Geodesic
Polynomial-time computation of the degree of a
Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 203-239

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Consider a projective algebraic variety $W$ which is an irreducible component of the set of all common zeros of a family of homogeneous polynomials of degrees less than $d$ in $n+1$ variables in zero characteristic. Consider a dominant rational morphism from $W$ to $W'$ given by homogeneous polynomials of degree $d'$. We suggest algorithms for constructing objects in general position related to this morphism. These algorithms are deterministic and polynomial in $(dd')^n$ and the size of the input. 
@article{ZNSL_2007_344_a5,
     author = {A. L. Chistov},
     title = {Polynomial-time computation of the degree of a},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {203--239},
     publisher = {mathdoc},
     volume = {344},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a5/}
}
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A. L. Chistov. Polynomial-time computation of the degree of a. Zapiski Nauchnykh Seminarov POMI, Representation theory, dynamical systems, combinatorial methods. Part XV, Tome 344 (2007), pp. 203-239. http://geodesic.mathdoc.fr/item/ZNSL_2007_344_a5/