# Symbols:D

### deci-

- $\mathrm d$

The Système Internationale d'Unités symbol for the metric scaling prefix **deci**, denoting $10^{\, -1 }$, is $\mathrm { d }$.

Its $\LaTeX$ code is `\mathrm {d}`

.

### deka-

- $\mathrm {da}$

The Système Internationale d'Unités symbol for the metric scaling prefix **deka**, denoting $10^{\, 1 }$, is $\mathrm { da }$.

Its $\LaTeX$ code is `\mathrm {da}`

.

### Hexadecimal

- $\mathrm D$ or $\mathrm d$

The hexadecimal digit $13$.

Its $\LaTeX$ code is `\mathrm D`

or `\mathrm d`

.

### Roman Numeral

- $\mathrm D$ or $\mathrm d$

The Roman numeral for $500$.

Its $\LaTeX$ code is `\mathrm D`

or `\mathrm d`

.

### Differential

- $\d$

Symbol used to indicate the **differential** of a function, used for example to denote the **derivative**:

- $\dfrac \d {\d x} f$

The $\LaTeX$ code for \(\dfrac \d {\d x} f\) is `\dfrac \d {\d x} f`

.

### Partial Derivative

- $\partial$

Symbol used to indicate the **partial derivative** of a function, used for example as follows**:**

- $\dfrac \partial {\partial x} \map f {x, y}$

The $\LaTeX$ code for \(\dfrac \partial {\partial x} \map f {x, y}\) is `\dfrac \partial {\partial x} \map f {x, y}`

.

### Integral Domain

- $D$

Used as a variable denoting the general integral domain.

### Integral Domain as Algebraic Structure

- $\struct {D, +, \circ}$

The full specification for an integral domain, where $+$ and $\circ$ are respectively the ring addition and ring product operations.

Its $\LaTeX$ code is `\struct {D, +, \circ}`

.

### Ordered Integral Domain

- $\struct {D, +, \circ, \le}$

This specifies an ordered integral domain which is totally ordered by the ordering $\le$.

Its $\LaTeX$ code is `\struct {D, +, \circ, \le}`

.

### Non-Zero Elements of Integral Domain

- $D^*$

Let $\struct {D, +, \circ}$ be an integral domain whose zero is $0_D$.

Then $D^*$ denotes the set $D \setminus \set {0_D}$.

Its $\LaTeX$ code is `D^*`

.

### Non-Negative Elements of Ordered Integral Domain

- $D_+$

Let $\struct {D, +, \circ, \le}$ be an ordered integral domain whose zero is $0_D$.

Then $D_+$ denotes the set $\set {x \in D: 0_D \le x}$, that is, the set of all positive (that is, **non-negative**) elements of $D$.

Its $\LaTeX$ code is `D_+`

.

### Positive Elements of Ordered Integral Domain

- $D_+^*$

Let $\struct {D, +, \circ, \le}$ be an ordered integral domain whose zero is $0_D$.

Then $D_+^*$ denotes the set $\set {x \in D: 0_D < x}$, that is, the set of all strictly positive elements of $D$.

Some sources denote this as $D^+$, but this style of notation makes it difficult to distinguish between this and $D_+$.

Its $\LaTeX$ code is `D_+^*`

.

### Electric Displacement Field

- $\mathbf D$

The **electric displacement field** is a vector quantity defined as the electric field strength multiplied by the permittivity of the medium through which it passes:

- $\mathbf D = \varepsilon \mathbf E$

where:

- $\varepsilon$ is the permittivity of the medium
- $\mathbf E$ is the electric field strength

Its $\LaTeX$ code is `\mathbf D`

.

### Divisor Counting Function

- $\map d n$

Often seen as the symbol used to denote the Divisor Counting Function.

This is usually denoted on $\mathsf{Pr} \infty \mathsf{fWiki}$ using the symbol as $\sigma_0$ (the Greek letter **sigma**).

The $\LaTeX$ code for \(\map d n\) is `\map d n`

.

### Decimetre

- $\mathrm {dm}$

The symbol for the **decimetre** is $\mathrm {dm}$:

Its $\LaTeX$ code is `\mathrm {dm}`

.

### Pennyweight

- $\mathrm {dwt}$

The symbol for the pennyweight is $\text{dwt}$.

This derives from the Latin **denarius**, which evolved into the (old) penny.

Its $\LaTeX$ code is `\mathrm {dwt}`

.