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Project: run sage
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var('x,y,z,w') R=x+y-z-w s=x-y+z-w t=x-y-z+w h(x,y,z,w)=R^2+s^2+t^2+R^2*s^2+R^2*t^2+s^2*t^2+R*s*t r(a,b,c,d)=0 for i in range(7): g(x,y,z)=h(x,y,z,0) q(a,b,c)=0 for n in range(8): f(x,y)=g(x,y,0) p(a,b)=0 for m in range(11): p(a,b)=p(a,b)+f(a,0)*b^m f(x,y)=expand((f(x,y)-f(x+y,0))/x/y) q(a,b,c)=q(a,b,c)+p(a,b)*c^n g(x,y,z)=expand((g(x,y,z)-p(x+y+z,x*y+x*z+y*z))/x/y/z) r(a,b,c,d)=r(a,b,c,d)+q(a,b,c)*d^i h(x,y,z,w)=expand((h(x,y,z,w)-q(x+y+z+w,x*y+x*z+x*w+y*z+y*w+z*w,x*y*z+x*y*w+x*z*w+y*z*w))/x/y/z/w) print r(a,b,c,d), '\n'