On Wed, Jan 7, 2009 at 9:16 AM, Santanu Sarkar
<[email protected]> wrote:
> Let f(x,y,z) is polynomial in x,y,z with degree 4. But we don't know
> the coefficient of the monomials of f. And we know  f(x0,y0,z0)  for
> different x0,y0,z0  which are known to us.  Can we find the coefficient
> of the monomials of f  using SAGE easily?

For every value f(x0,y0,z0) you get a single linear constraint on the
coefficients of f(x,y,z).  If you have enough such constraints, then
all coefficients will be uniquely determined, and finding them is
straightforward linear algebra that Sage could certainly do
efficiently.

If you need more details, please respond.

William

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