Polynomials with floating-point coefficients may be manipulated in GAP; though they behave, in subtle ways, quite differently than polynomials over rings.
The "pseudo-field" of floating-point numbers is an object in GAP, called FLOAT_PSEUDOFIELD
. (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
gap> x := Indeterminate(FLOAT_PSEUDOFIELD,"x"); x gap> 2*x^2+3; 2.0*x^2+3.0 gap> Value(last,10); 203.0
The Jenkins-Traub algorithm has been implemented, in arbitrary precision for MPFR and MPC.
Furthermore, CXSC can provide complex enclosures for the roots of a complex polynomial.
A faster implementation of the LLL lattice reduction algorithm has also been implemented. It is accessible via the commands FPLLLReducedBasis(m)
and FPLLLShortestVector(m)
.
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