Trouble understanding MUPAD output.... solving a non-linear system analytically.
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Hi everyone,
I'm trying to solve a relatively small non-linear system of 15 eqns in 15 unknowns, and keep getting output that (as far as I can tell) doesn't seem helpful. Basically, the output just seems to reduce the system, and rewrites "solve([.....])". Any idea what is causing me to get this output? Any help would be great, thanks!
Assumptions:
A:=Dom::Interval(0,1):
assume(w>0 and r>0):
assumeAlso(mk<min(vk,l) and mn<min(vn,(1-n))):
assumeAlso(chin>0 and chik>0):
assumeAlso(n in A):
assumeAlso(dele>=delu and dele in A and delu in A):
assumeAlso(bet in A):
assumeAlso(lamn in A and lamk in A):
assumeAlso(an>=0 and ak>=0):
assumeAlso(thetk>0 and thetn>0):
assumeAlso(c>0):
assumeAlso(alph in A):
assumeAlso(epk in A and epn in A):
assumeAls0(z>0):
System:
fpi_sys:=[
w*n+r*ke+lamk*(1-dele)*ke+ku=c+l-d,
d=y-w*n-r*ke-an*vn-ak*vk,
ke=(1-dele)*(1-lamk)*ke+mk,
ku=(l-mk)*(1-delu),
n=(1-lamn)*n+mn,
(ak/qk)=bet*(alph*z*ke^(alph-1)*n^(1-alph)-r+(1-lamk)*(1-dele)*(ak/qk)),
(an/qn)=bet*((1-alph)*z*ke^(alph)*n^(-alph)-w+(1-lamn)*(an/qn)),
y=z*ke^alph*n^(1-alph),
(uc-(1-pk)*(1-delu)*bet*uc)/pk=bet*(uc*(r+lamk*(1-dele))+(1-dele)*(1-lamk)*((uc-(1-pk)*(1-delu)*bet*uc)/pk)),
mk=chik*vk^epk*l^(1-epk),
mn=chin*vn^epn*(1-n)^(1-epn),
pk=mk/l,
pn=mn/(1-n),
qk=mk/vk,
qn=mn/vn]:
solve(fpi_sys,[n,ke,ku,c,l,d,y,vn,vk,mk,mn,pk,pn,qk,qn],Real)
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