Cognidia supports entering detailed step-by-step mathematical solutions in a specific structured format. The solution format is designed to be both human-readable and computer-analyzable. In order to achieve this, Cognidia uses a specific solution format (syntax) that combines typical mathematical notation with additional constructs.

The Cognidia syntax utilizes three main components: Statements, Expressions, and Reasons. The solutions are entered using one or more Statement blocks. Each Statement block contains a series of steps. Each step contains an Expression and a Reason.

The syntax follows the pattern:

• equality_chain {} that encloses are a sequence of steps

• Each step contains an <expression> and a <reason>

• Each step starts with an equals sign

• The final step has just the final expression and no reason

In the example below, the solution uses a Statement called equality_chain with 2 steps. 2*x - 2 + 5*x is an Expression in the first step with a Reason combineLikeTerms. The result step has the Expression 7*x - 2.

You'll learn about Statements and Reasons in subsequent sections of the guide. This section focuses on Expressions and the requirements of a valid Expression.