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Qu'est-ce (qui) est arithmetic and logic unit - définition

Arithmetic Frobenius; Geometric Frobenius; Frobenius mapping; Arithmetic and geometric frobenius

Arithmetic and Logic Unit         
  • The [[combinational logic]] circuitry of the [[74181]] integrated circuit, an early four-bit ALU
COMBINATIONAL DIGITAL CIRCUIT THAT PERFORMS ARITHMETIC AND BITWISE OPERATIONS ON BINARY-CODED INTEGER NUMBERS
Arithmetic and logic unit; Arithmetic-logic unit; Arithmetical and logical unit; Arithmetic Logic Unit; Arithmetic and logical unit; Arithmetic and logic structures; Computer arithmetic; Arithmetic and Logical Unit; Arithmetic logic unit\; Integer arithmetic operation; Integer operation; Arithmetic–logic unit; Arithmetic / logic unit; Multiple-precision arithmetic; Arithmetic logic units; Arithmetic logical unit
<processor> (ALU or "mill") The part of the {central processing unit} which performs operations such as addition, subtraction and multiplication of integers and bit-wise AND, OR, NOT, XOR and other Boolean operations. The CPU's instruction decode logic determines which particular operation the ALU should perform, the source of the operands and the destination of the result. The width in bits of the words which the ALU handles is usually the same as that quoted for the processor as a whole whereas its external busses may be narrower. Floating-point operations are usually done by a separate "{floating-point unit}". Some processors use the ALU for address calculations (e.g. incrementing the program counter), others have separate logic for this. (1995-03-24)
Arithmetic logic unit         
  • The [[combinational logic]] circuitry of the [[74181]] integrated circuit, an early four-bit ALU
COMBINATIONAL DIGITAL CIRCUIT THAT PERFORMS ARITHMETIC AND BITWISE OPERATIONS ON BINARY-CODED INTEGER NUMBERS
Arithmetic and logic unit; Arithmetic-logic unit; Arithmetical and logical unit; Arithmetic Logic Unit; Arithmetic and logical unit; Arithmetic and logic structures; Computer arithmetic; Arithmetic and Logical Unit; Arithmetic logic unit\; Integer arithmetic operation; Integer operation; Arithmetic–logic unit; Arithmetic / logic unit; Multiple-precision arithmetic; Arithmetic logic units; Arithmetic logical unit
In computing, an arithmetic logic unit (ALU) is a combinational digital circuit that performs arithmetic and bitwise operations on integer binary numbers. This is in contrast to a floating-point unit (FPU), which operates on floating point numbers.
Arithmetic geometry         
  • The [[hyperelliptic curve]] defined by <math>y^2=x(x+1)(x-3)(x+2)(x-2)</math> has only finitely many [[rational point]]s (such as the points <math>(-2, 0)</math> and <math>(-1, 0)</math>) by [[Faltings's theorem]].
BRANCH OF ALGEBRAIC GEOMETRY FOCUSED ON PROBLEMS IN NUMBER THEORY
Arithmetical algebraic geometry; Arithmetic Geometry; Arithmetic algebraic geometry; Arithmetic Algebraic Geometry
In mathematics, arithmetic geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine geometry, the study of rational points of algebraic varieties.

Wikipédia

Arithmetic and geometric Frobenius

In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number. Namely, the mapping φ that takes r in R to rp is a ring endomorphism of R.

The image of φ is then Rp, the subring of R consisting of p-th powers. In some important cases, for example finite fields, φ is surjective. Otherwise φ is an endomorphism but not a ring automorphism.

The terminology of geometric Frobenius arises by applying the spectrum of a ring construction to φ. This gives a mapping

φ*: Spec(Rp) → Spec(R)

of affine schemes. Even in cases where Rp = R this is not the identity, unless R is the prime field.

Mappings created by fibre product with φ*, i.e. base changes, tend in scheme theory to be called geometric Frobenius. The reason for a careful terminology is that the Frobenius automorphism in Galois groups, or defined by transport of structure, is often the inverse mapping of the geometric Frobenius. As in the case of a cyclic group in which a generator is also the inverse of a generator, there are in many situations two possible definitions of Frobenius, and without a consistent convention some problem of a minus sign may appear.