# W10,Sagemath 8.4 solve() does not give a response

why Sagemath solve() does not give a response, and no indication on what it is missing ? (by hand a_1=a_2=3/15)

var('X_1 X_2 a_1 a_2 b Theta')
assume(a_1,'real');assume(a_2,'real')
assume(X_1,'real');assume(X_2,'real')
assume(b,'real') ;assume(Theta,'real')
f_1=2*X_1^2*a_1 + 2*X_1*X_2*a_2 - 2*Theta*X_1 + 2*X_1*b
f_2=2*X_1*X_2*a_1 + 2*X_2^2*a_2 - 2*Theta*X_2 + 2*X_2*b
S=solve ([f_1==0,f_2==0,X_1*X_2==1,Theta*X_1==1,Theta*X_2==1,X_1*X_1==4,X_2*X_2==4,Theta*Theta==4,b==0],a_1,a_2)
show(S)
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Even on Linux there is no solution : since X_1^2==4 and X_2^2==4, then both X_1 and X_2 are even integers, hence it is not possible that X_1*X_2==1.

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Thank you tmonteil, when I have solved these equations by hand, I have not seen these inconsistencies, we do not pay attention to these inconsistencies! ;-). Sagemath is more rigorous.

( 2018-11-12 15:12:03 +0200 )edit

Is there a way to get information when "solve()" delivers an empty response?,

kind of "inconsistencies with X_1,X_2 !"

These inconsistencies come from the fact that I have over-simplified these equations in fact it should be E[X_1X_2] E[X_1X_1],E[X_1,Theta]... ...in order to obtain the factors a_1 a_2

( 2018-11-12 15:23:07 +0200 )edit

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Last updated: Nov 12 '18