In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for su...In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.展开更多
基金This research is supported by the National Key Basic Research Project of China under Grant No. 2011CB302400 and the National Natural Science Foundation of China under Grant No. 10901163.
文摘In this paper, a class of lattice supports in the lattice space Zm is found to be inherently improper because any rational parametrization from Cm to Cm defined on such a support is improper. The improper index for such a lattice support is defined to be the gcd of the normalized volumes of all the simplex sub-supports. The structure of an improper support S is analyzed and shrinking transformations are constructed to transform S to a proper one. For a generic rational parametrization RP defined on an improper support S, we prove that its improper index is the improper index of S and give a proper reparametrization algorithm for RP. Finally, properties for rational parametrizations defined on an improper support and with numerical coefficients are also considered.
