/usr/share/axiom-20170501/src/algebra/PACPERC.spad is in axiom-source 20170501-3.
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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 | )abbrev category PACPERC PseudoAlgebraicClosureOfPerfectFieldCategory
++ Authors: Gaetan Hache
++ Date Created: may 1997
++ Date Last Updated: April 2010, by Tim Daly
++ Description:
++ This category exports the function for domains
++ 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 coming from
++ a set of related tower extensions.
PseudoAlgebraicClosureOfPerfectFieldCategory() : Category == SIG where
INT ==> Integer
K ==> Fraction Integer
NNI ==> NonNegativeInteger
SUP ==> SparseUnivariatePolynomial
BOOLEAN ==> Boolean
PI ==> PositiveInteger
FFFACTSE ==> FiniteFieldFactorizationWithSizeParseBySideEffect
SIG ==> Field with
definingPolynomial : () -> SUP(%)
definingPolynomial : % -> SUP %
lift : % -> SUP(%)
lift : (%,%) -> SUP(%)
reduce : SUP(%) -> %
distinguishedRootsOf : (SparseUnivariatePolynomial %,%) -> List %
++ distinguishedRootsOf(p,a) returns a (distinguised) root for each
++ irreducible factor of the polynomial p (factored over the field
++ defined by the element a).
ground_? : % -> Boolean
maxTower : List % -> %
++ maxTower(l) returns the tower in the list having the maximal
++ extension degree over the ground field. It has no meaning if the
++ towers not related.
extDegree : % -> PI
++ extDegree(a) returns the extension degree of the extension tower
++ over which the element is defined.
previousTower : % -> %
++ previousTower(a) returns the previous tower extension over which
++ the element a is defined.
vectorise : (%,%) -> Vector(%)
conjugate : % -> %
newElement : (SUP(%), %, Symbol) -> %
newElement : (SUP(%), Symbol) -> %
setTower_! : % -> Void
fullOutput : % -> OutputForm
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