Here " rational " means that it is a purely transcendental extension of, generated by an algebraically independent set.
2.
The case of the purely transcendental functions ( which do not involve roots of polynomials ) is relatively easy and was implemented early in most computer algebra systems.
3.
For defining the separability of a transcendental extension, it is natural to use the fact that every field extension is an algebraic extension of a purely transcendental extension.
4.
This allows to reduce the factorization over a purely transcendental field extension of " F " to the factorization of multivariate polynomials over " F ".
5.
Though he considers women and men equally capable of Enlightenment and ordained them equally right from the start, he has also said he had " tentatively reached the conclusion that the spiritual life is more difficult for women because they are less able than men to envisage . . . something purely transcendental . . . " He also criticised heterosexual nuclear relationships as tending to neuroticism.
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