  
  [1X13 [33X[0;0YExternal packages[133X[101X
  
  [33X[0;0YThe use of the packages [10XNormalizInterface[110X [GHS14] (an interface to [10XNormalize[110X
  [BIRC14];   or   in   its   absence   [10X4ti2Interface[110X[Gut],  an  interface  to
  [10X4ti2[110X[{4ti}]),  [10XSingularInterface[110X  (an  interface to [10XSingular[110X [DGPS12]; or in
  its absence [10XSingular[110X [Cd12]) is highly recommended for many of the functions
  presented in this chapter. However, whenever possible a method not depending
  on these packages is also provided (though slower). The package tests if the
  user   has   downloaded   any   of  the  above  packages,  and  if  so  puts
  [10XNumSgpsCanUsePackage[110X to true, where [10XPackage[110X is any of the above.[133X
  
  
  [1X13.1 [33X[0;0YUsing external packages[133X[101X
  
  [33X[0;0YAs  mentioned  above  some  methods  are  specifically  implemented  to take
  advantage  of several external packages. The following functions can be used
  in case these packages have not been loaded prior to [10Xnumericalsgps[110X.[133X
  
  [1X13.1-1 NumSgpsUse4ti2[101X
  
  [33X[1;0Y[29X[2XNumSgpsUse4ti2[102X(  ) [32X function[133X
  
  [33X[0;0YTries  to  load the package [10X4ti2Interface[110X. If the package is available, then
  it also loads methods implemented using functions in this package.[133X
  
  [1X13.1-2 NumSgpsUse4ti2gap[101X
  
  [33X[1;0Y[29X[2XNumSgpsUse4ti2gap[102X(  ) [32X function[133X
  
  [33X[0;0YTries to load the package [10X4ti2gap[110X. If the package is available, then it also
  loads methods implemented using functions in this package.[133X
  
  [1X13.1-3 NumSgpsUseNormalize[101X
  
  [33X[1;0Y[29X[2XNumSgpsUseNormalize[102X(  ) [32X function[133X
  
  [33X[0;0YTries  to  load  the package [10XNormalizInterface[110X. If the package is available,
  then it also loads methods implemented using functions in this package.[133X
  
  [1X13.1-4 NumSgpsUseSingular[101X
  
  [33X[1;0Y[29X[2XNumSgpsUseSingular[102X(  ) [32X function[133X
  
  [33X[0;0YTries  to  load  the  package [10Xsingular[110X. If the package is available, then it
  also loads methods implemented using functions in this package.[133X
  
  [33X[0;0YTo prevent incompatibilities, the package will not load if [10XSingularInterface[110X
  has been already loaded.[133X
  
  [1X13.1-5 NumSgpsUseSingularInterface[101X
  
  [33X[1;0Y[29X[2XNumSgpsUseSingularInterface[102X(  ) [32X function[133X
  
  [33X[0;0YTries  to  load  the package [10XSingularInterface[110X. If the package is available,
  then it also loads methods implemented using functions in this package.[133X
  
  [33X[0;0YTo prevent incompatibilities, the package will not load if [10Xsingular[110X has been
  already loaded.[133X
  
