Large-integer arithmetic in BASIC Files

Modulo-polynomial arithmetic for FreeBasic, PDS and VBdos.

I wrote these programs to play with the multiple homomorphic image method:
instead of doing all calculations with large integers, the approach here is
to compute a family of homomorphic images in distinct small finite fields,
and lift the intersection of the resulting equivalence classes to a unique
big number solution. This will usually work as long as the coefficients are
no larger than 127 digit integers, or fractions with 42/85 digit numerator
and denominator (QB-version limits). Lifting and rational reconstruction is
done by "CRTtrans.bas", a largeint-version of the Chinese remainder algorithm.
This module must be linked with my largeint-library in "LargeInt.zip".


Version w/date 11-01-2012:

Replaced library polymod2.bas - using bitwise operations in the
binary field GF(2) - by lib polygf2n.bas, using word operations
in extension fields GF(2^ n), with n ranging from 1 to 14.

Arranged all library subroutines in hierarchical order,
removed $-suffixes on string functions (quickbasic remnant).

Implemented fractional coefficients in libraries realpoly.bas
and polymodp.bas (-output through largeint-module CRTtrans.bas).

Added modules Hensel_p.bas, PolyDisc.bas, Resultnt.bas,
GF2nroot.bas, GF2nfact.bas, IrredPol.bas, PrimiPol.bas,
R-S_enco.bas and R-S_deco.bas


date 01-10-2010:

Updated CRTtrans.bas, using function Bufl(p) and 2-argument CnvSt.

Replaced module-level DEF###'s with the $LANG "qb" metacommand
and a single DEF-line in the -lang QB section of largeint.bi.

Replaced 'ByVal arg AS STRING' with 'ByVal arg AS ZSTRING PTR'.

Added modules p-Adic0s.bas and TanhPoly.bas


date 12-01-2008:

Changed CRTtrans.bas for variable number of primes,
added modules EigenSys.bas and Poly_SNF.bas


date 11-22-2007:

Added many new functions in library polymodp.bas;
implemented factorization of polynomials,
finding the minimal polynomial of a root over Z_p,
generating Fibonacci and cyclotomic polynomials,
and the ElGamal cryptosystem in finite fields GF(p^ n).

Library polymod2.bas is designed exclusively for working
in fields with characteristic 2.

Library realpoly.bas is designed mainly for playing
with polynomial factorization over C and Z.

S.J.S.