Applications of Computational Algebraic Geometry

A-homotopy a₁ algebraic curve algebraic geometry algebraic sets algorithm applications b₁ base point basis G Bézier curve binomial Buchberger's algorithm codeword coefficients combinatorial components computer algebra corresponding cost vector cubic cyclic code decoding defined degree denote determinant dimensional Editor eigenvalue eigenvectors elements elimination theory encoding example finite formula given Goppa codes graph Graver basis Gröbner fan Hence homotopy ideal implicit equation integer programs intersection inverse inverse kinematics IPA,c(b leading terms LEMMA linear linear code m₁ Mathematical matrix polynomial methods minimal monomial order multiple nonzero optimal solution P₁ parametric path plane polynomial equations polynomial systems polytope problem PROOF PROPOSITION q-chain q-connected rational reduced Gröbner basis Reed-Solomon codes robotics roots S-polynomial Section simplex simplicial complex singular solving sparse resultant Sturmfels surface system of polynomial term order test set Theorem UGBA unique variables vertex zero