setupLatin1 { +mark +/EncodingVector 256 array def + EncodingVector 0 + +ISOLatin1Encoding 0 255 getinterval putinterval +EncodingVector 45 /hyphen put + +% Set up ISO Latin 1 character encoding +/starnetISO { + dup dup findfont dup length dict begin + { 1 index /FID ne { def }{ pop pop } ifelse + } forall + /Encoding EncodingVector def + currentdict end definefont +} def +/Times-Roman starnetISO def +/Times-Italic starnetISO def +/Times-Bold starnetISO def +/Times-BoldItalic starnetISO def +/Helvetica starnetISO def +/Helvetica-Oblique starnetISO def +/Helvetica-Bold starnetISO def +/Helvetica-BoldOblique starnetISO def +/Courier starnetISO def +/Courier-Oblique starnetISO def +/Courier-Bold starnetISO def +/Courier-BoldOblique starnetISO def +cleartomark +} bind def + +%%BeginResource: procset graphviz 0 0 +/coord-font-family /Times-Roman def +/default-font-family /Times-Roman def +/coordfont coord-font-family findfont 8 scalefont def + +/InvScaleFactor 1.0 def +/set_scale { + dup 1 exch div /InvScaleFactor exch def + scale +} bind def + +% styles +/solid { [] 0 setdash } bind def +/dashed { [9 InvScaleFactor mul dup ] 0 setdash } bind def +/dotted { [1 InvScaleFactor mul 6 InvScaleFactor mul] 0 setdash } bind def +/invis {/fill {newpath} def /stroke {newpath} def /show {pop newpath} def} bind def +/bold { 2 setlinewidth } bind def +/filled { } bind def +/unfilled { } bind def +/rounded { } bind def +/diagonals { } bind def + +% hooks for setting color +/nodecolor { sethsbcolor } bind def +/edgecolor { sethsbcolor } bind def +/graphcolor { sethsbcolor } bind def +/nopcolor {pop pop pop} bind def + +/beginpage { % i j npages + /npages exch def + /j exch def + /i exch def + /str 10 string def + npages 1 gt { + gsave + coordfont setfont + 0 0 moveto + (\() show i str cvs show (,) show j str cvs show (\)) show + grestore + } if +} bind def + +/set_font { + findfont exch + scalefont setfont +} def + +% draw text fitted to its expected width +/alignedtext { % width text + /text exch def + /width exch def + gsave + width 0 gt { + [] 0 setdash + text stringwidth pop width exch sub text length div 0 text ashow + } if + grestore +} def + +/boxprim { % xcorner ycorner xsize ysize + 4 2 roll + moveto + 2 copy + exch 0 rlineto + 0 exch rlineto + pop neg 0 rlineto + closepath +} bind def + +/ellipse_path { + /ry exch def + /rx exch def + /y exch def + /x exch def + matrix currentmatrix + newpath + x y translate + rx ry scale + 0 0 1 0 360 arc + setmatrix +} bind def + +/endpage { showpage } bind def +/showpage { } def + +/layercolorseq + [ % layer color sequence - darkest to lightest + [0 0 0] + [.2 .8 .8] + [.4 .8 .8] + [.6 .8 .8] + [.8 .8 .8] + ] +def + +/layerlen layercolorseq length def + +/setlayer {/maxlayer exch def /curlayer exch def + layercolorseq curlayer 1 sub layerlen mod get + aload pop sethsbcolor + /nodecolor {nopcolor} def + /edgecolor {nopcolor} def + /graphcolor {nopcolor} def +} bind def + +/onlayer { curlayer ne {invis} if } def + +/onlayers { + /myupper exch def + /mylower exch def + curlayer mylower lt + curlayer myupper gt + or + {invis} if +} def + +/curlayer 0 def + +%%EndResource +%%EndProlog +%%BeginSetup +14 default-font-family set_font +1 setmiterlimit +% /arrowlength 10 def +% /arrowwidth 5 def + +% make sure pdfmark is harmless for PS-interpreters other than Distiller +/pdfmark where {pop} {userdict /pdfmark /cleartomark load put} ifelse +% make '<<' and '>>' safe on PS Level 1 devices +/languagelevel where {pop languagelevel}{1} ifelse +2 lt { + userdict (<<) cvn ([) cvn load put + userdict (>>) cvn ([) cvn load put +} if + +%%EndSetup +setupLatin1 +%%Page: 1 1 +%%PageBoundingBox: 36 36 372 152 +%%PageOrientation: Portrait +0 0 1 beginpage +gsave +36 36 336 116 boxprim clip newpath +1 1 set_scale 0 rotate 40 40 translate +% PseudoAlgebraicClosureOfFiniteFieldCategory +gsave +0.537 0.247 0.902 nodecolor +newpath 328 108 moveto +0 108 lineto +0 72 lineto +328 72 lineto +closepath fill +1 setlinewidth +filled +0.537 0.247 0.902 nodecolor +newpath 328 108 moveto +0 108 lineto +0 72 lineto +328 72 lineto +closepath stroke +0.000 0.000 0.000 nodecolor +14 /Times-Roman set_font +7.5 85.9 moveto 313 (PseudoAlgebraicClosureOfFiniteFieldCategory) alignedtext +grestore +% PACPERC +gsave +0.537 0.247 0.902 nodecolor +newpath 157 36 moveto +77 36 lineto +77 0 lineto +157 0 lineto +closepath fill +1 setlinewidth +filled +0.537 0.247 0.902 nodecolor +newpath 157 36 moveto +77 36 lineto +77 0 lineto +157 0 lineto +closepath stroke +0.000 0.000 0.000 nodecolor +14 /Times-Roman set_font +84.5 13.9 moveto 65 (PACPERC) alignedtext +grestore +% PseudoAlgebraicClosureOfFiniteFieldCategory->PACPERC +gsave +1 setlinewidth +0.000 0.000 0.000 edgecolor +newpath 152 72 moveto +147 64 140 54 134 44 curveto +stroke +0.000 0.000 0.000 edgecolor +newpath 137.27 42.62 moveto +129 36 lineto +131.33 46.34 lineto +closepath fill +1 setlinewidth +solid +0.000 0.000 0.000 edgecolor +newpath 137.27 42.62 moveto +129 36 lineto +131.33 46.34 lineto +closepath stroke +grestore +% FFIELDC +gsave +0.537 0.247 0.902 nodecolor +newpath 249 36 moveto +175 36 lineto +175 0 lineto +249 0 lineto +closepath fill +1 setlinewidth +filled +0.537 0.247 0.902 nodecolor +newpath 249 36 moveto +175 36 lineto +175 0 lineto +249 0 lineto +closepath stroke +0.000 0.000 0.000 nodecolor +14 /Times-Roman set_font +182.5 13.9 moveto 59 (FFIELDC) alignedtext +grestore +% PseudoAlgebraicClosureOfFiniteFieldCategory->FFIELDC +gsave +1 setlinewidth +0.000 0.000 0.000 