Codex @codex  0

A fresh internal name introduced during compilation to hold an intermediate result. Its lifetime and uses can be exposed to instruction selection and allocation of processor registers; it need not correspond to a variable named in the source.

For an integer $n$ to be factored, John Pollard's method chooses an integer $a$ coprime to $n$ and an exponent $M$ divisible by many small prime powers. Compute $d=\gcd (a^M-1,n)$ by modular exponentiation and the Euclidean algorithm. If $1<d<n$, it is a proper divisor. If a prime divisor $p$ of $n$ has $p-1\mid M$, Fermat's little theorem ensures $p\mid d$; success requires some other prime divisor not to divide $a^M-1$. Common choices are $M=B!$ and $M=\mathrm{lcm}(1,\dots ,B)$. The method exploits a smooth $p-1$, rather than a small divisor $p$ itself.

For a Turing machine, the one-step binary relation between Turing machine configurations specified by its Turing machine instructions. Its reflexive transitive closure ${⊢}_M^{\ast }$ describes any finite number of computation steps, including zero.

An inode number identifies an allocated inode within one file system. A directory entry stores a name and this number; it does not normally store the file data block addresses. Different volumes can reuse the same number for unrelated files, and a reclaimed number can later be reused on the same volume. This is therefore a local, current identity, rather than a permanent identifier.

A persistent collection of inodes indexed by inode numbers in an inode-based file system. The same term can also denote an operating system's in-memory collection of active inodes; these must be distinguished. A persistent table belongs to a particular volume, while the system-wide active collection keys entries by both volume identity and inode number.

An address in a traditional inode-based file system that points to a block of further disk block numbers, rather than directly to user contents. If a block can store $q$ addresses, one singly indirect block can locate up to $q$ file data blocks, and a doubly indirect arrangement can locate up to $q^2$. The address blocks themselves consume allocated storage and must be reclaimed when their file no longer needs them. This lets small files use a short direct layout while supporting larger files.

An inflorescence with a thickened axis bearing closely attached flowers, commonly associated with a spathe.

An inflorescence with stalks arising together at the top of a peduncle.^[ref]

The stalk of one flower within an inflorescence.

An inflorescence of closely packed flowers on a common expanded support, as in the common daisy.

Material that leaves the blood vessels during inflammation. Historical theories of its formation and removal should be distinguished from current pathology.

Fluid and associated material leaving the blood circulation because of altered vascular permeability, typically during inflammation. Its composition differs from fluid accumulating mainly through pressure or protein-balance changes.

An organized aggregate of immune cells, commonly including activated macrophages. It is a pattern of tissue response with infectious and noninfectious causes, not a synonym for tuberculosis.

A localized collection of pus.

Inflammation of the synovial lining of an anatomical joint. It can cause swelling and contribute to tissue injury through infectious, autoimmune or other mechanisms.

Inflammation of the pleura.

Inflammation of the spinal cord. Its effects depend on the affected pathways and level, distinguishing an anatomical syndrome from one unique infectious or immune cause.

For the infinite square well of length $a$, the energy eigenvalues are $E_n=n^2{E}_1$, with $E_1={\pi }^2{\hslash }^2/(2m{a}^2)$. At $t_{\ast }=\pi \hslash /E_1$, the dynamical phase is $e^{-i{E}_n{t}_{\ast }/\hslash }=(-1{)}^n$. Since the midpoint parity operator has eigenvalues $(-1{)}^{n+1}$ in the same complete orthonormal basis, the time-evolution operator is exactly $U(t_{\ast })=-R_a$ on every state. At $2t_{\ast }$ every phase is one, giving a full revival.

Thus a state becomes its reflected copy, up to a global phase, at the half revival. Its position probability density is reflected, while its mean momentum changes sign because $P{R}_a=-R_{a}P$. For an initially reflection-symmetric probability density, the initial and half-revival position distributions agree even when their probability currents point in opposite directions.

Widen an $m$-bit binary representation to $w>m$ bits by retaining the original low positions and filling every new high position with zero. This preserves the unsigned interpretation. A MIPS instruction such as ori uses zero extension of its immediate operand, whereas addi uses sign extension.

An instruction encoding that stores an eight-bit byte and a two-bit byte-position selector, expanding them to a 32-bit machine word as $b{2}^{8j}$ for $0\le j\le 3$. Four such values can construct any 32-bit constant using bitwise OR or addition modulo $2^{32}$.