Fulton’s algorithm is used to calculate the intersection multiplicity of two plane curves about a rational point. This work extends Fulton’s algorithm first to algebraic points (encoded by regular chains) and then, with some generic assumptions, to l many hypersurfaces. Out of necessity, we give a standard-basis free method (i.e. practically efficient method) for calculating tangent cones at po...

The necessity for some techniques which can be used in investigating equations arising in mathematical models describing real-life situations in population biology and economics has increased the interest in studying nonlinear and rational difference equations for the last four decades, see, for example, [1–23] and the references therein. In [8] the authors proposed the following research project.

ijtihad, jurisprudence in religion and imitation that is fojiowing a just religious leader in divine commandments, are fundamental issues in islamic society and are necessary for continuation of divine religion. this article turns to understanding the conception, necessity, beginning and evolution of ijtihad and imitation (taqlid), if s rational and traditional reasons using quran, and also ref...