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**public sources and our publisher partners.**We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and… Continue Reading

We revisit the problem of computing the topology and geometry of a real algebraic plane curve. The topology is of prime interest but geometric information, such as the position of singular and… Continue Reading

An algorithm is proposed to determine the topology of an implicit real algebraic surface in ℝ3. The algorithm consists of three steps: surface projection, projection curve topology determination and… Continue Reading

In this paper, an algorithm is given for determining the topology of an algebraic space curve and to compute a certified G^1 rational parametric approximation of the algebraic space curve. The… Continue Reading

We present a complete numerical algorithm of isolating all the real zeros of a zero-dimensional triangular polynomial system <i>F</i><sub>n</sub> Z[<i>x</i><sub>1</sub>…,<i>x</i><sub>n</sub>]. Our… Continue Reading

We present a complete numerical algorithm for isolating all the real zeros of a zero-dimensional triangular polynomial system F"n@?Z[x"1...x"n]. Our system F"n is general, with no further… Continue Reading

In this paper, a multiplicity-preserving triangular set decomposition algorithm is proposed for a system of two polynomials, which involves only computing the primitive polynomial remainder sequence… Continue Reading

We consider the computational problem of isolating all the real zeros of a zero-dimensional triangular polynomial system Fn ⊆ Z[x1, . . . , xn]. We present a complete numerical algorithm for this… Continue Reading

A local generic position method is proposed to isolate the real roots of a bivariate polynomial system ∑={<i>f</i>(<i>x,y</i>),<i>g</i>(<i>x,y</i>)}. In this method, the roots of the system are… Continue Reading

In this paper, a linear univariate representation for the roots of a zero-dimensional polynomial equation system is presented, where the complex roots of the polynomial system are represented as… Continue Reading