Formula Editing Faster Than Handwriting

Liii STEM provides a new formula input workflow that is simple and easy to memorize. With about one week of practice, your formula typing speed can match handwriting.

1. LEGO Symbols

LEGO symbols generate math symbols by combining characters with shape-based rules.

For example, < and > represent direction, and @ represents a circle. Typing < + = gives $\leqslant$.

Symbol	Liii STEM LEGO input
$\rightarrow$	- >
$\longrightarrow$	- - >
$\nRightarrow$	= > /
$\infty$	@ @
$\oplus$	@ +
$\otimes$	@ *
$\mathbb{R}$	R R
$\mathbb{Q}$	Q Q
...

2. Tab Cycling

In math mode, any typed character can cycle through related symbols using Tab, based on shape similarity or pronunciation similarity.

Use Shift + Tab to cycle backward.

Example: type A, press Tab twice to get $\forall$.

Symbol	Liii STEM Tab input
$\langle$	< Tab
$\sqsubset$	< Tab
$\alpha$	a Tab
$\varepsilon$	e Tab
$\forall$	A Tab
$\exists$	E Tab
...

3. Shortcut Lookup and Memorization

Mastering shortcuts improves writing speed significantly.

1. Hover over symbols in the math-mode toolbar to view shortcut hints.

2. See all shortcuts in the official shortcut guide: Liii STEM Keyboard Shortcuts
3. Guess shortcuts using LEGO symbols and Tab cycling. Video example: Ultra-fast Formula Editing

4. Extended Reading: Tab Equivalence Class

If you are familiar with abstract algebra, this design is very similar to cyclic groups.

Definition (Tab Equivalence Class)

Symbols $a$ and $b$ are equivalent under key $c$ if they can be reached in the same Tab cycle of $c$ (where $c$ itself is directly typable). The set of all such symbols is the Tab equivalence class of $c$, denoted by $[c]$.

For example, $[h] = \{ h, \eta, \hbar \}$.

Examples

• Greek-letter classes:
  • $[a] = \{ a, \alpha \}$
  • $[b] = \{ b, \beta, \flat \}$
  • $[d] = \{ d, \delta, \mathrm{d}, \partial \}$
  • $[D] = \{ D, \Delta, \mathrm{D}, \daleth, \nabla \}$
• Logic symbols:
  • $[A] = \{ A, \forall, \aleph \}$
  • $[E] = \{ E, \exists \}$
• Calculus-related classes:
  • $[I] = \{ I, \int, \mathrm{I}, \Im \}$
  • $[II] = \{ \mathbb{I}, \iint, \mathcal{I}, \ldots \}$
• Font families:
  • $[RR] = \{ \mathbb{R}, \mathcal{R}, \mathscr{R}, \mathfrak{R}, \boldsymbol{R}, \mathrm{R}, \mathbf{R} \}$