Overview of the SNAP Package - Maple Programming Help

Overview of the SNAP Package

 Calling Sequence SNAP[command](arguments) command(arguments)

Description

 • The SNAP (Symbolic-Numeric Algorithms for Polynomials) package provides routines for the algebraic manipulation of numerical polynomials in a reliable way.
 • The tools in the package include support for operations such as quotient, remainder, and numeric GCD. For the last operation you can compute an epsilon-GCD or a quasi-GCD. Additional operations include numerical computations that determine the last numerically stable Euclidean reduction, an approximation to the distance of a closest common root of two relatively prime numeric polynomials, and other similar quantities.
 • Each command in the SNAP package can be accessed by using either the long form or the short form of the command name in the command calling sequence.
 As the underlying implementation of the SNAP package is a module, it is also possible to use the form SNAP:-command to access a function from the package. For more information,  see Module Members.

List of SNAP Package Command

 The following is a list of available commands.

 To display the help page for a particular SNAP command, see Getting Help with a Command in a Package.

Examples

 > $\mathrm{with}\left(\mathrm{SNAP}\right)$
 $\left[{\mathrm{AreCoprime}}{,}{\mathrm{DistanceToCommonDivisors}}{,}{\mathrm{DistanceToSingularPolynomials}}{,}{\mathrm{EpsilonGCD}}{,}{\mathrm{EuclideanReduction}}{,}{\mathrm{IsSingular}}{,}{\mathrm{QRGCD}}{,}{\mathrm{QuasiGCD}}{,}{\mathrm{Quotient}}{,}{\mathrm{Remainder}}\right]$ (1)

1. Coprimeness test

 > $a≔0.1{z}^{2}+1.5z-0.2$
 ${a}{≔}{0.1}{}{{z}}^{{2}}{+}{1.5}{}{z}{-}{0.2}$ (2)
 > $b≔0.2{z}^{3}+0.15$
 ${b}{≔}{0.2}{}{{z}}^{{3}}{+}{0.15}$ (3)
 > $\mathrm{AreCoprime}\left(a,b,z,0.5\right)$
 ${\mathrm{false}}$ (4)
 > $\mathrm{AreCoprime}\left(a,b,z,0.1\right)$
 ${\mathrm{true}}$ (5)

2. Distance to the polynomial pairs with a common root

 > $\mathrm{DistanceToCommonDivisors}\left(a,b,z\right)$
 ${0.123978712017601}$ (6)

References

 Jeannerod, C-P., and Labahn, G. "The SNAP package for numerical polynomial arithmetic in Maple" Computer Science Technical Report University of Waterloo, 2002.