----------------------------------------------------------------------
-- Anna Bigatti: CoCoA tutorial in Linz semester 2006
----------------------------------------------------------------------
Unset Indentation;
----------------------------------------------------------------------
-- 2 -- CoCoA-4 in action: (exact) ideal of points

  Use R ::= Q[x,y];
  Pts := [  [1/N, (1/N)^2]  | N In 2..7 ];
  Pts;

  Set Indentation;
  IdealOfPoints(Pts);

  X := IdealAndSeparatorsOfPoints(Pts);
  S := X.Separators;
  Foreach P In Pts Do  Print Eval(S[2], P), "   ";  EndForeach;

  F := Interpolate(Pts, [10, 1, 4, 5, 1/7, 1/4]);
  F;
  Foreach P In Pts Do  Print Eval(F, P), "   ";  EndForeach;

----------------------------------------------------------------------
-- approximate the original points:
  Unset Indentation;
  Use R;
  ApproxPts := [ [FloatApprox(P[1],10^(-9)),FloatApprox(P[2],10^(-9))]
		  | P In Pts];
  ApproxPts;
  LT(IdealOfPoints(Pts));
  LT(IdealOfPoints(ApproxPts));
  LT(IdealOfPoints(GenericPoints(Len(Pts))));

----------------------------------------------------------------------
-- the implementation is very efficient (modular algorithm)

  Use Q[x[1..10]];
  RandomPts := [  [ Rand(-10,10) | I In 1..NumIndets()]   | N In 1..20 ];
  Time I := IdealOfPoints(RandomPts);
  I;
-- but the answer is very big:
-- "your memory runs out before your patience does"


----------------------------------------------------------------------
-- 3 -- CoCoA-4 & CoCoAServer: a step into the future

  Use Q[x[0..4]];
  RandomPolys := [ Randomized(DensePoly(3)) | N In 1..4 ];
  RandomPolys;

-- LT(Ideal(RandomPolys)); -- 30 min    (60 min using battery)
-- X := LT5(Ideal(RandomPolys)); -- 1 min      (2 min Using battery)
  Y := LT5x(Ideal(RandomPolys), Record[FloatPrecision = 128]);
  Y := GBasis5x(Ideal(RandomPolys), Record[FloatPrecision = 128]);

-- what happens if the precision is not enough?
  Z := LT5x(Ideal(RandomPolys), Record[FloatPrecision = 32]);

-- And more: multigradings, parameters, ...

----------------------------------------------------------------------
-- 4 -- CoCoALib: the full experience [John Abbott]