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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.
 • The long form, SNAP:-command, is always available. The short form can be used after loading the package.

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.

 See Also