The theoretical purpose of today's road trip is to buy a copy of Royalty magazine.

Therefore, for theoretical purposes, equality constraints are redundant; however, it can be beneficial to treat them specially in practice.

The number and definition of factors varies, depending on theoretical purpose, empirical emphasis, or school of economics.

For theoretical purposes, the integral equation version is often very useful.

(The measure of what is satisfactory will, as always, be fixed by a given practical or theoretical purpose.)

This is undoubtedly an idealization and may be used for abstract or theoretical purposes.

The Riemann integral is unsuitable for many theoretical purposes.

For both theoretical and practical purposes, barrier function or path-following methods have been the most popular since the 1990s.

However, techniques that are developed for theoretical purposes or for other applications may have relevance to the present project, and this is indicated where appropriate.

TCG is used so far mainly for theoretical purposes in astronomy.