How Corca Works?

What is Corca?

Corca is a collaborative math editor designed to make typing and working with math as simple and intuitive as possible. Collaborative means multiple people can work on the same document simultaneously—like standing in front of a blackboard and solving a problem together. A math editor means you can type math as quickly as you type text, making it much faster than working on math problems with pen and paper.

This page was made in Corca, so you’re looking at a Corca document right now. Here's an example of the kind of math you can type easily:

$\{ƒ,g\}={\sum }_{i=1}^n(\frac{\partial ƒ}{\partial q_i}\frac{\partial g}{\partial p_i}-\frac{\partial ƒ}{\partial p_i}\frac{\partial g}{\partial q_i})$

How to start typing math?

Text input in Corca works like a search field. When you type something like "root" or "sum," a suggestion popup appears with various options. Choose the option you need and press Enter.

Example: When you type "sum," the suggestion popup offers options like Summation, Plus, Plus-Minus, and more.

Once you select an option, the result will appear, like this:${\sum }_{}^{}$

This means you don’t need to know or learn anything beforehand to start working on math in Corca. Simply search for what you need.

What if I don't want math and just want to keep the text?

When you type something like "integral," Corca shows a suggestion popup with different integral options. If you just want to keep the word "integral" without selecting any math, simply press Space after typing the word. Corca will do nothing and keep the word as text.

This means you need to proactively choose the math you want from the suggestions by pressing Enter or using other hotkeys.

If you want to keep the text, simply ignore the suggestion popup and continue typing. To add math, proactively press Enter .

What is math objects or nodes?

When you type "x" and press Space, Corca will treat it as plain text. However, if you type "x" and press Enter, it will become a math object: $x$. These math objects are called nodes.

For example: If you type "x" and select "Variable or function", Corca will display it as a math object like $x$.

Currently, Corca supports two types of objects:

1. Variables or functions – Variables like $x$ and functions like $ƒ\left(x\right)$ are treated as the same type of object.

2. Constants – Constants are displayed differently, like $c$.

This distinction between variables and constants makes equations easier to read. For example, in the equation $E=m{c}^2$ you can easily see that $m$ and $E$ is variables and $c$ is constant.

If you don’t know whether to define something as a variable or a constant, simply keep it as a variable. You can always change it later as needed.

!! For now, Corca has only these two objects—variables/functions and constants—but more are coming soon, including sets, vectors, matrices, and more.

How to create a function?

Let’s say you’ve created a variable $B$. If you type an open parenthesis ( after, you will see two options in the suggestion popup: Apply Function to Variable and Round Parentheses.

• The first option creates a function, such as $B\left(\right)$

• The second option adds parentheses after the node, like $B\left(\right)$

Simple operations

You can type basic operators directly from your keyboard, such as $+$ or $=$, it’s straightforward. For more specific symbols, like proportional to or union, simply type the word you need, and Corca will suggest the correct symbol, such as $\propto$ or $\cup$.

Division:

For division (fractions), you can type /, or you can also write fraction or division to get options:

This is how division looks:

$\frac{2x}{4x+y}=\frac{16}{3}$

Exponents:

To add exponent, type ^ by pressing Shift + 6.

This is how exponents look:

$e^{\pi i}+1=0$ $y^2={15}^y+4$

Functions

Corca includes many preset functions, from simple ones like $\sin x$ and $\Delta y$ to more complex ones like ${\lim }_{x\to 0}ƒ\left(x\right)$ or ${\int }_0^{\infty }(ƒ\left(x\right))d^{}x$.

To type a function, simply type its name, like this:

Complex operators

Sometimes you need to type operators, and the operator's name might not immediately come to mind. For example, you may need $x\to \infty$ in a limit. To type complex operators, try typing symbols similar to the operator you need.

Examples:

• To get $\to$ type ->

• For $\leftrightarrow$ type <->

• For $\ge$ just type >-

• For $\equiv$ type ===

• For $\in$ you can type E

• For $\forall$ just type A

• For $\notin$ type E/

  and so on...

If you have ideas for additional shortcuts or notice something missing, send us a message, and we’ll add it!

How to type Greek Alphabet?

