# Why does Sage not find any solutions using .solve()?

asked 2014-11-25 12:56:59 +0200

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Hello everyone,

please consider this attempt to solve simultaneous equations:

P,M,R,rho,kappa,T,F,n = var('P, M, R, rho, kappa, T, F, n')

eqns = [
P==M^2*R^-4,
R^3==M*rho^-1,
T^4==M*kappa*F*R^-4,
F==M*rho*T^n,
P==rho*T,
kappa==rho*T^(-7/2),
n==4
]

eqns

assume(P>0,M>0,R>0,rho>0,T>0,F>0,kappa>0)

sols = solve(eqns,(F,R,T))
sols


(returns [])

I would like to understand why Sage can not arrive at a relation for F,M,T (and n) which I was able to do by hand. Is solve inappropriate for isolating one or more variables from a set of equations?

Thank you for your help!

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## Comments

something close works

sage: solve(eqns, (F,R))
[kappa == rho/T^(7/2), n == 4, F == M*T^n*rho, P == M^2/R^4, P == T*rho, R^3 == M/rho, T^4 == F*M*kappa/R^4]

( 2014-11-25 21:59:54 +0200 )edit

Well, the solution is only a copy/paste of the equations (which i agree is equivalent, so at least there is no lie), no variable isolation happened.

( 2014-11-29 05:42:52 +0200 )edit