Numerical Coefficient Decomposition via Complexity Cost
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Conventional methods for decomposing numerical coefficients into constituent components often result in a multitude of mathematical expressions, many of which do not accurately represent the actual constituents, leading to confusion and difficulty in understanding the underlying makeup of the coefficient.
Innovation Solution
A computer-implemented method that decomposes numerical coefficients into mathematical expressions by considering complexity costs, user input on relevant and irrelevant numerical constants and operators, and optimizing for expressions of lower complexity to focus on accurate constituent representation, thereby reducing erroneous representations.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Quantity of substance
If conventional decomposition methods are used to break down numerical coefficients, then multiple mathematical expressions are generated, but the accuracy and reliability of representing actual constituent components deteriorates
Solution Approach 1:
The patent changes the parameter of complexity cost associated with each mathematical expression. By assigning lower complexity costs to expressions that use recognizable mathematical constants (pi, e, golden ratio) and higher complexity costs to expressions using arbitrary numerical combinations, the system selectively generates expressions that are more likely to accurately represent the actual constituent components of the numerical coefficient.
Solution Approach 2:
The system incorporates feedback by evaluating the complexity cost of generated expressions and using this information to guide further decomposition steps. Expressions with lower complexity costs (indicating use of recognizable constants) are preferred and used to guide the decomposition process, while expressions with higher complexity costs are discarded or used only as fallback options.
2Adaptability or versatility
If decomposition into multiple mathematical expressions is performed without complexity consideration, then completeness of decomposition is improved, but ease of operation and understanding deteriorates
Solution Approach 1:
The patent introduces a complexity cost parameter that transforms the decomposition process from generating all possible expressions to selectively generating expressions with desirable properties (lower complexity costs). This parameter change makes the decomposition process more manageable and easier to understand by focusing on expressions that use recognizable mathematical constants rather than arbitrary numerical combinations.
Solution Approach 2:
The system extracts and removes expressions with high complexity costs (arbitrary numerical combinations) from the decomposition results, retaining only expressions with lower complexity costs that use recognizable mathematical constants. This extraction process simplifies the output while maintaining the essential decomposition information, making it easier for users to understand and interpret.
Data Source
AI summary
A method includes receiving, by a controller, a numerical coefficient to decompose into at least one mathematical expression. The method also includes decomposing, by the controller, the numerical coefficient into the at least one mathematical expression. Decomposing takes into account a complexity cost of the at least one mathematical expression. The method also includes generating an output data that comprises the at least one mathematical expression.