Math expressions

Download notebook View on GitHubRun when the site was built.

tikzfigure includes a math module that lets you build PGF mathematical expressions in Python. This is useful for creating parametric or symbolic geometries without manually writing TikZ syntax.

Instead of hardcoding coordinates like (1.5, 2.0), you can write (sin(60), cos(60)) or (Var("radius") * 2, Var("angle")) — all as Python code, with full composability and operator support.

This tutorial covers:

Building expressions with functions and operators
Using expressions as node coordinates
Using expressions in variables
Composing complex expressions
Available PGF functions and constants

from tikzfigure import TikzFigure, arrows
from tikzfigure.math import Var, cos, max, pi, sin, sqrt

Your first expression

Any PGF math function is available as a Python function. Calling it returns an Expr object that knows how to render itself into valid PGF syntax.

# Basic expressions
expr1 = sin(60)
expr2 = cos(45)
expr3 = sqrt(2)

print(f"sin(60) → {expr1}")
print(f"cos(45) → {expr2}")
print(f"sqrt(2) → {expr3}")

sin(60) → sin(60)
cos(45) → cos(45)
sqrt(2) → sqrt(2)

When you pass an Expr to a TikZ method, it’s automatically converted to a string via __str__.

Using expressions as node coordinates

Any coordinate parameter (x, y, or in a tuple) accepts expressions:

fig = TikzFigure(figsize=(10, 8))

# Place nodes at trigonometric coordinates
fig.node(
    (sin(0), cos(0)),
    label="P0",
    content="(sin 0°, cos 0°)",
    fill="red!30",
    shape="circle",
)
fig.node(
    (sin(45), cos(45)),
    label="P45",
    content="(sin 45°, cos 45°)",
    fill="blue!30",
    shape="circle",
)
fig.node(
    (sin(90), cos(90)),
    label="P90",
    content="(sin 90°, cos 90°)",
    fill="green!30",
    shape="circle",
)
fig.node(
    (sin(180), cos(180)),
    label="P180",
    content="(sin 180°, cos 180°)",
    fill="yellow!30",
    shape="circle",
)

# Draw a path using expressions
fig.draw(
    [
        (sin(0), cos(0)),
        (sin(45), cos(45)),
        (sin(90), cos(90)),
        (sin(180), cos(180)),
    ],
    arrows=arrows.forward,
    color="gray",
    line_width=1.5,
)

fig.show()

/home/runner/work/tikzfigure/tikzfigure/.venv/lib/python3.12/site-packages/fitz/__init__.py:17: FutureWarning: The `fitz` API is deprecated and will be removed in future. Use `import pymupdf` instead.
  warnings.warn(

$Notebook output$

Show the TikZ code

% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=red!30] (P0) at ({sin(0)}, {cos(0)}) {(sin 0°, cos 0°)};
    \node[shape=circle, fill=blue!30] (P45) at ({sin(45)}, {cos(45)}) {(sin 45°, cos 45°)};
    \node[shape=circle, fill=green!30] (P90) at ({sin(90)}, {cos(90)}) {(sin 90°, cos 90°)};
    \node[shape=circle, fill=yellow!30] (P180) at ({sin(180)}, {cos(180)}) {(sin 180°, cos 180°)};
    \draw[->, color=gray, line width=1.5] ({sin(0)}, {cos(0)})
        to
        ({sin(45)}, {cos(45)})
        to
        ({sin(90)}, {cos(90)})
        to
        ({sin(180)}, {cos(180)});
\end{tikzpicture}

