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Disclosing and claiming equations

Updated: Jan 28, 2022

Author: Howard Sheerin,

Complex technology patent applications typically include some form of mathematical subject matter disclosed and potentially even claimed as equations; however, a problem can arise when these equations are not transposed correctly when the USPTO issues the patent. When equations are disclosed (or claimed) in the written part of the patent application (e.g., using Word's equation editor), it is not surprising that a transposition error might occur due to the intricacies of the equations. In some cases, if a transposition error in an equation is not corrected after issuance (via a certificate of correction), it may render the specification non-enabling and/or render the claims indefinite.

A possible solution to this dilemma of transposition error is to disclose the equations in the drawings rather than in the written description of the specification, and then refer to the figure number when describing an equation. This avoids the possibility of transposition errors since the drawings are published exactly as submitted to the USPTO (i.e., as an electronic PDF file that is not transposed). As long as the equations are depicted correctly in the drawings (as they should be), then a correct version of the equations is guaranteed to be included in the issued patent.

Referring to a figure number in the claims is not allowed, and so when claiming an equation the equation must be included in the claim (e.g., using Word's equation editor) which means there can still be a transposition error in the claims. However, an equation transposition error in a claim will most likely be considered an "obvious error" that can be corrected by the court during litigation since a correct version of the equation is included in the specification (in the drawings). That is, a defendant should not be allowed to avoid patent infringement when the subject matter of a claim has been fully and correctly disclosed in the issued patent (in the drawings) even though the claim may have an obvious transposition error.

In recent years it appears transposition errors with equations are rare (maybe even non-existent?). The USPTO may have discovered how to transpose a PDF file so that equations are always published correctly, and this may be even less of a concern when the USPTO transitions to the DOCX file format. Even so, including important (enabling) equations in the drawings can help the inventors when reviewing the patent application to ensure the accuracy of the equations. Equations in the drawings can be enlarged for easier review. In addition, equations in the drawings are emphasized as something the inventors should take more time to review.

An example patent I drafted with important equations disclosed in the drawings is US Patent No. 10,629,234:

Download PDF • 843KB

An example patent I drafted with important equations disclosed in the drawings as well as recited in the claims is US Patent No. 9,286,927:

Download PDF • 979KB

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