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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 | )abbrev category PACEXTC PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory
++ Authors: Gaetan Hache
++ Date Created: jan 1998
++ Date Last Updated: May 2010 by Tim Daly
++ Description:
++ This category exports the function for the domain
++ PseudoAlgebraicClosureOfAlgExtOfRationalNumber 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.
PseudoAlgebraicClosureOfAlgExtOfRationalNumberCategory() :
Category == SIG where
Q ==> PseudoAlgebraicClosureOfRationalNumber
PAC ==> PseudoAlgebraicClosureOfRationalNumberCategory
RT ==> RetractableTo(Q)
EF ==> ExtensionField(Q)
SIG ==> Join(PAC,RT,EF)
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