; Demonstration of eliminate command usage from a Mathomatic user.

; John Hopper example from the paper:
; WITTE, J.S., CARLIN, J.B., HOPPER, J.L. A likelihood approach to 
; estimating twin concordance for dichotomous traits. Genetic Epidemiology 
; 1999; 16: 290-304.

; Fisher information matrix for analysis of
; resemblance in disease status for pairs of relatives
; under complete ascertainment, which is needed to give
; a sampling variance for the concordance.
;
; Observed data is a tabulation of the form
;
; Both Affected   One Affected  None affected
;   x_a pairs       x_d pairs    x_u pairs
;
; Probandwise concordance = 2*x_a/(2*x_a+x_d) = Pr(D in Y | D in X)
; in the original paper a,b,c,d were left unsimplified
;
clear all ; restart Mathomatic
P_c=2*x_a/(x_a+S)
S=x_a+x_d
N=x_a+x_u+x_d
a= 4*N^3*(x_a+x_d)/(x_u*(2*x_a+x_d)^2)
b=-N^2/x_u
c=(2*x_a+x_d)^2*(1/(4*x_a)+1/x_d+1/(4*x_u))
d=1/(a*c-b^2)
V=a*d ; The current equation is usually the last equation entered.
eliminate repeat all ; Combine all of the above equations.
simplify