D.7.5 zeroset_lib
-----------------
Library:
zeroset.lib
Purpose:
      Procedures For Roots and Factorization
Author:
Thomas Bayer, email: tbayer@mathematik.uni-kl.de

http://wwwmayr.informatik.tu-muenchen.de/personen/bayert/
Current Adress: Institut fuer Informatik, TU Muenchen

Overview:
Algorithms for finding the zero-set of a zero-dim. ideal in Q(a)[x_1,..,x_n],
Roots and Factorization of univariate polynomials over Q(a)[t]
where a is an algebraic number. Written in the frame of the
diploma thesis (advisor: Prof. Gert-Martin Greuel) 'Computations of moduli
spaces of semiquasihomogeneous singularities and an implementation in Singular'.
This library is meant as a preliminary extension of the functionality
of Singular for univariate factorization of polynomials over simple algebraic
extensions in characteristic 0.

Subprocedures with postfix 'Main' require that the ring contains a variable
'a' and no parameters, and the ideal 'mpoly', where 'minpoly' from the
basering is stored.


Procedures:
* EGCD:: gcd over an algebraic extension field of Q
* Factor:: factorization of f over an algebraic extension field
* Quotient:: quotient q of f w.r.t. g (in f = q*g + remainder)
* Remainder:: remainder of the division of f by g
* Roots:: computes all roots of f in an extension field of Q
* SQFRNorm:: norm of f (f must be squarefree)
* ZeroSet:: zero-set of the 0-dim. ideal I
Auxiliary procedures:
* EGCDMain:: gcd over an algebraic extension field of Q
* FactorMain:: factorization of f over an algebraic extension field
* InvertNumberMain:: inverts an element of an algebraic extension field
* QuotientMain:: quotient of f w.r.t. g
* RemainderMain:: remainder of the division of f by g
* RootsMain:: computes all roots of f, might extend the ground field
* SQFRNormMain:: norm of f (f must be squarefree)
* ContainedQ:: f in data ?
* SameQ:: a == b (list a,b)

<font size="-1">
&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; User manual for <a href="http://www.singular.uni-kl.de/"><i>Singular</i></a> version 2-0-4, October 2002,
generated by <a href="http://www.gnu.org/software/texinfo/"><i>texi2html</i></a>.
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