Equations and LaTeX Reference
Basic LaTeX
`python
eq = MathTex(r"E = mc^2")
eq = MathTex(r"f(x) &= x^2 + 2x + 1 \\ &= (x + 1)^2") # multi-line aligned
`
Always use raw strings (r"").
Step-by-Step Derivations
`python
step1 = MathTex(r"a^2 + b^2 = c^2")
step2 = MathTex(r"a^2 = c^2 - b^2")
self.play(Write(step1), run_time=1.5)
self.wait(1.5)
self.play(TransformMatchingTex(step1, step2), run_time=1.5)
`
Selective Color
`python
eq = MathTex(r"a^2", r"+", r"b^2", r"=", r"c^2")
eq[0].set_color(RED)
eq[4].set_color(GREEN)
`
Building Incrementally
`python
parts = MathTex(r"f(x)", r"=", r"\sum_{n=0}^{\infty}", r"\frac{f^{(n)}(a)}{n!}", r"(x-a)^n")
self.play(Write(parts[0:2]))
self.wait(0.5)
self.play(Write(parts[2]))
self.wait(0.5)
self.play(Write(parts[3:]))
`
Highlighting
`python
highlight = SurroundingRectangle(eq[2], color=YELLOW, buff=0.1)
self.play(Create(highlight))
self.play(Indicate(eq[4], color=YELLOW))
`
Annotation
`python
brace = Brace(eq, DOWN, color=YELLOW)
label = brace.get_text("Fundamental Theorem", font_size=24)
self.play(GrowFromCenter(brace), Write(label))
`
Common LaTeX
`python
MathTex(r"\frac{a}{b}") # fraction
MathTex(r"\alpha, \beta, \gamma") # Greek
MathTex(r"\sum_{i=1}^{n} x_i") # summation
MathTex(r"\int_{0}^{\infty} e^{-x} dx") # integral
MathTex(r"\vec{v}") # vector
MathTex(r"\lim_{x \to \infty} f(x)") # limit
`
Matrices
MathTex supports standard LaTeX matrix environments via amsmath (loaded by default):
`python
Bracketed matrix
MathTex(r"\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}")
Parenthesized matrix
MathTex(r"\begin{pmatrix} a & b \\ c & d \end{pmatrix}")
Determinant (vertical bars)
MathTex(r"\begin{vmatrix} a & b \\ c & d \end{vmatrix}")
Plain (no delimiters)
MathTex(r"\begin{matrix} x_1 \\ x_2 \\ x_3 \end{matrix}")
`
For matrices you need to animate element-by-element or color individual entries, use the IntegerMatrix, DecimalMatrix, or MobjectMatrix mobjects instead — see mobjects.md.
Cases and Piecewise Functions
`python
MathTex(r"""
f(x) = \begin{cases}
x^2 & \text{if } x \geq 0 \\
-x^2 & \text{if } x < 0
\end{cases}
""")
`
Aligned Environments
For multi-line derivations with alignment, use aligned inside MathTex:
`python
MathTex(r"""
\begin{aligned}
\nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\
\nabla \cdot \mathbf{B} &= 0 \\
\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
\nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}
\end{aligned}
""")
`
Note: MathTex wraps content in align* by default. Override with tex_environment if needed:
`python
MathTex(r"...", tex_environment="gather*")
`
Derivation Pattern
`python
class DerivationScene(Scene):
def construct(self):
self.camera.background_color = BG
s1 = MathTex(r"ax^2 + bx + c = 0")
self.play(Write(s1))
self.wait(1.5)
s2 = MathTex(r"x^2 + \frac{b}{a}x + \frac{c}{a} = 0")
s2.next_to(s1, DOWN, buff=0.8)
self.play(s1.animate.set_opacity(0.4), TransformMatchingTex(s1.copy(), s2))
`
substrings_to_isolate for Complex Equations
For dense equations where manually splitting into parts is impractical, use substrings_to_isolate to tell Manim which substrings to track as individual elements:
`python
Without isolation — the whole expression is one blob
lagrangian = MathTex(
r"\mathcal{L} = \bar{\psi}(i \gamma^\mu D_\mu - m)\psi - \tfrac{1}{4}F_{\mu\nu}F^{\mu\nu}"
)
With isolation — each named substring is a separate submobject
lagrangian = MathTex(
r"\mathcal{L} = \bar{\psi}(i \gamma^\mu D_\mu - m)\psi - \tfrac{1}{4}F_{\mu\nu}F^{\mu\nu}",
substrings_to_isolate=[r"\psi", r"D_\mu", r"\gamma^\mu", r"F_{\mu\nu}"]
)
Now you can color individual terms
lagrangian.set_color_by_tex(r"\psi", BLUE)
lagrangian.set_color_by_tex(r"F_{\mu\nu}", YELLOW)
`
Essential for TransformMatchingTex on complex equations — without isolation, matching fails on dense expressions.
Multi-Line Complex Equations
For equations with multiple related lines, pass each line as a separate argument:
`python
maxwell = MathTex(
r"\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}",
r"\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}"
).arrange(DOWN)
Each line is a separate submobject — animate independently
self.play(Write(maxwell[0]))
self.wait(1)
self.play(Write(maxwell[1]))
`
TransformMatchingTex with key_map
Map specific substrings between source and target equations during transformation:
`python
eq1 = MathTex(r"A^2 + B^2 = C^2")
eq2 = MathTex(r"A^2 = C^2 - B^2")
self.play(TransformMatchingTex(
eq1, eq2,
key_map={"+": "-"}, # map "+" in source to "-" in target
path_arc=PI / 2, # arc the pieces into position
))
`
set_color_by_tex — Color by Substring
`python
eq = MathTex(r"E = mc^2")
eq.set_color_by_tex("E", BLUE)
eq.set_color_by_tex("m", RED)
eq.set_color_by_tex("c", GREEN)
`
TransformMatchingTex with matched_keys
When matching substrings are ambiguous, specify which to align explicitly:
`python
kw = dict(font_size=72, t2c={"A": BLUE, "B": TEAL, "C": GREEN})
lines = [
MathTex(r"A^2 + B^2 = C^2", **kw),
MathTex(r"A^2 = C^2 - B^2", **kw),
MathTex(r"A^2 = (C + B)(C - B)", **kw),
MathTex(r"A = \sqrt{(C + B)(C - B)}", **kw),
]
self.play(TransformMatchingTex(
lines[0].copy(), lines[1],
matched_keys=["A^2", "B^2", "C^2"], # explicitly match these
key_map={"+": "-"}, # map + to -
path_arc=PI / 2, # arc pieces into position
))
`
Without matched_keys, the animation matches the longest common substrings, which can produce unexpected results on complex equations (e.g., "^2 = C^2" matching across terms).