Show the standalone LaTeX document

\documentclass[border=10pt]{standalone}
\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{groupplots}
\usetikzlibrary{arrows.meta}
\begin{document}
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \node[shape=circle, fill=red!30] (P0) at ({sin(0)}, {cos(0)}) {(sin 0°, cos 0°)};
    \node[shape=circle, fill=blue!30] (P45) at ({sin(45)}, {cos(45)}) {(sin 45°, cos 45°)};
    \node[shape=circle, fill=green!30] (P90) at ({sin(90)}, {cos(90)}) {(sin 90°, cos 90°)};
    \node[shape=circle, fill=yellow!30] (P180) at ({sin(180)}, {cos(180)}) {(sin 180°, cos 180°)};
    \draw[->, color=gray, line width=1.5] ({sin(0)}, {cos(0)})
        to
        ({sin(45)}, {cos(45)})
        to
        ({sin(90)}, {cos(90)})
        to
        ({sin(180)}, {cos(180)});
\end{tikzpicture}

\end{document}

Operators and composition

Expressions support Python’s arithmetic operators (+, -, *, /) and exponentiation (**). The operators are translated to valid PGF syntax:

# Build complex expressions using operators
expr_sum = sin(60) + cos(60)
expr_product = sin(60) * 2
expr_power = sin(45) ** 2  # Note: ** becomes ^ in PGF
expr_composed = (sin(45) ** 2 + cos(45) ** 2) / Var("scale")

print(f"sin(60) + cos(60) = {expr_sum}")
print(f"sin(60) * 2 = {expr_product}")
print(f"sin(45) ** 2 = {expr_power}")
print(
    f"(sin(45)^2 + cos(45)^2) / scale = {expr_composed}",
)

sin(60) + cos(60) = (sin(60) + cos(60))
sin(60) * 2 = (sin(60) * 2)
sin(45) ** 2 = (sin(45)^2)
(sin(45)^2 + cos(45)^2) / scale = (((sin(45)^2) + (cos(45)^2)) / \scale)

Variable references with `Var()`

Use Var(name) to reference a PGF variable by name. This is useful when you define variables with variable() and want to use them in expressions:

fig = TikzFigure()

# Define a variable
fig.variable("radius", 3.5)

# Use it in node coordinates
node_a = fig.node(
    (Var("radius"), 0),
    label="A",
    content="(r, 0)",
    fill="blue!30",
    shape="circle",
)
node_b = fig.node(
    (0, Var("radius")),
    label="B",
    content="(0, r)",
    fill="red!30",
    shape="circle",
)

# Draw using the variable
fig.draw(
    [(Var("radius"), 0), (0, Var("radius"))],
    arrows=arrows.forward,
    color="gray",
)

fig.show()

$Notebook output$

Show the TikZ code

% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\radius}{3.5}
    \node[shape=circle, fill=blue!30] (A) at ({\radius}, {0}) {(r, 0)};
    \node[shape=circle, fill=red!30] (B) at ({0}, {\radius}) {(0, r)};
    \draw[->, color=gray] ({\radius}, 0) to (0, {\radius});
\end{tikzpicture}

Show the standalone LaTeX document

\documentclass[border=10pt]{standalone}
\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{groupplots}
\usetikzlibrary{arrows.meta}
\begin{document}
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\radius}{3.5}
    \node[shape=circle, fill=blue!30] (A) at ({\radius}, {0}) {(r, 0)};
    \node[shape=circle, fill=red!30] (B) at ({0}, {\radius}) {(0, r)};
    \draw[->, color=gray] ({\radius}, 0) to (0, {\radius});
\end{tikzpicture}

\end{document}

Expressions in variables

You can pass expressions directly to variable(). This is powerful for defining derived or computed values at compile time:

fig = TikzFigure()

# Define base variables (coordinates of a point)
fig.variable("x", 3)
fig.variable("y", 4)

# Compute distance from origin and angle
fig.variable(
    "distance",
    sqrt(Var("x") ** 2 + Var("y") ** 2),
)
fig.variable("angle", "atan2(\\y, \\x)")  # PGF math: angle in radians
fig.variable("scaled", Var("distance") * 2)

# Place nodes at (x, y), (distance, 0), and (scaled, 0)
fig.node(
    (Var("x"), Var("y")),
    label="xy_point",
    content="(x, y)",
    fill="blue!20",
    shape="circle",
)
fig.node(
    (Var("distance"), 0),
    label="distance",
    content="distance",
    fill="green!30",
    shape="circle",
)
fig.node(
    (Var("scaled"), 0),
    label="scaled",
    content="scaled",
    fill="purple!30",
    shape="circle",
)

