Once existence is known, how can a harmonic map be constructed explicitly?

It is natural to ask whether a countable nonstandard model can be explicitly constructed.

Using this method, the area of the union can be computed without explicitly constructing the union itself.

It has been an elusive goal to prove the normality of numbers which were not explicitly constructed for the purpose.

A space of spinors can be constructed explicitly with concrete and abstract constructions.

Implicit k-d trees are in general not constructed explicitly.

One can explicitly construct the spinors, and then examine how they behave under the action of the relevant Lie groups.

Several techniques can be used to explicitly construct reversible cellular automata with known inverses.

The Inoue surfaces are constructed explicitly as follows.

The general study of Calabi-Yau manifolds is mathematically complex and for a long time examples have been hard to construct explicitly.