Abstract: Systems and methods for manipulating mathematical expressions in a computer system. A system can include a builddown module programmed to builddown a mathematical expression from a two-dimensional format to a linear format, the builddown module being programmed to associate a special property of the two-dimensional format of the mathematical expression with a corresponding character of the linear format of the mathematical expression. A method can include receiving a request to builddown the mathematical expression from a two-dimensional format to a linear format, building down the mathematical expression to the linear format, and associating a special property of the two-dimensional format of the mathematical expression with a corresponding character of the linear format of the mathematical expression.

Abstract: Architecture that transforms a built-up mathematical object into a modified linear format object using a customized build down. To transform objects, appropriate changes can be introduced in association with (e.g., prior to or as part of) the build down process to obtain linear format representations for the modified math objects. For example, prior to build-down, linear format operators can be inserted. As part of the build-down, linear format operators can be deleted or changed, and object arguments can be deleted. The modified linear format math object is then built back up into a modified built-up object.

Abstract: Systems and methods for automatically building up an equation entered into a computer system can include an input module that accepts input of the equation in a linear string format, and an interpret module that interprets the input and automatically determines when a buildup point is reached. Systems can further include a formatting module that, upon reaching the buildup point, automatically formats at least a portion of the equation into a two-dimensional format. A display module can display the portion of the equation in the two-dimensional format. A revision module allows the equation to be edited.

Abstract: A method and system through which an application program can access textual data through a common text accessing interface. The system provides a hierarchy of interfaces through which various text manipulation functions can be accessed. These functions control the editing and displaying of text. The hierarchy of interfaces include an interface for manipulating a document and for manipulating a range of characters within the document. By using these interfaces, a server can expose its text to various clients.