Most inventions involved costly, intricate mechanisms and required the user to perform complex manipulations.

The increasing ability of desk-top computers to perform sophisticated mathematical manipulations, in addition to massive calculations, is rapidly extending the applicability of mathematical techniques.

It seemed possible that it might have been purely psychological reasons which had barred me from performing such manipulations earlier.

By the late 1960s, computer systems could perform symbolic algebraic manipulations well enough to pass college-level calculus courses.

Instead of stopping a cab, he stepped to a darkened doorway and performed manipulations with his briefcase.

Such techniques were used before calculators, by referring to numerical tables and performing manipulations such as those above.

Quantity calculus describes how to perform mathematical manipulations of quantities.

When a model is expressed in this formalism, a computer is able to perform algebraic manipulations to best formulate the solution algorithm.

Autonomy Humans have to learn how to walk, skip, and ride a bicycle but inside our bodies perform specific manipulations from birth that we do not need to learn.

They sit between two end-point systems and arbitrate data movement between them, performing manipulations on the data sets as they move back and forth.