Object-Field Data Structure for Unified Equation Editing
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Solution Overview
Problem
Prior equation editors do not inherently consider mathematical meaning during the entry, editing, and manipulation of mathematical expressions, requiring both presentation and content tree data structures for editing and solving, which limits the user interface to a non-natural format.
Innovation Solution
An object-field-based mathematics system that uses a data structure allowing users to create and edit mathematical expressions in a 'what-you-see-is-what-you-get' style, converting between this structure and conventional content-tree data structures for use with CAS programs, incorporating object-oriented programming to assign mathematical significance to each object and field for enhanced editing and formatting.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Ease of operation
If conventional presentation tree and content tree data structures are used for equation editing and CAS computation, then both editing and solving capabilities are achieved, but the user interface becomes less natural and more complex
Solution Approach 1:
The patent merges the previously separate presentation tree and content tree data structures into a unified object-field data structure. This single structure simultaneously supports both the visual presentation of mathematical expressions and the symbolic manipulation required by CAS programs, eliminating the need for users to switch between different interface modes and reducing overall system complexity.
Solution Approach 2:
The object-field data structure is designed to serve multiple functions: it acts as both a presentation structure for visual editing and a content structure for CAS computation. Each object within the structure carries both visual and semantic information, allowing the same data structure to fulfill both editing and solving requirements without needing separate specialized structures.
2Reliability
If prior art equation editors are used, then basic editing functionality is provided, but mathematical meaning is not inherently considered during entry and manipulation
Solution Approach 1:
The object-field data structure enables the equation editor to automatically understand and process mathematical meaning during the editing process. As users input expressions, the system inherently interprets the mathematical semantics through the structured object-field relationships, automatically maintaining correctness without requiring manual intervention or separate validation steps.
Solution Approach 2:
The unified object-field structure provides continuous feedback to the user about the mathematical meaning of expressions being entered. The system can immediately detect and correct mathematical errors, suggest improvements, and guide users through proper notation, making the editing process more intuitive and reliable simultaneously.
3Adaptability or versatility
If both presentation tree and content tree structures are maintained, then editing and CAS solving are both supported, but conversion between formats is required
Solution Approach 1:
The object-field data structure serves as a universal intermediate format that can directly interface with CAS programs while maintaining visual presentation capabilities. This eliminates the need for time-consuming conversions between separate presentation and content trees, as the unified structure can be directly processed by CAS systems while preserving the visual formatting information.
Data Source
AI summary
An apparatus includes a processor, a computer memory, a user interface, and computer-executable instructions which enable a user to formulate mathematical expressions via the user interface. The mathematical expression is composed from objects selected from a library of object types in the memory. The object types include primitive objects and non-primitive objects. Non-primitive objects contain at least one field which in turn can contain additional objects; primitive objects have no fields. The mathematical expression is defined by a computer-readable data structure in the memory, and each object and field has a mathematical significance assigned thereto. The data structure uniquely identifies each object and each field, and includes pointers to define nesting of the objects and fields in the mathematical expression. The computer-executable instructions include steps to identify user inputs with at least some of the objects, and to display the mathematical expression represented by the data structure via the display.