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Why does solve ignore if a variable is assumed real or positive?

Asked by Prabhakar on 18 Jan 2011
When I use 'solve' on a complicated equation with variables assumed to be real or positive, these assumptions are sometimes ignored.
syms a positive;
solve('5*ln(a) - 32*exp(a/16) + 8*a^2 + 4*a^4=0','a')
ans = 0.22609034746836648974751899999113*i - 1.3900380484673922332261785846175

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1 Answer

Answer by Prabhakar on 18 Jan 2011

This behaviour occurs because the solver cannot find an analytical solution, and switches to the numeric solver. The numeric solver ignores any assumptions made on variables. There are a couple of workarounds to this issue:
1. You can force the result to follow the desired assumption, for example:
abs(solve('5*ln(abs(a)) - 32*exp(abs(a)/16) + 8*abs(a)^2 + 4*abs(a)^4=0','a') )
2. You can access the numeric solver directly, giving the input it requires to find the desired result:
evalin(symengine, 'numeric::fsolve(5*ln(a) - 32*exp(a/16) + 8*a^2 + 4*a^4=0,a=0..infinity)')

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Interestingly, Maple's solve() is not able to find a symbolic solution for the version with abs().
Note that with the assumption that a be positive, your abs(a) is automatically simplified to a and your first command returns an incorrect solution (try subs('5*ln(a) ... 4*a^4', 'a', ans), I get -1.63.)

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