# 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}`

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### 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}`

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### Hexadecimal

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

The hexadecimal digit $13$.

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

or `\mathrm d`

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### Roman Numeral

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

The Roman numeral for $500$.

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

or `\mathrm d`

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### 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`

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### 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}`

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### 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}`

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### 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}`

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### 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^*`

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### 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_+`

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### 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_+^*`

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### 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`

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### 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`

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### Divergence Operator

- $\operatorname {div}$

Let $R$ be a region of space embedded in a Cartesian coordinate frame.

Let $\mathbf V$ be a vector field acting over $R$.

The **divergence** of $\mathbf V$ at a point $A$ in $R$ is defined as:

\(\ds \operatorname {div} \mathbf V\) | \(:=\) | \(\ds \nabla \cdot \mathbf V\) | ||||||||||||

\(\ds \) | \(=\) | \(\ds \dfrac {\partial V_x} {\partial x} + \dfrac {\partial V_y} {\partial y} + \dfrac {\partial V_z} {\partial z}\) |

where:

- $\nabla$ denotes the Del operator
- $\cdot$ denotes the dot product
- $V_x$, $V_y$ and $V_z$ denote the magnitudes of the components of $\mathbf V$ at $A$ in the directions of the coordinate axes $x$, $y$ and $z$ respectively.

The $\LaTeX$ code for \(\operatorname {div} \mathbf V\) is `\operatorname {div} \mathbf V`

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### Decimetre

- $\mathrm {dm}$

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

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

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### 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}`

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