Complementary triangular forms
نویسندگان
چکیده
منابع مشابه
Binary quadratic forms and sums of triangular numbers
Notation: Z the set of integers, N the set of positive integers, [x] the greatest integer not exceeding x, ( a m) the Legendre-JacobiKronecker symbol, ordpm the nonnegative integer α such that pα | m but pα+1 m, (a, b) the greatest common divisor of a and b, (a, b, c) the form ax2 + bxy + cy2, [a, b, c] the equivalence class containing the form (a, b, c), H(d) the form class group of discrimina...
متن کاملComputing Hermite and Smith normal forms of triangular integer matrices
This paper considers the problem of transforming a triangular integer input matrix to canonical Hermite and Smith normal form. We provide algorithms and prove deterministic running times for both transformation problems that are optimal in the matrix dimension. The algorithms are easily implemented, assume standard integer arithmetic, and admit excellent performance in practice. The results pre...
متن کاملMixed Sums of Triangular Numbers and Certain Binary Quadratic Forms
In this paper, we prove that for d = 3, . . . , 8, every natural number can be written as tx+ty +3tz +dtw, where x, y, z, and w are nonnegative integers and tk = k(k+1)/2 (k = 0, 1, 2, . . .) is a triangular number. Furthermore, we study mixed sums of triangular numbers and certain binary quadratic forms.
متن کاملTriangular canonical forms for lattice rules of prime-power order
In this paper we develop a theory of t-cycle D−Z representations for s-dimensional lattice rules of prime-power order. Of particular interest are canonical forms which, by definition, have a D-matrix consisting of the nontrivial invariants. Among these is a family of triangular forms, which, besides being canonical, have the defining property that their Z-matrix is a column permuted version of ...
متن کاملDisentangling Forms of Lorentz Violation With Complementary Clock Comparison Experiments
Atomic clock comparisons provide some of the most precise tests of Lorentz and CPT symmetries in the laboratory. With data from multiple such experiments using different nuclei, it is possible to constrain new regions of the parameter space for Lorentz violation. Relativistic effects in the nuclei allow us to disentangle forms of Lorentz violation which could not be separately measured in purel...
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: Banach Center Publications
سال: 1997
ISSN: 0137-6934,1730-6299
DOI: 10.4064/-38-1-443-452