Custom LaTeX Commands

This section provides an overview of the custom LaTeX commands available in this project. These commands have been defined to comply with the standards from the International Organization for Standardization (ISO).

Sets (ISO 80000-2:2019, §6)

Macro	Expansion	Description	Notes
\set	Set	Set notation (2-6.3). Defined to follow ISO standards.	Defined by default in KaTeX.
\abs	Absolute value	Cardinality of a set (2-6.5). Used for absolute values.	Defined by default in KaTeX.

Miscellaneous Symbols (ISO 80000-2:2019, §8)

Macro	Expansion	Description	Notes
\colonhyphen	Colon-equals	Redefines \coloneq symbol to be used as \colonhyphen.	This macro is rarely used, if ever. It is only defined to avoid the use of both \coloneq and \coloneqq in the code, as that may be confusing.
\coloneqq	Colon equals definition	Equal by definition (2-8.3).	Defined by default in KaTeX.

Operations (ISO 80000-2:2019, §10)

Macro	Expansion	Description
\cbrt	Cubic root	Represents the cubic root (2-10.11).
\avg	Arithmetic mean	Represents the arithmetic mean (2-10.12).
\sgn	Signum	Signum function (2-10.13).

Functions (ISO 80000-2:2019, §12)

Macro	Expansion	Description
\ran	Domain	Domain of a function (2-12.3).
\dom	Range	Range of a function (2-12.4).
\cod	Codomain	Codomain of a function.
\inv	Inverse	Inverse of a function (2-12.10).
\der	Derivative	Represents a derivative (2-12.18).
\tder	Textstyle derivative	Textstyle derivative.
\dder	Displaystyle derivative	Displaystyle derivative.
\nder	Nth derivative	Nth derivative (2-12.20).
\tnder	Textstyle nth derivative	Textstyle nth derivative.
\dnder	Displaystyle nth derivative	Displaystyle nth derivative.
\parder	Partial derivative	Partial derivative (2-12.21).
\tparder	Textstyle partial derivative	Textstyle partial derivative.
\dparder	Displaystyle partial derivative	Displaystyle partial derivative.
\nparder	Nth partial derivative	Nth partial derivative.
\tnparder	Textstyle nth partial derivative	Textstyle nth partial derivative.
\dnparder	Displaystyle nth partial derivative	Displaystyle nth partial derivative.
\du	Total differential	Total differential (2-12.22).
\indint	Indefinite integral	Indefinite integral (2-12.24).
\defint	Definite integral	Definite integral (2-12.25).

Exponential and Logarithmic Functions (ISO 80000-2:2019, §13)

Macro	Expansion	Description
\lb	Binary logarithm	Binary logarithm (2-13.7).

Circular and Hyperbolic Functions (ISO 80000-2:2019, §14)

Macro	Expansion	Description
\arccot	Inverse cotangent	Inverse cotangent (2-14.11).
\arcsec	Inverse secant	Inverse secant (2-14.12).
\arccsc	Inverse cosecant	Inverse cosecant (2-14.13).
\sech	Hyperbolic secant	Hyperbolic secant (2-14.18).
\csch	Hyperbolic cosecant	Hyperbolic cosecant (2-14.19).
\arsinh	Inverse hyperbolic sine	Inverse hyperbolic sine (2-14.20).
\arcosh	Inverse hyperbolic cosine	Inverse hyperbolic cosine (2-14.21).
\artanh	Inverse hyperbolic tangent	Inverse hyperbolic tangent (2-14.22).
\arcoth	Inverse hyperbolic cotangent	Inverse hyperbolic cotangent (2-14.23).
\arsech	Inverse hyperbolic secant	Inverse hyperbolic secant (2-14.24).
\arcsch	Inverse hyperbolic cosecant	Inverse hyperbolic cosecant (2-14.25).

Complex Numbers (ISO 80000-2:2019, §15)

Macro	Expansion	Description
\iu	Imaginary unit	Imaginary unit (2-15.1).
\Rep	Real part	Real part of a complex number (2-15.2).
\Imp	Imaginary part	Imaginary part of a complex number (2-15.3).

Matrices (ISO 80000-2:2019, §16)

Macro	Expansion	Description
\bmat	Bold matrix	Matrix notation in bold (2-16.1).
\transpose	Transpose matrix	Transpose of a matrix (2-16.7).
\hermitian	Hermitian conjugate matrix	Hermitian conjugate of a matrix (2-16.9).
\rank	Rank	Rank of a matrix (2-16.11).
\tr	Trace	Trace of a matrix (2-16.12).
\norm	Norm	Norm of a matrix or vector (2-16.13).

Scalars, Vectors, and Tensors (ISO 80000-2:2019, §18)

Macro	Expansion	Description
\bvec	Bold vector	Vector notation in bold (2-18.1).
\grad	Gradient	Gradient of a function (2-18.14).
\div	Divergence	Divergence of a vector field (2-18.15).
\rot	Rotation	Rotation of a vector field (2-18.16).

Special Functions (ISO 80000-2:2019, §20)

Macro	Expansion	Description
\erf	Error function	Error function (2-20.9).
\erfc	Complementary error function	Complementary error function (2-20.9).

Additional Math

Macro	Expansion	Description
\uveci	i unit vector	i unit vector: dotless, with hat, upright boldface
\uvecj	j unit vector	j unit vector: dotless, with hat, upright boldface
\uvec	Unit vector	Unit vectors with hat in upright boldface.
\proy	Projection	Projection of a vector.
\adj	Adjugate matrix	Adjugate of a matrix.
\im	Image	Image of a linear transformation.
\lcm	Least common multiple	Least common multiple of two numbers.

Custom Environments

Environment	Description
apmatrix	Augmented parenthesis matrix.
abmatrix	Augmented bracket matrix.