# Draw a line from origin to (x, y)
fig.draw(
    [(0, 0), (Var("x"), Var("y"))],
    arrows=arrows.forward,
    color="gray",
)

fig.show()

$Notebook output$

Show the TikZ code

% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\x}{3}
    \pgfmathsetmacro{\y}{4}
    \pgfmathsetmacro{\distance}{sqrt(((\x^2) + (\y^2)))}
    \pgfmathsetmacro{\angle}{atan2(\y, \x)}
    \pgfmathsetmacro{\scaled}{(\distance * 2)}
    \node[shape=circle, fill=blue!20] (xy_point) at ({\x}, {\y}) {(x, y)};
    \node[shape=circle, fill=green!30] (distance) at ({\distance}, {0}) {distance};
    \node[shape=circle, fill=purple!30] (scaled) at ({\scaled}, {0}) {scaled};
    \draw[->, color=gray] (0, 0) to ({\x}, {\y});
\end{tikzpicture}

Show the standalone LaTeX document

\documentclass[border=10pt]{standalone}
\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{groupplots}
\usetikzlibrary{arrows.meta}
\begin{document}
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\x}{3}
    \pgfmathsetmacro{\y}{4}
    \pgfmathsetmacro{\distance}{sqrt(((\x^2) + (\y^2)))}
    \pgfmathsetmacro{\angle}{atan2(\y, \x)}
    \pgfmathsetmacro{\scaled}{(\distance * 2)}
    \node[shape=circle, fill=blue!20] (xy_point) at ({\x}, {\y}) {(x, y)};
    \node[shape=circle, fill=green!30] (distance) at ({\distance}, {0}) {distance};
    \node[shape=circle, fill=purple!30] (scaled) at ({\scaled}, {0}) {scaled};
    \draw[->, color=gray] (0, 0) to ({\x}, {\y});
\end{tikzpicture}

\end{document}

Note: the generated TikZ emits \pgfmathsetmacro commands with the expression as-is. PGF evaluates these at compile time.

Mathematical functions

The math module includes 60+ PGF functions:

Trigonometric: sin, cos, tan, asin, acos, atan, atan2, sec, cosec, cot, sinh, cosh, tanh

Rounding: abs, ceil, floor, round (⚠️ shadows Python built-ins)

Power & logarithm: sqrt, pow, exp, ln, log2, log10

Min/max: min, max (⚠️ shadows Python built-ins)

Arithmetic: neg, mod, div, frac, gcd, factorial

Logic: and_, or_, not_, iseven, isodd, isprime

Comparison: equal, greater, less, notequal, notgreater, notless

Geometry: width, height, depth, veclen

Other: deg, rad, int_, real, scalar, bin_, oct_, hex_, ifthenelse

from tikzfigure.math import (
    cos,
    deg,
    factorial,  # Arithmetic
    iseven,  # Logic
    ln,
    sin,
    sqrt,
)

# Examples
print(f"sqrt(2) = {sqrt(2)}")
print(f"max(3, 5) = {max(3, 5)}")
print(f"ln(e) = {ln('e')}")
print(f"deg(pi) = {deg('pi')}")
print(f"factorial(5) = {factorial(5)}")
print(f"iseven(4) = {iseven(4)}")

sqrt(2) = sqrt(2)
max(3, 5) = max(3, 5)
ln(e) = ln(e)
deg(pi) = deg(pi)
factorial(5) = factorial(5)
iseven(4) = iseven(4)

Constants

Pre-defined constants are available as expressions:

from tikzfigure.math import e, false, rnd, true

print(f"pi = {pi}")
print(f"e = {e}")
print(f"rnd = {rnd}")  # Random [0, 1)
print(f"true = {true}")
print(f"false = {false}")

pi = pi
e = e
rnd = rnd
true = true
false = false

A practical example: plotting a circle

Here’s a complete example using expressions to parametrically place points around a circle:

from tikzfigure.math import Var, cos, pi, sin

fig = TikzFigure(figsize=(8, 8))

