Introduction to the Rif Package Version 1.1
1) Full handling of polynomially nonlinear systems
2) Automatic case splitting
3) Flexible nonlinear ranking
4) Handling of inequation constraints (expr<>0)
5) Speed and memory efficiency
1) New function
maxdimsystems
to find the most general
solutions for case splitting problems
2) Improvements to case visualization and initial data
computation
3) Greater flexibility in
rifsimp
with the addition of
new options for control of case splitting, declaration
of arbitrary functions and/or constants, detection
of empty cases, and much more
4) More efficient handling of nonlinear systems via new
nonlinear equation methods
5) Significant overall speed and memory enhancements
6) Automatic adjustment of results to remove inconsistent
cases, and their effect on the returned consistent
cases.
rifsimp
Simplifies systems of polynomially nonlinear ODEs and PDEs
to canonical form. Splits nonlinear equations into cases,
using Groebner basis techniques to handle algebraic
consequences of the system. Accounts for all differential
consequences of the system.
maxdimsystems
Also simplifies systems of polynomially nonlinear ODEs
and PDEs, but performs case splitting automatically,
returning the most general cases (those with the highest
number of parameters in the initial data).
rifread
Loads a partially completed
rifsimp
calculation for
viewing and/or manual manipulation.
rifsimp
must be
told to save partial calculations using the
storage
options.
checkrank
Provides information on ranking to allow determination
of an appropriate ranking to use with
rifsimp
.
caseplot
Takes the case split output of
rifsimp
, and provides
a graphical display of the solution case tree.
initialdata
Obtains the initial data required by an ODE/PDE system to
fully specify formal power series solutions of the system.
Typically the output of
rifsimp
is used as input for this
procedure, but any ODE/PDE system in the correct form can
be used.
rtaylor
Calculates the Taylor series of solutions of an ODE/PDE
system to any order. Just as for
initialdata
, any
ODE/PDE system in the correct form can be used.
Rif , caseplot , PDEtools[casesplit] , checkrank , diffalg , dsolve,system , initialdata , maxdimsystems , pdsolve,system , rifsimp , rtaylor