  
  [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], and interface to [10X4ti2[110X[tt]),
  [10XSingularInterface[110X  (an  interface  to  [10XSingular[110X  [DGPS12]; or in its absence
  [10XSingular[110X  [CdG12]);  or  in  its  absence  [10XGradedModules[110X  [BGJ+14] 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
  
  [1X13.1-6 NumSgpsUseSingularGradedModules[101X
  
  [33X[1;0Y[29X[2XNumSgpsUseSingularGradedModules[102X(  ) [32X function[133X
  
  [33X[0;0YTries  to  load the package [10XGradedModules[110X. If the package is available, then
  it also loads methods implemented using functions in this package.[133X
  
  [33X[0;0YIt also creates a ring of rationals [10XNumSgpsRationals[110X.[133X
  
