The TikZ and PGF Packages
Manual for version 3.1.10

\usetikzlibrary{math} % LaTeX and plain TeX
\usetikzlibrary[math] % ConTeXt

This library defines a simple mathematical language to define simple functions and perform sequences of basic mathematical operations.

This command process a series of ⟨statements⟩ which can represent assignments, function definitions, conditional evaluation, and iterations. It provides, in effect, a miniature mathematical language to perform basic mathematical operations. Perhaps the most important thing to remember is that every statement should end with a semi-colon. This is likely to be the most common reason why the \tikzmath command fails.

This key simply executes \tikzmath{⟨statements⟩}.

This keyword assigns ⟨expression⟩ to ⟨variable⟩ without evaluation. The ⟨expression⟩ is however fully expanded using \edef. Any spaces preceding ⟨expression⟩ are removed, but any trailing spaces (before the semi-colon) are included.

The integer keyword indicates that assignments to the ⟨variable⟩ or the comma separated list of ⟨additional variables⟩ should be truncated (not rounded) to integers. The variables should be ordinary macros – not TeX registers. In addition the variables should not be indexed.

Short version of the integer keyword.

The real keyword ensures that assignments ⟨variable⟩ (and ⟨additional variables⟩) will not be truncated to integers.

This keyword enables TikZ-style coordinates such as (2cm,3pt) or (my node.east) to be parsed and assigned to ⟨variable⟩ in the form \(x,y\), which can then be used in a tikzpicture:

If the TikZ calc library is loaded, coordinate calculations can be performed; the coordinate expression does not have to be surrounded by ($…$).

In addition to assigning the \(x\) and \(y\) coordinates to ⟨variable⟩ (possibly with an optional index), two further variables are defined. The first takes the name of ⟨variable⟩ (e.g., \c) suffixed with x (i.e., \cx) and is assigned the \(x\) coordinate of \c. The second takes the name of ⟨variable⟩ suffixed with y (i.e., \cy) and is assigned the \(y\) coordinate of \c.

This is a “trimmed down” version of the \foreach command available as part of pgf and TikZ, but cannot currently be used outside of the \tikzmath command. It is important to note the following:

• • Every value in ⟨list⟩ is evaluated using the pgf mathematical engine. However, if an item in ⟨list⟩ contains a comma, it must be surrounded by braces, for example, {mod(5, 2)}.

  

  copy \usetikzlibrary {math}
\tikzmath{
int \x, \v;
\v=1;
for \x in {1,...,{random(3,10)}} {
\v=\v*2;
};
print {$x=\x, v=\v$};
}


• • Because each item is evaluated, you cannot use TikZ coordinates in ⟨list⟩.

• • Only single variable assignment is supported.

• • The “dots notation” (e.g., 1,2,...,9) can be used in ⟨list⟩, but is not as sophisticated as the pgf \foreach command. In particular, contextual replacement is not possible.

• • Assignments that occur in the loop body are not scoped. They last beyond the body of each iteration and the end of the for statement. This includes the values assigned to the ⟨variable⟩.

  

  copy \usetikzlibrary {math}
\tikzmath{
int \x, \y;
\y = 0;
for \x1 in {1,...,5} {
for \x2 in {10,20,...,50} {
\y = \y+\x1*\x2;
};
};
}
$x_1=\x1, x_2=\x2, y=\y$


This keyword executes ⟨if-non-zero-statements⟩ if the expression in ⟨condition⟩ evaluates to any value other than zero.

This keyword executes ⟨if-non-zero-statements⟩ if the expression in ⟨condition⟩ evaluates to any value other than zero and the ⟨if-zero-statements⟩ are executed if the expression in ⟨condition⟩ evaluates to zero.

This keyword works much like the declare function provided by the pgf math-engine. The function ⟨name⟩ can be any name that is not already a function name in the current scope. The list of ⟨arguments⟩ are comma separated TeX macros such as \x, or \y (it is not possible to declare functions that take variable numbers of arguments). If the function takes no arguments then the parentheses need not be used. It is very important to note that the arrays that the pgf math engine supports cannot currently be passed as arguments to functions.

The function ⟨definition⟩ should be a sequence of statements that can be parsed by the \tikzmath command and should use the commands specified in the ⟨arguments⟩. The return keyword (described below) should be used to indicate the value returned by the function. Although ⟨definition⟩ can take any statements accepted by \tikzmath, it is not advisable try to define functions inside other functions.

This keyword should be used as the last executed statement in a function definition to indicate the value that should be returned.

Execute ⟨code⟩ immediately. This is intended as convenience keyword for displaying information in a document (analogous to the print command in real programming languages). The ⟨code⟩ is executed inside a TeX group.