There are few ways to type Greek letters in Corca:

• Type the name of the letter

  Simply type the name of the Greek letter, like lambda, omega, or epsilon. Corca will automatically suggest creating a math object or show existing functions and operators. For example, typing omega brings up different variations, including lowercase ω, uppercase

  Ω, and other related symbols like closed omega ɷ.

• Start with a capital letter
  If you start typing with a capital letter, like Lambda, Omega, or Epsilon, the suggestions will include the corresponding uppercase Greek letters.

• Use the Greek Alphabet Palette
  If you’re unsure of the name of a specific Greek letter, you can use the Greek Alphabet Palette in the right panel. Browse the palette, find the symbol you need, and click to insert it into your document. This includes both uppercase and lowercase letters.

The same applies to double stroke letters:

!! More letter styles are coming soon—we’re working on it.

How to add index (subscript) or label (superscript)?

To add an index (subscript) like $x_i$ or a label (superscript) like $x^j$ type _ by pressing Shift+- and choose relevant option in suggest:

You can also add labels and indexes to the left side of an object, like: ${}_m{}^{n}L$ or embed entire expressions into indexes, like $P_{C\{b\left(t\right)g\left(t\right)\}}$. Labels and indexes can also be applied to operators (e.g., $<$), or functions (e.g., ${\sin }_{2}x$).

You can also use the right panel to add indexes or labels.

Why are indexes and labels separate from exponents?

The main reason is to improve readability. For example, in ${x^{ij}}^2$, you can easily distinguish between the label $ij$ and the exponent $2$.

Indexes and labels are part of the name of an object, like $x_1,x_2$, which is why they are placed inside a rectangle. In contrast, exponents are operations applied outside the object, which is why they are positioned outside.

Another example is the transpose operation: T, when placed outside $A$, indicates a matrix transpose: $A⊺$. However, if T is inside the node, it represents a label: $A^T$. Operation is outside a node, while labels or indexes are inside.

How to create matrices?

You can create a matrix starting from any parentheses. For example, if you have a set of parentheses:

$\left(1\right)$, place your cursor inside and use:

• Shift + Enter to create a new row

• Shift + Space to create a new column

This will give you a 2x2 matrix:

$\left(\begin{array}{cc}1& \\ & \end{array}\right)$

You can continue adding as many rows and columns as you need.

$A=\left(\begin{array}{ccc}{a}_{11}& a_{12}& a_{13}\\ a_{21}& a_{21}& a_{31}\\ a_{31}& a_{32}& a_{33}\end{array}\right)$

You can also manage matrices in the right panel. Here, you can: Add or remove rows and columns, change the type of parentheses or even transpose your matrix.

If you prefer, you can also type matrix and select it from the suggestion popup to start creating a matrix.

How to Import/Export to LaTeX?

Importing from LaTeX

To import from LaTeX is simple—just paste LaTeX code into a document, and Corca will recognize it. !! Keep in mind that not all LaTeX notations are supported yet, but we are continuously working to expand compatibility.

Exporting to LaTeX

Exporting is straightforward: Select any part of your document in Corca $\to$ Copy the selection and paste it wherever you want.

For example, if you select and copy the following equation:

$C\{ƒ\left(t\right),g\left(t\right)\}≔{\int }_0^t(ƒ\left(\tau \right))g(t-\tau )d^{}\tau$

$C\{ƒ\left(t\right),g\left(t\right)\}≔{\int }_0^t(ƒ\left(\tau \right))g(t-\tau )d^{}\tau$

When you paste it, you’ll get the LaTeX code:

$ C \left\{ f(t) , g(t) \right\} ≔ \int^{t}_{0} f(\tau) g(t - \tau) \text{d} \tau $

$ C \left\{ f(t) , g(t) \right\} ≔ \int^{t}_{0} f(\tau) g(t - \tau) \text{d} \tau $

This means you can work on math problems in Corca and seamlessly paste the results into any LaTeX-compatible document—no friction.

Download LaTeX or PDF

You can download a whole document in LaTeX or PDF. Just click the Download button.

It’s still early, so a lot of stuff isn’t working yet. Some notations, operations, functions might be broken or missing. But we’re working fast to implement everything you might need. That’s why we really need your feedback to make this awesome! Please shoot us a message.