# Define the radius as a variable
fig.variable("R", 3)

# Place 12 points around a circle at 30° intervals
num_points = 12
for i in range(num_points):
    angle = i * 360 / num_points
    x = Var("R") * cos(angle)
    y = Var("R") * sin(angle)
    fig.node(
        (x, y),
        label=f"P{i}",
        content=str(i),
        shape="circle",
        fill="blue!40",
        minimum_size="0.5cm",
    )

# Draw the circle by connecting consecutive points
for i in range(num_points):
    angle1 = i * 360 / num_points
    angle2 = ((i + 1) % num_points) * 360 / num_points

    p1 = (Var("R") * cos(angle1), Var("R") * sin(angle1))
    p2 = (Var("R") * cos(angle2), Var("R") * sin(angle2))

    fig.draw(
        [p1, p2],
        options=["very thin"],
        color="gray",
    )

# Add a central node
fig.node(
    (0, 0),
    label="center",
    content="C",
    shape="circle",
    fill="red!40",
)

fig.show()

$Notebook output$

Show the TikZ code

% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\R}{3}
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P0) at ({\R * cos(0.0)}, {\R * sin(0.0)}) {0};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P1) at ({\R * cos(30.0)}, {\R * sin(30.0)}) {1};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P2) at ({\R * cos(60.0)}, {\R * sin(60.0)}) {2};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P3) at ({\R * cos(90.0)}, {\R * sin(90.0)}) {3};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P4) at ({\R * cos(120.0)}, {\R * sin(120.0)}) {4};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P5) at ({\R * cos(150.0)}, {\R * sin(150.0)}) {5};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P6) at ({\R * cos(180.0)}, {\R * sin(180.0)}) {6};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P7) at ({\R * cos(210.0)}, {\R * sin(210.0)}) {7};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P8) at ({\R * cos(240.0)}, {\R * sin(240.0)}) {8};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P9) at ({\R * cos(270.0)}, {\R * sin(270.0)}) {9};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P10) at ({\R * cos(300.0)}, {\R * sin(300.0)}) {10};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P11) at ({\R * cos(330.0)}, {\R * sin(330.0)}) {11};
    \draw[very thin, color=gray] ({\R * cos(0.0)}, {\R * sin(0.0)}) to ({\R * cos(30.0)}, {\R * sin(30.0)});
    \draw[very thin, color=gray] ({\R * cos(30.0)}, {\R * sin(30.0)}) to ({\R * cos(60.0)}, {\R * sin(60.0)});
    \draw[very thin, color=gray] ({\R * cos(60.0)}, {\R * sin(60.0)}) to ({\R * cos(90.0)}, {\R * sin(90.0)});
    \draw[very thin, color=gray] ({\R * cos(90.0)}, {\R * sin(90.0)}) to ({\R * cos(120.0)}, {\R * sin(120.0)});
    \draw[very thin, color=gray] ({\R * cos(120.0)}, {\R * sin(120.0)}) to ({\R * cos(150.0)}, {\R * sin(150.0)});
    \draw[very thin, color=gray] ({\R * cos(150.0)}, {\R * sin(150.0)}) to ({\R * cos(180.0)}, {\R * sin(180.0)});
    \draw[very thin, color=gray] ({\R * cos(180.0)}, {\R * sin(180.0)}) to ({\R * cos(210.0)}, {\R * sin(210.0)});
    \draw[very thin, color=gray] ({\R * cos(210.0)}, {\R * sin(210.0)}) to ({\R * cos(240.0)}, {\R * sin(240.0)});
    \draw[very thin, color=gray] ({\R * cos(240.0)}, {\R * sin(240.0)}) to ({\R * cos(270.0)}, {\R * sin(270.0)});
    \draw[very thin, color=gray] ({\R * cos(270.0)}, {\R * sin(270.0)}) to ({\R * cos(300.0)}, {\R * sin(300.0)});
    \draw[very thin, color=gray] ({\R * cos(300.0)}, {\R * sin(300.0)}) to ({\R * cos(330.0)}, {\R * sin(330.0)});
    \draw[very thin, color=gray] ({\R * cos(330.0)}, {\R * sin(330.0)}) to ({\R * cos(0.0)}, {\R * sin(0.0)});
    \node[shape=circle, fill=red!40] (center) at ({0}, {0}) {C};
\end{tikzpicture}

