  
  [1X3 [33X[0;0YPolynomials[133X[101X
  
  
  [1X3.1 [33X[0;0YThe Floats pseudo-field[133X[101X
  
  [33X[0;0YPolynomials  with  floating-point  coefficients  may  be manipulated in [5XGAP[105X;
  though  they behave, in subtle ways, quite differently than polynomials over
  rings.[133X
  
  [33X[0;0YThe  "pseudo-field"  of  floating-point  numbers is an object in [5XGAP[105X, called
  [10XFLOAT_PSEUDOFIELD[110X.  (It  is  not  really  a  field, e.g. because addition of
  floating-point  numbers  in  not  associative).  It  may  be  used to create
  indeterminates, for example as[133X
  
  [4X[32X  Example  [32X[104X
    [4X[25Xgap>[125X [27Xx := Indeterminate(FLOAT_PSEUDOFIELD,"x");[127X[104X
    [4X[28Xx[128X[104X
    [4X[25Xgap>[125X [27X2*x^2+3;[127X[104X
    [4X[28X2.0*x^2+3.0[128X[104X
    [4X[25Xgap>[125X [27XValue(last,10);[127X[104X
    [4X[28X203.0[128X[104X
  [4X[32X[104X
  
  
  [1X3.2 [33X[0;0YRoots of polynomials[133X[101X
  
  [33X[0;0YThe Jenkins-Traub algorithm has been implemented, in arbitrary precision for
  MPFR and MPC.[133X
  
  [33X[0;0YFurthermore,  CXSC can provide complex enclosures for the roots of a complex
  polynomial.[133X
  
  
  [1X3.3 [33X[0;0YLLL lattice reduction[133X[101X
  
  [33X[0;0YA faster implementation of the LLL lattice reduction algorithm has also been
  implemented.  It  is  accessible  via  the commands [10XFPLLLReducedBasis(m)[110X and
  [10XFPLLLShortestVector(m)[110X.[133X
  
