Quaternion Algebras and Quadratic Forms - UWSpace
... and only if M1 and M2 are invertible. The result then follows from the definition of regular spaces immediately. For d ∈ F , we write hdi to denote the isometry class of the 1-dimensional space corresponding to the quadratic form dX 2 , or equivalently the bilinear pairing dXY . Clearly, hdi is reg ...
... and only if M1 and M2 are invertible. The result then follows from the definition of regular spaces immediately. For d ∈ F , we write hdi to denote the isometry class of the 1-dimensional space corresponding to the quadratic form dX 2 , or equivalently the bilinear pairing dXY . Clearly, hdi is reg ...
Parametric Integer Programming in Fixed Dimension
... algorithm to decide the sentence (1) in the case when n, p and the affine dimension of Q are fixed. This result was applied to deduce a polynomial algorithm that solves the Frobenius problem when the number of input integers is fixed, see (Kannan, 1992). Kannan’s algorithm proceeds in several steps. ...
... algorithm to decide the sentence (1) in the case when n, p and the affine dimension of Q are fixed. This result was applied to deduce a polynomial algorithm that solves the Frobenius problem when the number of input integers is fixed, see (Kannan, 1992). Kannan’s algorithm proceeds in several steps. ...
Hindawi Publishing Corporation EURASIP Journal on Bioinformatics and Systems Biology
... where X is a finite set and f is a function that maps X into itself, that is, f : X → X. The state space of an fds (X, f ) is a digraph (i.e., directed graph) whose nodes are labeled by the elements of X and whose edges consist of all ordered pairs (x, y) ∈ X × X such that f (x) = y. We say that two ...
... where X is a finite set and f is a function that maps X into itself, that is, f : X → X. The state space of an fds (X, f ) is a digraph (i.e., directed graph) whose nodes are labeled by the elements of X and whose edges consist of all ordered pairs (x, y) ∈ X × X such that f (x) = y. We say that two ...
Document
... if r is a root of an irreducible polynomial p, that is, p(r)=0, we will also talk about a ring or field extended by r: Q[r]. E.g. p(r)=r2-1=0 means r = p(-1) or i, and we have just constructed the complex rationals Q[r]. Z[i] is called “Gaussian integers" The set of elements a+bi, with a, b, integer ...
... if r is a root of an irreducible polynomial p, that is, p(r)=0, we will also talk about a ring or field extended by r: Q[r]. E.g. p(r)=r2-1=0 means r = p(-1) or i, and we have just constructed the complex rationals Q[r]. Z[i] is called “Gaussian integers" The set of elements a+bi, with a, b, integer ...
Dowling, T.A.; (1972)A class of geometric lattices based on finite groups."
... tice, and in general, every interval is a direct product of partition lattices. The Whitney numbers of the partition lattices are the familiar Stirling numbers, and the characteristic polynomial is simply a descending factorial, hence all its roots are integers. ...
... tice, and in general, every interval is a direct product of partition lattices. The Whitney numbers of the partition lattices are the familiar Stirling numbers, and the characteristic polynomial is simply a descending factorial, hence all its roots are integers. ...
Sec 5: Affine schemes
... Proof. By definition, I(V (I)) is the intersection of all prime ideals which contain I. This is easily seen to be the radical of I: By passing to R/I, we may assume that I = 0. Then the statement is that the intersection of all prime ideals is equal to the set of nilpotent elements. To see this take ...
... Proof. By definition, I(V (I)) is the intersection of all prime ideals which contain I. This is easily seen to be the radical of I: By passing to R/I, we may assume that I = 0. Then the statement is that the intersection of all prime ideals is equal to the set of nilpotent elements. To see this take ...
Math 676. Some basics concerning absolute values A remarkable
... We now consider the case F = Q. We wish to determine all non-trivial absolute values on Q. We shall write | · |∞ to denote the usual absolute value, so (as one easily sees by working in R) | · |e∞ is an absolute value on Q for e > 0 if and only if e ≤ 1. In view of Theorem 1.1, these are precisely t ...
... We now consider the case F = Q. We wish to determine all non-trivial absolute values on Q. We shall write | · |∞ to denote the usual absolute value, so (as one easily sees by working in R) | · |e∞ is an absolute value on Q for e > 0 if and only if e ≤ 1. In view of Theorem 1.1, these are precisely t ...
