US 2006/0235920 A1 · Smart evaluation in computer algebra

Abstract

In a computing system, evaluating a mathematical expression in presented hierarchically according to the rules of precedence of operations, initial operations at the bottom of the hierarchy may yield values too large to be calculated conventionally, even if the ultimate value of the expression may represent a calculable value. The mathematical expression is evaluated top down to determine if portions of the mathematical expression are re-expressible to simplify the expression and avoid initial or intermediate calculations that would prevent calculation of the mathematical expression. Portions of the original mathematical expression are re-expressible by substituting known mathematical identities, applying arithmetic rules, or treating a portion of the mathematical expression as a variable on which other operations are performed. Once the mathematical expression has been re-expressed, the mathematical expression is simplified, and, if possible, its value calculated.

Claims20

Dependent claims

A method of calculating a presented mathematical expression in a computing system, where the presented mathematical expression includes at least one first operation and a second operation where the first operation is calculated before the second expression according to rules of precedence of operators, the method comprising the steps of:

(a) evaluating the second operation to determine if a combination of the second operation acting on the at least one first operation is replaceable with a mathematically identical expression that involves reduced computational effort to calculate than the presented mathematical expression;
(b) re-expressing the combination of the second operation acting on the at least one first combination with the mathematically identical expression;
and
(c) calculating the mathematically identical expression.

1 more element

(a) evaluating the at least one first operation to determine if the first operation will result in a computational effort exceeding a predetermined computational effort threshold before evaluating the second operation
(b) evaluating the second operation to determine if a combination of the second operation acting on the at least one first operation is replaceable with a mathematically identical expression to replace computation of values with computation of smaller values;
(c) re-expressing the combination of the second operation acting on the at least one first combination with the mathematically identical expression;
and
(d) calculating the mathematically identical expression.

2 more elements

A system for calculating a presented mathematical expression including at least one first operation and a second operation where the first operation is calculated before the second expression according to rules of precedence of operators, the system comprising:

(a) at least one user input device;
(b) a display;
(c) a processor in communication with the input device and the display;
and
(d) a memory in communication with the processor, the memory storing data and machine instructions that cause the processor to carry out a plurality of functions, including:
(i) evaluating the at least one first operation to determine if the first operation will result in a computational effort exceeding a predetermined computational effort threshold before evaluating the second operation;
(ii) evaluating the second operation to determine if a combination of the second operation acting on the at least one first operation is replaceable with a mathematically identical expression to replace computation of values with computation of smaller values;
(iii) re-expressing the combination of the second operation acting on the at least one first combination with the mathematically identical expression;
and
(iv) calculating the mathematically identical expression.

7 more elements

Dependencies are inferred from the claim text.

Smart evaluation in computer algebra

Life of this patent

Smart evaluation in computer algebra

Life of this patent

Abstract

Claims20