  The Lagrangian technique of Niven (2004, Physica A, 334(3-4): 444) is used to
determine the constrained forms of the Tsallis entropy function - i.e.
Lagrangian functions in which the probabilities of each state are independent -
for each constraint type reported in the literature (here termed the Mark I, II
and III forms). In each case, a constrained form of the Tsallis entropy
function exists, which at q=1 reduces to its Shannon equivalent. Since they are
fully constrained, each constrained Tsallis function can be "dismembered" to
give its partial or local form, providing the means to independently examine
each state i relative to its local stationary (maximum entropy) position. The
Mark II and III functions depend on q, the probability, the stationary
probability, and the respective q-partition function; in contrast the Mark I
form depends only on the first three parameters. The Mark II and III forms
therefore depend on the structure of the system. The utility of the
dismemberment method is illustrated for a system with equispaced energy levels.
