19. A computer-readable storage device encoded with computer-executable instructions for controlling a computer to process data representative of a handwritten mathematical expression, the computer-executable instructions comprising: at least one component configured to identify sub-expressions based on dominant symbols and to determine a character for potential dominant symbols based on sub-expression information by accessing a mapping of dominant symbols to their corresponding characters and locations of sub-expressions relative to the dominant symbol; identifying potential dominant symbols within the handwritten mathematical expression, each potential dominant symbol having shape information; and for each potential dominant symbol that is identified, identifying sub-expressions of the potential dominant symbol; determining the location of each identified sub-expression relative to the potential dominant symbol; and recognizing a character that the potential dominant symbol represents from the accessed mapping based on the determined locations of the sub-expressions relative to the potential dominant symbol and from shape information of the potential dominant symbol; a component configured to: receive from the user a selection of a potential dominant symbol; display to the user a list of characters as potentially representing the selected potential dominant symbol and receiving from the user a selection of a character from the list; display to the user the selected character to replace the potential dominant symbol in the handwritten mathematical expression along with a placeholder corresponding to a sub-expression of the selected character; and receive from the user a symbol to be inserted into the placeholder, the symbol representing a sub-expression of the selected character; and at least one application program interface to access the component through which an application can provide a handwritten mathematical expression and receive an indication of the character that a dominant symbol represents and any sub-expressions of the dominant symbol.
19. A computer-readable storage device encoded with computer-executable instructions for controlling a computer to process data representative of a handwritten mathematical expression, the computer-executable instructions comprising: at least one component configured to identify sub-expressions based on dominant symbols and to determine a character for potential dominant symbols based on sub-expression information by accessing a mapping of dominant symbols to their corresponding characters and locations of sub-expressions relative to the dominant symbol; identifying potential dominant symbols within the handwritten mathematical expression, each potential dominant symbol having shape information; and for each potential dominant symbol that is identified, identifying sub-expressions of the potential dominant symbol; determining the location of each identified sub-expression relative to the potential dominant symbol; and recognizing a character that the potential dominant symbol represents from the accessed mapping based on the determined locations of the sub-expressions relative to the potential dominant symbol and from shape information of the potential dominant symbol; a component configured to: receive from the user a selection of a potential dominant symbol; display to the user a list of characters as potentially representing the selected potential dominant symbol and receiving from the user a selection of a character from the list; display to the user the selected character to replace the potential dominant symbol in the handwritten mathematical expression along with a placeholder corresponding to a sub-expression of the selected character; and receive from the user a symbol to be inserted into the placeholder, the symbol representing a sub-expression of the selected character; and at least one application program interface to access the component through which an application can provide a handwritten mathematical expression and receive an indication of the character that a dominant symbol represents and any sub-expressions of the dominant symbol. 20. The computer-readable storage medium of claim 19 , wherein the at least one component is further configured to determine whether an expression structure candidate is valid and to store information of the valid at least one expression structure candidate in a parse tree.