Solve command doesnt give proper results

asked 2020-06-25 10:59:42 -0500

Then I type this:

z1 = 15 
df1 = 37.18 
dh1 = 45.8
e1 = 7.11

z2 = -19
df2 = -57.34
dh2 = -49.04
e2 = 5.81

m,x1,x2,a = var('m,x1,x2,a')  
assume (a>0)
assume (a<0.5*pi)
assume (m<5)
assume (m>1)

b = arccos ( ( z1*m*cos(a)) / dh1 )  
c = arccos ( ( z2*m*cos(a)) / dh2 )

eq1 = x1 == 0.5*( (df1 / m) - z1 +2.5)   
eq2 = x2 == 0.5*( (df2 / m) - z2 +2.5)

eq3 = e1 == dh1* ( ( (0.5*pi-2*x1*tan(a) ) / z1) - tan(a)+tan(a)+tan(b)-tan(b) )
eq4 = e2 == dh2* ( ( (0.5*pi-2*x2*tan(a) ) / z2) - tan(a)+tan(a)+tan(c)-tan(c) )

solve ([eq1,eq2,eq3,eq4],m,x1,x2,a)

Sage gives me this as a answer, which isn't helpul to me:

[5.81 == 1.290526315789474*pi - 5.162105263157894*x2*tan(a), 7.11 == 1.526666666666667*pi - 6.106666666666666*x1*tan(a), x1 == 18.59/m - 6.25, x2 == -28.67/m + 10.75]

Anyone know how I can solve this?

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Comments

It is hard to understand the sense of the equations, so as they are written. First of all, do we need that part - tan(a)+tan(a)+tan(b)-tan(b) in eq3, and the corresponding part in eq4?! If not, we also do not need b,c in the story. Substitute $t$ for $\tan a$, and ask for the solution of the corresponding system in m, x1, x2, t. (Assuming that sage solves every fancy system of equation is not a good idea. Sometimes it is best to do the best job on the mathematical part, then offer sage a clean setting.)

dan_fulea gravatar imagedan_fulea ( 2020-06-29 04:19:12 -0500 )edit