In this paper,we consider symbolic(hybrid trigonometric)parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials,with the restricti...In this paper,we consider symbolic(hybrid trigonometric)parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials,with the restriction that variables in each block of functions are different.We prove that the varieties parametrizable in this way are exactly the class of real unirational varieties of any dimension.In addition,we provide symbolic algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one,and vice versa.We illustrate by some examples the applicability of having these different types of parametrizations,namely,hybrid trigonometric and unirational.展开更多
Urban Movement Design事务所是2012年度青年建筑师项目的获胜者,他们设计的UNIRE/UNITE夏日互动装置为市民提供了良好的放松身心的设施。这个装置不同于传统的城市公共设施,对当今公共健康危机问题予以积极响应,其优美的曲线为城市生...Urban Movement Design事务所是2012年度青年建筑师项目的获胜者,他们设计的UNIRE/UNITE夏日互动装置为市民提供了良好的放松身心的设施。这个装置不同于传统的城市公共设施,对当今公共健康危机问题予以积极响应,其优美的曲线为城市生活注入舞蹈元素。事务所将建筑和运动原理结合起来,这个装置能将人最真实的状态体现出来,促进人与人的联系。装置位于MAXXI广场。展开更多
In this paper, we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P. （1）To find a characteristic set for the implicit prime ideal o...In this paper, we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P. （1）To find a characteristic set for the implicit prime ideal of P; （2） To find a canonical representation for the image of P; （3）To decide whether the parameters of P are independent, and if not, to re-parameterize P so that the new parametric equations have independent parameters; （4） To compute the inversion maps of P, and as a consequence, to decide whether P is proper.展开更多
基金the CRUE-CSIC agreement with Springer Nature.the project ID2019-105621GB-I00 of Ministerio de Ciencia e Innovación.+1 种基金the GrantPID2020-113192GB-100(Math-ematical Visualization:Foundations,Algorithms and Applications)from the Spanish MICINN.A.Lastra is member of the Research Group ASYNACS(Ref.CT-CE2019/683).
文摘In this paper,we consider symbolic(hybrid trigonometric)parametrizations defined as tuples of real rational expressions involving circular and hyperbolic trigonometric functions as well as monomials,with the restriction that variables in each block of functions are different.We prove that the varieties parametrizable in this way are exactly the class of real unirational varieties of any dimension.In addition,we provide symbolic algorithms to implicitize and to convert a hybrid trigonometric parametrization into a unirational one,and vice versa.We illustrate by some examples the applicability of having these different types of parametrizations,namely,hybrid trigonometric and unirational.
文摘Urban Movement Design事务所是2012年度青年建筑师项目的获胜者,他们设计的UNIRE/UNITE夏日互动装置为市民提供了良好的放松身心的设施。这个装置不同于传统的城市公共设施,对当今公共健康危机问题予以积极响应,其优美的曲线为城市生活注入舞蹈元素。事务所将建筑和运动原理结合起来,这个装置能将人最真实的状态体现出来,促进人与人的联系。装置位于MAXXI广场。
基金Research supported by the Foundation of Mathematics MechanizationIts Applications in Information Technology(65432A0)of China.
文摘In this paper, we propose algorithms for the following problems in the implicitization of a set of partial differential rational parametric equations P. （1）To find a characteristic set for the implicit prime ideal of P; （2） To find a canonical representation for the image of P; （3）To decide whether the parameters of P are independent, and if not, to re-parameterize P so that the new parametric equations have independent parameters; （4） To compute the inversion maps of P, and as a consequence, to decide whether P is proper.
