FFT
... Given N-bit integers (N ≥ 64) I and J, compute IJ. Assume: we can multiply words of O(log N) bits in constant time. Setup: Find a prime p=cn+1 that can be represented in one word, and set m=(log p)/3, so that we can view I and J as n-length vectors of m-bit words. Finding a primitive root of unity. ...
... Given N-bit integers (N ≥ 64) I and J, compute IJ. Assume: we can multiply words of O(log N) bits in constant time. Setup: Find a prime p=cn+1 that can be represented in one word, and set m=(log p)/3, so that we can view I and J as n-length vectors of m-bit words. Finding a primitive root of unity. ...
Standard Monomial Theory and applications
... geometric properties. Here we suppose that G is a reductive algebraic group defined over an algebraically closed field k, B is a fixed Borel subgroup, and Lλ is the line bundle on the flag variety G/B associated to a dominant weight. The purpose of the program is to extend the Hodge-Young standard m ...
... geometric properties. Here we suppose that G is a reductive algebraic group defined over an algebraically closed field k, B is a fixed Borel subgroup, and Lλ is the line bundle on the flag variety G/B associated to a dominant weight. The purpose of the program is to extend the Hodge-Young standard m ...
*7. Polynomials
... The division Theorem above is very similar to a result in integers. Other ideas can be generalized to polynomials such as Definition Let F be one of Q, R, C or Zp , with p prime. Let f, g ∈ F [x] be polynomials not both identically zero. Then a greatest common divisor is a polynomial d ∈ F [x] such ...
... The division Theorem above is very similar to a result in integers. Other ideas can be generalized to polynomials such as Definition Let F be one of Q, R, C or Zp , with p prime. Let f, g ∈ F [x] be polynomials not both identically zero. Then a greatest common divisor is a polynomial d ∈ F [x] such ...
4.) Groups, Rings and Fields
... Here is a short survey of the material presented in these notes: 1. Chapter I: Groups. Here we discuss the basic notions of group theory: Groups play an important rôle nearly in every part of mathematics and can be used to study the symmetries of a mathematical object. 2. Chapter II: Rings. Commuta ...
... Here is a short survey of the material presented in these notes: 1. Chapter I: Groups. Here we discuss the basic notions of group theory: Groups play an important rôle nearly in every part of mathematics and can be used to study the symmetries of a mathematical object. 2. Chapter II: Rings. Commuta ...
