文档介绍：Elimination Metho ds in
P puter Algebra
V alery Byk o v
Alexander Kytmano v
Mark Lazman
ELIMINA TION METHODS
IN POL PUTER
ALGEBRA
Klu w er Academic Publishers
Elimination metho ds in p puter algebra
V alery Byk o v
Alexander
Kytmano v
Mark Lazman
Klu w er Academic Publishers
The b o ok presen ts a mo di
ed metho d
based on m ultidimensional residue theory
for the elimination of unkno wns from a system of nonlinear algebraic equations
An
algorithm is giv en for constructing the resultan t of the system
and puter
implemen tation making use of form ula manipulation soft w are is carried out
The
texts of the w ork ed out programs in the system Maple are pro vided
The obtained algorithms and programs are then applied to questions from the
theory of c hemical ics
suc h as the searc h for all stationary solutions of ic
equations and the construction of ic p olynomials
The sub ject of this b o ok is closely connected with a wide range of curren t prob
lems in the analysis of nonlinear systems
T able of Con ten ts
INTR ODUCTION vii
PREF A CE TO THE ENGLISH EDITION ix
PREF A CE BY THE ENGLISH EDITOR x
LIST OF SYMBOLS xi
Chapter
BASIC MA THEMA TICAL F A CTS
The logarithmic residue
The Newton recursion form ulas
Lo calization theorems for the real zeros of a p olynomial
The lo cal residue
of Grothendiec k
The m ultidimensional logarithmic residue
The classical sc heme for elimination of unkno wns
Chapter
A MODIFIED ELIMINA TION METHOD
A generalized transformation form ula for lo cal residues
A mo di
ed elimination metho d
A form ula for the logarithmic deriv ativ eofthe resultan t
Multidimensional analogues of the Newton form ulas
Elimination of unkno wns in di
eren t v ariables
Real ro ots
Chapter
APPLICA TIONS IN MA THEMA TICAL ICS
Short sc hemes
The parallel sc heme
The sequen tial sc