Help with solving system of equations please

asked 2015-11-13 15:55:49 -0600

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Hi guys, I am new to Sage, and I would be grateful if someone could help me out with the following, please. I am trying to solve the following system of equations, which I have copied below:

h,j,k,l,m,n,p,q,B,C,D,R,S,T,U = var('h j k l m n p q B C D R S T U')

eq1 = (15/2)*((1/18+1/15+1/16)*(4+j))/((1/20+1/18+1/15+1/16)^2)-m*j==0,

eq2 = 15*((1/11+1/25+h)*(k+l))/((1/10+1/11+1/25+h)^2)-m==0,

eq3 = (15/2)*((1/20)/(1/20+1/18+1/15+1/16))-R+m*j*(1/20+1/18+1/15+1/16)/((4+j)^2)==0,

eq4 = (B/2)*((1/20+1/15+1/16)*(4+j))/((1/20+1/18+1/15+1/16)^2)-n*4==0,

eq5 = B*((1/10+1/25+h)*(k+l))/((1/10+1/11+1/25+h)^2)-n==0,

eq6 = (B/2)*((1/18)/(1/20+1/18+1/15+1/16))-S+n*4*(1/20+1/18+1/15+1/16)/((4+j)^2)==0,

eq7 = C*((1/10+1/11+h)*(k+l))/((1/10+1/11+1/25+h)^2)-p*l==0,

eq8 = (C/2)*((1/20+1/18+1/16)*(4+j))/((1/20+1/18+1/15+1/16)^2)-p==0,

eq9 = C*((1/15)/(1/20+1/18+1/15+1/16))-T+p*l*(1/20+1/18+1/15+1/16)/((4+j)^2)==0,

eq10 = D*((1/10+1/11+1/25)*(k+l))/((1/10+1/11+1/25+h)^2)-q*k==0,

eq11 = (D/2)*((1/20+1/18+1/15)*(4+j))/((1/20+1/18+1/15+1/16)^2)-q==0,

eq12 = D*((1/16)/(1/20+1/18+1/15+1/16))-U+q*k*(1/20+1/18+1/15+1/16)/((4+j)^2)==0

solve([eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,h>=0,j>0,k>0,l>0,m>0,n>0,p>0,q>0,B>0,C>0,D>0,R>0,S>0,T>0,U>0],h,j,k,l,m,n,p,q,B,C,D,R,S,T,U).

When I do not put any constraints on the variables, Sage keeps working and is never able to give any kind of answer. With these constraints imposed, I have obtained the following solutions; can anyone please help me interpret these?

[[0 < h, 0 < j, 0 < k, 0 < l, 0 < m, 0 < n, 0 < p, 0 < q, 0 < B, 0 < C, 0 < D, 0 < R, 0 < S, 0 < T, 0 < U, -32400*D*j^2 + 121680*U*j^2 - 259200*D*j + 973440*U*j - 28561*k*q - 518400*D + 1946880*U == 0, j + 4 != 0 ...
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Comments

1

This defines an algebraic variety of dimension 9 in the space of dimension 15. There is no meaning to the word "solve".

FrédéricC gravatar imageFrédéricC ( 2015-11-14 02:30:13 -0600 )edit