Goitre an underactive thyroid, thyroid supplements are used as treatment. Sometimes a partial or complete thyroidectomy is required. Goitre is more common among women, but this includes the many types of goitre caused by autoimmune problems, and not only those caused by simple lack of iodine. Chinese physicians of the Tang Dynasty (618–907) were the first to successfully treat patients with goitre by using the iodine-rich thyroid gland of animals such as sheep and pigs—in raw, pill, or powdered form. This was outlined in Zhen Quan's (d. 643 AD) book, as well as several others. One Chinese book, "The Pharmacopoeia of
Trace field of a representation Trace field of a representation In mathematics, the trace field of a linear group is the field generated by the traces of its elements. It is mostly studied for Kleinian and Fuchsian groups, though related objects are used in the theory of lattices in Lie groups, often under the name "field of definition". Fuchsian groups are discrete subgroups of formula_1. The trace of an element in formula_1 is well-defined up to sign (by taking the trace of an arbitrary preimage in formula_3) and the "trace field" of formula_4 is the field generated over formula_5 by the traces of all elements