… each polynomial in SPhas degree at most d, we prove that the number of cells defined by 0>
… Note that the combinatorial part of the bound depends on the dimension of the variety rather …

… We define the complexity of our algorithms to be the number of arithmetic operations in the …
We assume that the given variety … is described as the zero set of . The input of the algorithm is …

… only varieties defined by a single polynomial. If the variety is the zero set of a finite family
of polynomial Q we can just as well consider the zero set of the single polynomial Q = GMgg …

… polynomials. On the other hand, we study the geometry of Grassmannians, flag varieties,
and especially their Schubert varieties. The … interested in the family of Schur polynomials, the …

… consists in the following: real varieties defined by "simple" not … algebraic set defined by
a system of m polynomial equations. … cohomology group determined by r is equal to zero. …

… is polynomial rather than merely rational. 11One can also define the étale fundamental group
… projective) variety is defined over F if one can find polynomials P1,...,Pm with coefficients in …

… infinite family of instances of PIMP, including infinitely many n… an exact definition of the
dimension of an algebraic variety or … (the dimension of the algebraic variety defined by the gi (in n) …

… on s) in our bound, depends on the dimension of the variety … P, ofs polynomials with degrees
bounded by d, we can define a … to S, but which is defined by a family, P’, of polynomials …

… variety defined by the polynomials in Q and suppose that the real dimension of V is bounded
by k . We prove that the number … conditions of a family of polynomials in a variety. However, …

… defined by polynomial equalities, over a real closed extension, R(c) of R. Given a family of
polynomials P, we denote by P the family … In order, to recover points on the variety by letting C …