Letter symbols for physical quantities

lettsymb: a LaTeX package to provide standardized commands for the symbols of physical quantities.

Purpose

lettsymb allows LaTeX users to worry more about the content of their mathematics and less about the implementation. This package provides a simple set of commands to create custom commands for the symbols of quantities, along with a library of commands using standardized symbols of quantities. Instead of typing F for force, users can use \qForce instead for added clarity. These kind of commands allow the document to be read in natural language and make changing the notation later much easier.

Features (and status)

• Commands to create symbol commands (incomplete)

  • Dimensions

    • \newDimension (complete)

  • Quantities

    • \newQuantity (complete)

    • \newLabeledQuantity (complete)

    • \newExtensiveQuantity (complete)

    • \newSpecificQuantity (complete)

    • \newMolarQuantity (complete)

    • \newDimensionlessNumber (complete)

    • \newLabeledDimensionlessNumber (complete)

  • Vectors

    • \newVectorQuantity (complete)

  • Components of vectors

    • \newComponentQuantity (complete)

    • \newNumberedComponentQuantity (complete)

    • \newLabeledComponentQuantity (complete)

  • Index notation

    • \newIndexNotationQuantity (complete, old convention)

    • \newUIndexNotationQuantity, etc. (incomplete, new convention)

• A library of standardized symbols for quantities (incomplete)

  • General subjects

    • Mathematical quantities (incomplete)

    • Space and time (incomplete)

    • Mechanics (incomplete)

    • Thermodynamics (incomplete)

    • Electromagnetism (incomplete)

    • Light and radiation (incomplete)

    • Chemistry (incomplete)

    • Dimensionless numbers (incomplete)

    • Index notation (incomplete)

  • Specialized subjects

    • Fluid mechanics (incomplete)

• Package options to change the standardized symbols (incomplete)

  • bm - use bm package for bold vector symbols (default)

  • nostrikethroughvolume - use a plain V for the symbol for volume (default)

  • pmb - use the \pmb command from the amsmath package for bold vector symbols

  • strikethroughvolume - use a strikethrough V for the symbol for volume

Usage

Loading the package

\usepackage{lettsymb}

Creating symbol commands

To create a command, simply use one of the creation commands:

\newQuantity{\qHeight}{h}

The first argument is the name of the command to create, and the second argument is the symbol to use. Do not put any superscripts or subscripts in the second argument, since they interfere with labels or exponents.

If the symbol you want to create contains a subscript or a label, use \newLabeledQuantity instead:

\newLabeledQuantity{\qHeightOfTree}{h}{\mathrm{tree}}

This command will correctly place the subscript so that it does not interfere with any additional labels. Additional labels are available via the optional argument:

\qVolume[1]

\qVolume[\mathrm{cube}]

\qVolume[\mathrm{sphere}]

The commands \newExtensiveQuantity, \newSpecificQuantity, and \newMolarQuantity are used to create extensive and intensive variables. They follow how \newQuantity works but also change the given symbol automatically to adjust it to a standardized form, to better distinguish between extensive and intensive quantities.

Using symbol commands

To use any symbol command from the standard library, you first must know its name. All names in the standard library follow a simple pattern:

1. A letter denoting the type of the symbol. Different prefixes often require different arguments, optional and otherwise.

   • d for symbol of a dimension. The optional argument is the exponent.

   • q for the preferred symbol of a quantity. The optional argument is the label.

   • a for the alternative symbol of a quantity. Alternative symbols can be used when you need two symbols for a type of quantity or when another quantity uses the same symbol as the preferred symbol. The optional argument is the label.

   • v for the vector symbol of a quantity. The optional argument is the label.

   • c for the component symbol of a vector quantity. The required argument is the dimension number.

   • i for the index notation symbol of a quantity. The required argument is the lower indices and the optional argument is the upper indices.

2. The name of the concept in CamelCase (like SpecificHeat for "specific heat"). Note that only ASCII letters are accepted, so "Damköhler number" becomes DamkoehlerNumber, for example. Apostrophes, dashes, and other punctuation are also dropped ("Poisson's ratio" becomes PoissonsRatio).

Combine these two and you can easily know the command for any given symbol of a dimension or quantity.

Examples:

• \dTime is the command for symbol of the dimension of time and \qTime is the command for symbol of the quantity of time.

• \qLength is the command for the preferred symbol for the quantity of length and \aLength is the command for the alternative symbol for the quantity of length.

Finally, you can use any symbol command just as you would use any variable when writing equations.

Newton's second law is
%
\begin{equation}
    \vForce
    =
    \qMass
    \vAcceleration
    \,.
\end{equation}

The speed of sound in an ideal gas is
%
\begin{equation}
    \qSpeedOfSound[\mathrm{ig}]^2
    =
    \qHeatCapacityRatio
    \qSpecificGasConstant
    \qTemperature
    \,.
\end{equation}

\begin{equation}
    \frac{
        \partial
        \cRectangularVelocity{1}
    }{
        \partial
        \cRectangularCoordinate{1}
    }
    +
    \frac{
        \partial
        \cRectangularVelocity{2}
    }{
        \partial
        \cRectangularCoordinate{2}
    }
    =
    0
    \,.
\end{equation}

Using index notation (new convention)

The new convention for index notation (still being implemented) more explicitly notes which indices are subscripts (lower indices) and superscripts (upper indices). For example, the statement that the metric tensor and conjugate metric tensor are inverses of each other can be expressed as

\begin{equation}
    \iuuMetricTensor{i}{k}
    \illMetricTensor{k}{j}
    =
    \iulKroneckerDelta{i}{j}
    \,.
\end{equation}

The prefix l specifies a lower index and the prefix u specifies an upper index. These commands let you preserve the order of the subscripts and superscripts and make the equations more clear in some circumstances.

Using index notation (old convention)

This convention should be used for rectangular index notation only due to its ease of use.

Index notation commands operate differently. Each index notation command accepts the lower indices as the required argument and the upper indices as the optional argument. Many writers only use the lower indices (for rectangular coordinates only), so this choice minimizes the amount of typing for that particular case while still allowing for more general usage.

\begin{equation}
    \iAlternatingSymbol{ijk}
    \iAlternatingSymbol[imn]{}
    =
    \iKroneckerDelta[m]{j}
    \iKroneckerDelta[n]{k}
    -
    \iKroneckerDelta[n]{j}
    \iKroneckerDelta[m]{k}
    \,.
\end{equation}

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Copyright © 2020-2022 and 2026 Andrew Trettel

This work may be distributed and/or modified under the conditions of the LaTeX Project Public License, either version 1.3 of this license or (at your option) any later version. The latest version of this license is in http://www.latex-project.org/lppl.txt and version 1.3 or later is part of all distributions of LaTeX version 2005/12/01 or later.

This work has the LPPL maintenance status author-maintained.

The Current Maintainer of this work is Andrew Trettel.

This work consists of the files lettsymb.sty and README.md.