Show the standalone LaTeX document

\documentclass[border=10pt]{standalone}
\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{groupplots}
\usetikzlibrary{arrows.meta}
\begin{document}
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\R}{3}
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P0) at ({\R * cos(0.0)}, {\R * sin(0.0)}) {0};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P1) at ({\R * cos(30.0)}, {\R * sin(30.0)}) {1};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P2) at ({\R * cos(60.0)}, {\R * sin(60.0)}) {2};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P3) at ({\R * cos(90.0)}, {\R * sin(90.0)}) {3};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P4) at ({\R * cos(120.0)}, {\R * sin(120.0)}) {4};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P5) at ({\R * cos(150.0)}, {\R * sin(150.0)}) {5};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P6) at ({\R * cos(180.0)}, {\R * sin(180.0)}) {6};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P7) at ({\R * cos(210.0)}, {\R * sin(210.0)}) {7};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P8) at ({\R * cos(240.0)}, {\R * sin(240.0)}) {8};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P9) at ({\R * cos(270.0)}, {\R * sin(270.0)}) {9};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P10) at ({\R * cos(300.0)}, {\R * sin(300.0)}) {10};
    \node[shape=circle, fill=blue!40, minimum size=0.5cm] (P11) at ({\R * cos(330.0)}, {\R * sin(330.0)}) {11};
    \draw[very thin, color=gray] ({\R * cos(0.0)}, {\R * sin(0.0)}) to ({\R * cos(30.0)}, {\R * sin(30.0)});
    \draw[very thin, color=gray] ({\R * cos(30.0)}, {\R * sin(30.0)}) to ({\R * cos(60.0)}, {\R * sin(60.0)});
    \draw[very thin, color=gray] ({\R * cos(60.0)}, {\R * sin(60.0)}) to ({\R * cos(90.0)}, {\R * sin(90.0)});
    \draw[very thin, color=gray] ({\R * cos(90.0)}, {\R * sin(90.0)}) to ({\R * cos(120.0)}, {\R * sin(120.0)});
    \draw[very thin, color=gray] ({\R * cos(120.0)}, {\R * sin(120.0)}) to ({\R * cos(150.0)}, {\R * sin(150.0)});
    \draw[very thin, color=gray] ({\R * cos(150.0)}, {\R * sin(150.0)}) to ({\R * cos(180.0)}, {\R * sin(180.0)});
    \draw[very thin, color=gray] ({\R * cos(180.0)}, {\R * sin(180.0)}) to ({\R * cos(210.0)}, {\R * sin(210.0)});
    \draw[very thin, color=gray] ({\R * cos(210.0)}, {\R * sin(210.0)}) to ({\R * cos(240.0)}, {\R * sin(240.0)});
    \draw[very thin, color=gray] ({\R * cos(240.0)}, {\R * sin(240.0)}) to ({\R * cos(270.0)}, {\R * sin(270.0)});
    \draw[very thin, color=gray] ({\R * cos(270.0)}, {\R * sin(270.0)}) to ({\R * cos(300.0)}, {\R * sin(300.0)});
    \draw[very thin, color=gray] ({\R * cos(300.0)}, {\R * sin(300.0)}) to ({\R * cos(330.0)}, {\R * sin(330.0)});
    \draw[very thin, color=gray] ({\R * cos(330.0)}, {\R * sin(330.0)}) to ({\R * cos(0.0)}, {\R * sin(0.0)});
    \node[shape=circle, fill=red!40] (center) at ({0}, {0}) {C};
\end{tikzpicture}

\end{document}

The expressions are evaluated by PGF at compile time, not Python, so the generated LaTeX is clean and readable — not a long list of hardcoded coordinates.

