Contents

• 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
    • Linear algebra
  • 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
    • Simplification procedures
  • Parametric polynomial
    • Utilities
    • Simplification procedures
    • 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
    • Crash
  • Setting the debug option
  
  
• Changes
• Bibliography