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Bernstein polynomial
Task: Compute the roots of the (local) Bernstein polynomial  b = b(s), the minimal non-trivial complex polynomial, which satisfies
where
Here,   fs   is a formal notation for an indeterminate T on which we have the following actions:

Note that the roots of b are negative rational numbers and -1 is a root of b. To compute the roots of the Bernstein polynomial b excluding the root -1, we type:

ring R=0,(x,y),ds;
poly f=x5+x2y2+y5;
LIB "gaussman.lib";
bernstein(f); // an implementation based on Malgrange's results
==>
_[1]=-1/2
_[2]=-7/10
_[3]=-9/10
_[4]=-11/10
_[5]=-13/10
In particular, since -2 is smaller than all roots of the Bernstein polynomial of f, we have


KL, 06/03 http://www.singular.uni-kl.de