Expressions

%reload_ext rubberize
from rubberize import config

Display Modes

When Rubberize renders an expression, it produces one or more mathematical steps. These steps represent different stages of evaluating an expression.

%%tap
import math

x = 3.0  # @hide
y = 4.0  # @hide

math.sqrt(x**2 + y**2)

\( \displaystyle \sqrt{x^{2} + y^{2}} = \sqrt{3.00^{2} + 4.00^{2}} = 5.00 \)

Rubberize distinguishes three main display modes:

Display mode	Example
Definition	\(\displaystyle \sqrt{x^{2} + y^{2}}\)
Substitution	\(\displaystyle \sqrt{3.00^{2} + 4.00^{2}}\)
Result	\(\displaystyle 5.00\)

The following options and shortcuts can be used to configure which display modes are included during rendering:

Display Mode	Option (bool)	Shortcut to show only	Shortcut to hide only
Definition	@show_definition	@def	@nodef
Substitution	@show_substitution	@sub	@nosub
Result	@show_result	@res	@nosub

Additionally, the shortcut @none hides all display modes, while @all shows all the display modes.

%%tap
math.sqrt(x**2 + y**2)  # @show_definition=False
math.sqrt(x**2 + y**2)  # @nosub
math.sqrt(x**2 + y**2)  # @res
math.sqrt(x**2 + y**2)  # @none

\( \displaystyle \sqrt{3.00^{2} + 4.00^{2}} = 5.00 \)

\( \displaystyle \sqrt{x^{2} + y^{2}} = 5.00 \)

\( \displaystyle 5.00 \)

Multiline

@multiline controls if display modes should be stacked vertically when rendered or be shown as equalities on a single line.

This is useful for ensuring that very long equations don’t get cut off from the page.

config.multiline

False

@stack and @line can be used as a shortcuts to @multiline=True and @multiline=False, respectively.

%%tap @stack
math.sqrt(x**2 + y**2)

\( \displaystyle \sqrt{x^{2} + y^{2}} = \sqrt{3.00^{2} + 4.00^{2}} = 5.00 \)

Math Constants

Rubberize preserves the names for mathematical constants defined in @math_constants during substitution.

config.math_constants

{'e', 'phi', 'pi', 'varphi'}

%%tap @float_prec=0
import math
math.e**(1j * math.pi) + 1

\( \displaystyle e^{\mathrm{i}\,\pi} + 1 = 0.00 \)

In the example above, since math constant names are preserved, the rendered substitution is the same as the rendered definition so only one is shown.

To add or remove constants that should be preserved in substitution, use the config methods add_math_constant() or remove_math_constant(), respectively.

For example:

config.add_math_constant("euler")
config.remove_math_constant("e")

config.greek_starts

{'Delta', 'gamma', 'phi', 'psi'}

%%tap
math.e**(1j * math.pi) + 1  # `e` is substituted

euler= math.e
euler**(1j * math.pi) + 1  # `euler` is not substituted

\( \displaystyle e^{\mathrm{i}\,\pi} + 1 = 2.72^{\mathrm{i}\,\pi} + 1 = 0.00 \)

e is substituted

\( \displaystyle \mathrm{euler} = e = 2.72 \)

\( \displaystyle \mathrm{euler}^{\mathrm{i}\,\pi} + 1 = 0.00 \)

euler is not substituted