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Introduction
Contents
ALIAS-Maple
The Maple interface for
ALIAS
Version 2.7
September 2012
The COPRIN project
Introduction
Preliminaries
Installing the Maple library
On-line help and ALIAS-On-Line
Interval valuation of expression
Interval evaluation in ALIAS-Maple
Equations, Gradient and Hessian
MakeF, MakeJ, MakeH
Improving the efficiency of the code
Function involving determinants
Dealing with undefined expressions
Interval valuation and the
Problem_Expression
package
Interval evaluation of an expression in
Maple
Generating code
Transforming expressions into C++ code
Interval evaluation and Taylor remainder
The solving procedures
Introduction
Allowed mathematical operators
Basic principles
Bisection mode
Storage mode
Simplification procedures
General purpose system solving procedures
GeneralSolve
GradientSolve
and
HessianSolve
Specific solving procedures
The
SolveSimplex
and
SolveSimplexGradient
procedures
Systems of distance equations
The
SolveDistance
procedure
Specificity of the procedure
Linear algebra
Enclosure of an interval linear system
Regularity of parametric matrices
The
RohnConsistency
procedure
The
SpectralRadiusConsistency
procedure
The
LinearMatrixConsistency
procedure
The
GerschgorinConsistency
procedure
Non 0-dimensional system
Parameters for the solving procedures
General parameters for the solving procedures
Parameters for the procedures using the derivatives
Generating program without running it
Simplification procedures
Introduction
Filtering simplification procedures
The
HullConsistency
,
Simp2B
and
HullIConsistency
procedures
The
HullConsistencyTaylor
procedure
The
BiCenteredForm
procedure
The
GlobalConsistencyTaylor
procedure
The
SimpAngle
procedure
The
SimplexConsistency
procedure
The
IntervalNewton
procedure
Roots simplification procedures
TryNewton
Rouche
Concatenation of simplification procedures
Using the 3B method
Principle
Repeating the 3B method
Other parameters for the 3B method
Simplification procedures for matrix
Optimization
Introduction
Examples
Specific parameters for the optimization procedures
Integration
Integral in one variable
Integral in several variables
Continuation for one-dimensional system
Introduction
The
Continuation
procedure
Optional arguments
Example
Continuation with initially known starting points
Specific parameters for the continuation procedures
Drawing procedure
Univariate and parametric polynomial
Univariate polynomials
Utilities
Bounds for the real roots
Simplification procedures
Deflation
Parametric polynomial
Utilities
Decomposition
Simplification procedures
Routh table:
Routh
The
KharitonovConsistency
procedure
The
WeylFilter
procedure
Minimal and maximal real roots of a parametric polynomial
Possible parameters values for a given range for the roots
Condition number
Specificity for the analysis of parametric polynomials
Utilities procedures of ALIAS-Maple
Reusing a compiled program: the
Restart
procedure
Expression conversion:
Convert_Frac_Cons
Multiple occurrences of variables:
MultipleOccurence
Mathematical functions in an expression
Ordering a list of variables
Finding elementary components in a function
Transformation of an expression:
MinimalCout
Newton scheme
The
Bound_Distance
procedure
Drawing for non-0 dimensional systems:
DrawND
Parallel version of
ALIAS
-Maple
Introduction
Stopping an ALIAS-C++ procedure
Message passing mechanism and
pvm
Example of message passing mechanism
pvm
Parallel procedures in
Maple
Minimal parameters setting
Specific parameters for the parallel implementation
Customizing and improving the code produced by ALIAS-Maple
Source code
Some rules to improve efficiency
Function evaluation
A counter-example
Simplification procedures
Examples
6-body
Ferraris
Wilkinson polynomial
Troubleshooting:
ALIAS
-Maple does not work!
Compilation problems
Execution problems
Wrong results
Running out of memory
Large computation time
Changing the formulation of the problem
Choosing the right heuristics
Crash
Setting the debug option
Changes
Contents
Bibliography
About this document ...
Jean-Pierre Merlet 2012-12-20