Advanced: combining loops with expressions

For parametric figures like grids or circles, you can combine TikZ \foreach loops (from tutorial 6) with math expressions for even more compact code:

from tikzfigure.math import Var, cos, sin

fig = TikzFigure(figsize=(8, 8))

# Define radius
fig.variable("R", 2.5)

# Use TikZ \foreach loop with math expressions
with fig.loop(
    "i",
    range(8),
    comment="Circle with 8 points",
) as loop:
    # Position: (R * cos(i*45°), R * sin(i*45°))
    x = Var("R") * cos(r"\i * 45")
    y = Var("R") * sin(r"\i * 45")

    loop.node(
        (x, y),
        label=r"P\i",
        content=r"\i",
        shape="circle",
        fill="blue!40",
        minimum_size="0.6cm",
    )

# Add center
fig.node(
    (0, 0),
    label="O",
    content="O",
    shape="circle",
    fill="red!30",
)
fig.show()

$Notebook output$

Show the TikZ code

% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\R}{2.5}
    % Circle with 8 points
    \foreach \i in {0,1,...,7}{
        \node[shape=circle, fill=blue!40, minimum size=0.6cm] (P\i) at ({\R * cos(\i * 45)}, {\R * sin(\i * 45)}) {\i};
    }
    \node[shape=circle, fill=red!30] (O) at ({0}, {0}) {O};
\end{tikzpicture}

Show the standalone LaTeX document

\documentclass[border=10pt]{standalone}
\PassOptionsToPackage{dvipsnames,svgnames,x11names}{xcolor}
\usepackage{tikz}
\usepackage{pgfplots}
\pgfplotsset{compat=newest}
\usepgfplotslibrary{groupplots}
\usetikzlibrary{arrows.meta}
\begin{document}
% --------------------------------------------- %
% Tikzfigure generated by tikzfigure v0.5.0     %
% https://github.com/max-models/tikzfigure      %
% --------------------------------------------- %
\begin{tikzpicture}
    \pgfmathsetmacro{\R}{2.5}
    % Circle with 8 points
    \foreach \i in {0,1,...,7}{
        \node[shape=circle, fill=blue!40, minimum size=0.6cm] (P\i) at ({\R * cos(\i * 45)}, {\R * sin(\i * 45)}) {\i};
    }
    \node[shape=circle, fill=red!30] (O) at ({0}, {0}) {O};
\end{tikzpicture}

\end{document}

Notice how the loop variable \i is embedded in the math expressions. TikZ evaluates \i * 45 at each iteration, then passes it to cos() and sin().

Next step: parametric TikZ plots

If you want to go further and use declared PGF functions together with plain TikZ plot(...) commands, continue with Tokamak X-Point with Parametric TikZ Plots. That tutorial starts with a single simple sampled curve and builds up step by step to a stylized tokamak separatrix / X-point drawing.

Warning: shadowing Python built-ins

Some PGF functions have names that match Python built-ins:

abs, min, max, round from tikzfigure.math shadow Python’s built-ins

This is intentional and fine when using targeted imports:

from tikzfigure.math import sin, cos  # No shadowing
from tikzfigure.math import abs, max  # Shadows Python built-ins in this scope

To avoid confusion, avoid from tikzfigure.math import * (which would shadow globally).

Next steps

Combine expressions with loops for parametric grids
Use expressions in styling and transformations
See the PGF manual for the full list of functions and their behavior

Math expressions

Your first expression

Using expressions as node coordinates

Operators and composition

Variable references with Var()

Expressions in variables

Mathematical functions

Constants

A practical example: plotting a circle

Advanced: combining loops with expressions

Next step: parametric TikZ plots

Warning: shadowing Python built-ins

Next steps

Variable references with `Var()`