_index.md

bookCollapseSection	weight	draft	title
true	6	false	Algebra

The quadrille algebra provides a suite of static methods for applying logical operations to quadrille instances. Inspired by constructive solid geometry and boolean algebra, these methods combine and manipulate quadrilles, leading to new quadrilles as an aggregation of others.

Method Overview

• [neg(q, value)]({{< relref "neg" >}}): Performs a logical NOT operation, inverting empty and non-empty cells, filling empty cells with a provided value.
• [or(q1, q2, row, col)]({{< relref "or" >}}): Combines two quadrilles using a logical OR, merging their non-empty cells into a new quadrille.
• [xor(q1, q2, row, col)]({{< relref "xor" >}}): Returns a new quadrille containing all the non-empty cells that appear in either q1 or q2 but not in both.
• [and(q1, q2, row, col)]({{< relref "and" >}}): Returns a new quadrille containing only the cells that are non-empty in both q1 and q2.
• [diff(q1, q2, row, col)]({{< relref "diff" >}}): Returns a new quadrille containing the non-empty cells from q1 that do not appear in q2.
• [merge(q1, q2, operator, row, col)]({{< relref "merge" >}}): Returns a new quadrille by applying a specified logical operator to each corresponding cell of q1 and q2.

These algebraic methods offer powerful tools for composing quadrilles, enabling the construction of intricate patterns, designs, or logical transformations. Whether you're combining shapes, masking cells, or creating dynamic compositions, the quadrille algebra brings structure and precision to your work.