Concepts inUndo as concurrent inverse in group editors
Inverse element
In abstract algebra, the idea of an inverse element generalises the concept of a negation, in relation to addition, and a reciprocal, in relation to multiplication. The intuition is of an element that can 'undo' the effect of combination with another given element. While the precise definition of an inverse element varies depending on the algebraic structure involved, these definitions coincide in a group.
more from Wikipedia
Undo
Undo is a command in many computer programs. It erases the last change done to the document reverting it to an older state. In some more advanced programs such as graphic processing, undo will negate the last command done to the file being edited. The opposite of undo is redo. The redo command reverses the undo or advances the buffer to a more current state. In most Windows applications, the Undo command is activated by pressing Ctrl+Z or Alt+Backspace.
more from Wikipedia
Group (mathematics)
In mathematics, a group is an algebraic structure consisting of a set together with an operation that combines any two of its elements to form a third element. To qualify as a group, the set and the operation must satisfy four conditions called the group axioms, namely closure, associativity, identity and invertibility. Many familiar mathematical structures such as number systems obey these axioms: for example, the integers endowed with the addition operation form a group.
more from Wikipedia
Text editor
A text editor is a type of program used for editing plain text files. Text editors are often provided with operating systems or software development packages, and can be used to change configuration files and programming language source code.
more from Wikipedia
Operational transformation
Operational transformation (OT) is a technology for supporting a range of collaboration functionalities in advanced groupware systems. OT was originally invented for consistency maintenance and concurrency control in collaborative editing of plain text documents.
more from Wikipedia
Multiplicative inverse
In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x, is a number which when multiplied by x yields the multiplicative identity, 1. The multiplicative inverse of a fraction a/b is b/a. For the multiplicative inverse of a real number, divide 1 by the number. For example, the reciprocal of 5 is one fifth (1/5 or 0.2), and the reciprocal of 0.25 is 1 divided by 0.25, or 4.
more from Wikipedia
Inverse function
In mathematics, an inverse function is a function that undoes another function: If an input x into the function ¿ produces an output y, then putting y into the inverse function g produces the output x, and vice versa. i.e. , ¿(x)=y, and g(y)=x. More directly, g(¿)=x, meaning g(x) composed with ¿(x) leaves x unchanged.
more from Wikipedia
Total order
In set theory, a total order, linear order, simple order, or (non-strict) ordering is a binary relation (here denoted by infix ¿) on some set X. The relation is transitive, antisymmetric, and total. A set paired with a total order is called a totally ordered set, a linearly ordered set, a simply ordered set, or a chain. If X is totally ordered under ¿, then the following statements hold for all a, b and c in X: If a ¿ b and b ¿ a then a = b; If a ¿ b and b ¿ c then a ¿ c; a ¿ b or b ¿ a .
more from Wikipedia