List Algebra

1. Paste each list into its own box (one item per line).
2. Adjust normalization options if needed (case, accents, whitespace, punctuation).
3. Choose the operation you want (union, intersection, differences, or multiset counts).
4. Use Copy or download formats to export the result.

This tool compares multiple lists and makes their relationships explicit. It answers questions such as: “What appears in every source?”, “What is unique to one list?”, “Which items are shared by at least k lists?”, and “How many total occurrences does each item have across all inputs?” Typical use cases include merging datasets, reconciling inventory or contact lists, comparing research notes, and measuring consensus across multiple contributors.

There are two families of operations, and the choice changes how duplicates are treated:

• Family-of-sets operations treat each list as a set: duplicate lines inside one list do not change the result.
• Multiset operations treat duplicates as counts: repeated lines increase totals and can change the result.

Family-of-sets operations (duplicates inside each list are ignored):

• Union: every unique element that appears in at least one list.
• Intersection: elements that appear in every list (shared by all).
• Difference (A minus others): elements in the first list that never appear in the remaining lists.
• Symmetric difference: elements that are not shared by all lists (unique to some, but not common to all).
• At least k lists: elements that appear in k or more lists.
• Exactly k lists: elements that appear in exactly k lists (no more, no less).
• Support count: table showing how many lists contain each element.

Multiset operations (duplicates count):

• Total frequency: total number of occurrences across all lists for each element.
• Multiset union (max): for each element, take the highest count it has in any single list.
• Multiset intersection (min): for each element, take the lowest count across lists, excluding elements that are missing from any list.
• Multiset sum: for each element, add up its counts across all lists.

Vocabulary for translation plugins