  
  [1X4 [33X[0;0YImplemented packages[133X[101X
  
  
  [1X4.1 [33X[0;0YMPFR[133X[101X
  
  [1X4.1-1 IsMPFRFloat[101X
  
  [33X[1;0Y[29X[2XIsMPFRFloat[102X [32X filter[133X
  [33X[1;0Y[29X[2XTYPE_MPFR[102X [32X global variable[133X
  
  [33X[0;0YThe category of floating-point numbers.[133X
  
  [33X[0;0YNote  that  they  are  treated  as  commutative  and  scalar,  but  are  not
  necessarily associative.[133X
  
  
  [1X4.2 [33X[0;0YMPFI[133X[101X
  
  [1X4.2-1 IsMPFIFloat[101X
  
  [33X[1;0Y[29X[2XIsMPFIFloat[102X [32X filter[133X
  [33X[1;0Y[29X[2XTYPE_MPFI[102X [32X global variable[133X
  
  [33X[0;0YThe category of intervals of floating-point numbers.[133X
  
  [33X[0;0YNote  that  they  are  treated  as  commutative  and  scalar,  but  are  not
  necessarily associative.[133X
  
  
  [1X4.3 [33X[0;0YMPC[133X[101X
  
  [1X4.3-1 IsMPCFloat[101X
  
  [33X[1;0Y[29X[2XIsMPCFloat[102X [32X filter[133X
  [33X[1;0Y[29X[2XTYPE_MPC[102X [32X global variable[133X
  
  [33X[0;0YThe category of intervals of floating-point numbers.[133X
  
  [33X[0;0YNote  that  they  are  treated  as  commutative  and  scalar,  but  are  not
  necessarily associative.[133X
  
  
  [1X4.4 [33X[0;0YCXSC[133X[101X
  
  [1X4.4-1 IsCXSCReal[101X
  
  [33X[1;0Y[29X[2XIsCXSCReal[102X [32X filter[133X
  [33X[1;0Y[29X[2XIsCXSCComplex[102X [32X filter[133X
  [33X[1;0Y[29X[2XIsCXSCInterval[102X [32X filter[133X
  [33X[1;0Y[29X[2XIsCXSCBox[102X [32X filter[133X
  [33X[1;0Y[29X[2XTYPE_CXSC_RP[102X [32X global variable[133X
  [33X[1;0Y[29X[2XTYPE_CXSC_CP[102X [32X global variable[133X
  [33X[1;0Y[29X[2XTYPE_CXSC_RI[102X [32X global variable[133X
  [33X[1;0Y[29X[2XTYPE_CXSC_CI[102X [32X global variable[133X
  
  [33X[0;0YThe category of floating-point numbers.[133X
  
  [33X[0;0YNote  that  they  are  treated  as  commutative  and  scalar,  but  are  not
  necessarily associative.[133X
  
  
  [1X4.5 [33X[0;0YFPLLL[133X[101X
  
  [1X4.5-1 FPLLLReducedBasis[101X
  
  [33X[1;0Y[29X[2XFPLLLReducedBasis[102X( [3Xm[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10YA matrix spanning the same lattice as [3Xm[103X.[133X
  
  [33X[0;0YThis  function implements the LLL (Lenstra-Lenstra-Lovász) lattice reduction
  algorithm via the external library [5Xfplll[105X.[133X
  
  [33X[0;0YThe result is guaranteed to be optimal up to 1%.[133X
  
  [1X4.5-2 FPLLLShortestVector[101X
  
  [33X[1;0Y[29X[2XFPLLLShortestVector[102X( [3Xm[103X ) [32X operation[133X
  [6XReturns:[106X  [33X[0;10YA short vector in the lattice spanned by [3Xm[103X.[133X
  
  [33X[0;0YThis  function implements the LLL (Lenstra-Lenstra-Lovász) lattice reduction
  algorithm  via  the external library [5Xfplll[105X, and then computes a short vector
  in this lattice.[133X
  
  [33X[0;0YThe result is guaranteed to be optimal up to 1%.[133X
  
