User:Chenxlee/TType

In the mathematical field of transcendental number theory, the transcendence type of a field is an asymptotic measure of how small transcendental elements of the field can be in terms of their degree and height when viewed as polynomials in a transcendence basis for the field.

Definition
If K is a subfield of the complex numbers that is a finitely generated extension of the rational numbers then it can be written as
 * $$K=\mathbb{Q}(x_1,\ldots,x_m,y_1,\ldots,y_n)$$

where the set {x1,&hellip;,xm} is a transcendence basis for K over Q and the set {y1,&hellip;,yn} is a basis for K as a vector space over the field Q(x1,&hellip;,xm).