The Reduction of Degenerate Quadratic Differential Forms
نویسندگان
چکیده
منابع مشابه
Highly degenerate quadratic forms over F2
Let K be a finite extension of F2. We consider quadratic forms written as the trace of xR(x), where R(x) is a linearized polynomial. We determine the K and R(x) where the form has a radical of codimension 2. This is applied to constructing maximal Artin-Schreier curves. Set F = F2 and let K = F2k be an extension of degree k. Let
متن کاملApplications of quadratic D-forms to generalized quadratic forms
In this paper, we study generalized quadratic forms over a division algebra with involution of the first kind in characteristic two. For this, we associate to every generalized quadratic from a quadratic form on its underlying vector space. It is shown that this form determines the isotropy behavior and the isometry class of generalized quadratic forms.
متن کاملLinear-quadratic Control and Quadratic Differential Forms
We consider the infinite time linear-quadratic control problem from a behavioral point of view. The performance functional is the integral of a quadratic differential form. A characterization of the stationary trajectories and of the local minima with respect to (left) compact support variations, as well as their relation to stability, are obtained. Finally, several theorems are derived that de...
متن کاملOn rational quadratic differential forms
In linear system theory, we often encounter the situation of investigating some quadratic functionals which represent Lyapunov functions, energy storage, performance measures, e.t.c. Such a quadratic functional is called a quadratic differential form (QDF) in the context of the behavioral approach. In the past works, a QDF is usually defined in terms of a polynomial matrix. The contribution of ...
متن کاملFast Reduction of Ternary Quadratic Forms
We show that a positive de nite integral ternary form can be reduced with O(M(s) log s) bit operations, where s is the binary encoding length of the form and M(s) is the bit-complexity of s-bit integer multiplication. This result is achieved in two steps. First we prove that the the classical Gaussian algorithm for ternary form reduction, in the variant of Lagarias, has this worst case running ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1934
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.20.3.215