Goitre the Heavenly Husbandman", asserted that iodine-rich sargassum was used to treat goitre patients by the 1st century BC, but this book was written much later. In the 12th century, Zayn al-Din al-Jurjani, a Persian physician, provided the first description of Graves' disease after noting the association of goitre and a displacement of the eye known as exophthalmos in his "Thesaurus of the Shah of Khwarazm", the major medical dictionary of its time. Al-Jurjani also established an association between goitre and palpitation. The disease was later named after Irish doctor Robert James Graves, who described a case of goitre with exophthalmos
Trace field of a representation of formula_4 (see for example in ). The "invariant trace field" is equal to the trace field of the subgroup formula_7 generated by all squares of elements of formula_4 (a finite-index subgroup of formula_4). The invariant trace field of Fuchsian groups is stable under taking commensurable groups. This is not the case for the trace field; in particular the trace field is in general different from the invariant trace field. Let formula_4 be a Fuchsian group and formula_11 its trace field. Let formula_12 be the formula_11-subalgebra of the matrix algebra formula_14 generated by the preimages of elements of formula_4. The