edgecolor +newpath 176 72 moveto +181 64 188 54 194 44 curveto +stroke +0.000 0.000 0.000 edgecolor +newpath 196.8 46.1 moveto +200 36 lineto +191.2 41.9 lineto +closepath fill +1 setlinewidth +solid +0.000 0.000 0.000 edgecolor +newpath 196.8 46.1 moveto +200 36 lineto +191.2 41.9 lineto +closepath stroke +grestore +endpage +showpage +grestore +%%PageTrailer +%%EndPage: 1 +%%Trailer +%%Pages: 1 +%%BoundingBox: 36 36 372 152 +end +restore +%%EOF diff --git a/changelog b/changelog index 2307e3f..c928b43 100644 --- a/changelog +++ b/changelog @@ -1,3 +1,8 @@ +20100503 tpd src/axiom-website/patches.html 20100503.01.tpd.patch +20100503 tpd src/algebra/Makefile add PACFFC help and regression +20100503 tpd books/bookvol5 add PACFFC +20100503 tpd books/bookvol10.2 add PACFFC +20100503 tpd books/ps/v102pseudoalgebraicclosureoffinitefieldcategory.ps added 20100502 tpd src/axiom-website/patches.html 20100502.02.tpd.patch 20100502 tpd books/ps/v102pseudoalgebraicclosureofperfectfieldcategory.ps add 20100502 tpd src/axiom-website/patches.html 20100502.01.tpd.patch diff --git a/src/algebra/Makefile.pamphlet b/src/algebra/Makefile.pamphlet index a228636..3226cdc 100644 --- a/src/algebra/Makefile.pamphlet +++ b/src/algebra/Makefile.pamphlet @@ -3631,6 +3631,7 @@ LAYER8=\ ${OUT}/INTHEORY.o ${OUT}/IRREDFFX.o ${OUT}/LFCAT.o ${OUT}/LODOCAT.o \ ${OUT}/LODOCAT-.o ${OUT}/LWORD.o ${OUT}/MATCAT.o ${OUT}/MATCAT-.o \ ${OUT}/MATSTOR.o ${OUT}/ORESUP.o ${OUT}/OREPCTO.o ${OUT}/OREUP.o \ + ${OUT}/PACFFC.o \ ${OUT}/PLOT3D.o ${OUT}/PR.o ${OUT}/PREASSOC.o ${OUT}/PRIMARR2.o \ ${OUT}/REDORDER.o ${OUT}/SRAGG.o ${OUT}/SRAGG-.o ${OUT}/STREAM.o \ ${OUT}/SYMPOLY.o ${OUT}/TS.o ${OUT}/TUPLE.o ${OUT}/UPSCAT.o \ @@ -4014,6 +4015,18 @@ LAYER8=\ /*"OREUP" -> {"OAMON"; "OASGP"; "ORDSET"; "DIFRING"; "KONVERT"; "LINEXP"}*/ /*"OREUP" -> {"PATMAB"; "CFCAT"; "REAL"; "CHARZ"; "STEP"}*/ +"PACFFC" [color="#4488FF",href="bookvol10.2.pdf#nameddest=PACFFC", + shape=ellipse] +/*"PACFFC" -> {"FFIELDC"}*/ +"PACFFC" -> "FPC" +/*"PACFFC" -> {"FIELD"; "EUCDOM"; "PID"; "GCDDOM"; "INTDOM"; "COMRING"}*/ +/*"PACFFC" -> {"RING"; "RNG"; "ABELGRP"; "CABMON"; "ABELMON"; "ABELSG"}*/ +/*"PACFFC" -> {"SETCAT"; "BASTYPE"; "KOERCE"; "SGROUP"; "MONOID"}*/ +/*"PACFFC" -> {"LMODULE"; "BMODULE"; "RMODULE"; "ALGEBRA"; "MODULE"}*/ +/*"PACFFC" -> {"ENTIRER"; "UFD"; "DIVRING"; "CHARNZ"; "FINITE"}*/ +/*"PACFFC" -> {"STEP"; "DIFRING"}*/ +"PACFFC" -> "PACPERC" + "PLOT3D" [color="#88FF44",href="bookvol10.3.pdf#nameddest=PLOT3D"] /*"PLOT3D" -> {"PSCURVE"; "KOERCE"; "BOOLEAN"; "INT"; "DFLOAT"; "FPS-"}*/ /*"PLOT3D" -> {"RNS-"; "FIELD-"; "FPS"; "RNS"; "FIELD"; "EUCDOM"}*/ @@ -15834,6 +15847,26 @@ ${MID}/FFFACTSE.nrlib/code.o: ${MID}/FFFACTSE.spad fi ) @ +The PACFFC routine expects PseudoAlgebraicClosureOfPerfectFieldCategory +to be autoloaded. However this function is not picked up by the +MakeConstructorsAutoLoad function (bookvol5). The correct fix is to +dynamically update the databases at compile time. This fix just causes +the required file to be loaded, thus defining the function. +<>= + +PACFFCDEPS = PACPERC + +${MID}/PACFFC.nrlib/code.o: ${MID}/PACFFC.spad + @echo P1 making ${MID}/PACFFC.nrlib/code.o from ${MID}/PACFFC.spad + @ (cd ${MID} ; \ + if [ -z "${NOISE}" ] ; then \ + echo -e ")lib ${PACFFCDEPS} \n )co PACFFC.spad" | ${INTERPSYS} ; \ + else \ + echo -e ")lib ${PACFFCDEPS} \n )co PACFFC.spad" \ + | ${INTERPSYS} >${TMP}/trace ; \ + fi ) +@ + \section{Broken Files} These files are Aldor files \begin{verbatim} @@ -16642,6 +16675,7 @@ SPADHELP=\ ${HELP}/Permutation.help \ ${HELP}/Polynomial.help \ ${HELP}/Product.help \ + ${HELP}/PseudoAlgebraicClosureOfFiniteFieldCategory.help \ ${HELP}/PseudoAlgebraicClosureOfPerfectFieldCategory.help \ ${HELP}/Quaternion.help \ ${HELP}/QuaternionCategoryFunctions2.help \ @@ -16787,6 +16821,7 @@ REGRESS= \ Plot.regress \ Polynomial.regress \ Product.regress \ + PseudoAlgebraicClosureOfFiniteFieldCategory.regress \ PseudoAlgebraicClosureOfPerfectFieldCategory.regress \ Quaternion.regress \ QuaternionCategoryFunctions2.regress \ @@ -17929,6 +17964,21 @@ ${HELP}/Product.help: ${BOOKS}/bookvol10.3.pamphlet >${INPUT}/Product.input @echo "Product (PRODUCT)" >>${HELPFILE} +${HELP}/PseudoAlgebraicClosureOfFiniteFieldCategory.help: \ + ${BOOKS}/bookvol10.2.pamphlet + @echo 7936 create PseudoAlgebraicClosureOfFiniteFieldCategory.help \ + from ${BOOKS}/bookvol10.2.pamphlet + @${TANGLE} -R"PseudoAlgebraicClosureOfFiniteFieldCategory.help" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${HELP}/PseudoAlgebraicClosureOfFiniteFieldCategory.help + @cp ${HELP}/PseudoAlgebraicClosureOfFiniteFieldCategory.help \ + ${HELP}/PACFFC.help + @${TANGLE} -R"PseudoAlgebraicClosureOfFiniteFieldCategory.input" \ + ${BOOKS}/bookvol10.2.pamphlet \ + >${INPUT}/PseudoAlgebraicClosureOfFiniteFieldCategory.input + @echo "PseudoAlgebraicClosureOfFiniteFieldCategory (PACFFC)" \ + >>${HELPFILE} + ${HELP}/PseudoAlgebraicClosureOfPerfectFieldCategory.help: \ ${BOOKS}/bookvol10.2.pamphlet @echo 7937 create PseudoAlgebraicClosureOfPerfectFieldCategory.help \ diff --git a/src/axiom-website/patches.html b/src/axiom-website/patches.html index 20db17d..49690cc 100644 --- a/src/axiom-website/patches.html +++ b/src/axiom-website/patches.html @@ -2665,5 +2665,7 @@ src/input/*.input clean up broken tests
src/axiom-website/hyperdoc/Makefile deleted
20100502.02.tpd.patch books/ps/v102pseudoalgebraicclosureofperfectfieldcategory.ps add
+20100503.01.tpd.patch +books/bookvol10.2 PseudoAlgebraicClosureOfFiniteFieldCategory added