Hello,
I'm new to Sage and your help is appreciated. I am trying to find
numerical solutions for a system of three equations in three unknowns as
follows (the coefficients here are arbitrary for testing purposes, but I
have verified that there are in fact numerical solutions):
xyz + 2xy + 3yz + 4xz + 5x + 6y + 7z = 0
8xyz + 9xy + 10yz + 11xz + 12x + 13y + 14z = 0
15xyz + 16xy + 17yz + 18xz + 19x + 20y + 21z = 0
I have tried the following as shown in this terminal session:
sage: var ('x y z')
(x, y, z)
sage: eq1 = x*y*z + 2*x*y + 3*y*z + 4*x*z + 5*x + 6*y + 7*z == 0
sage: eq2 = 8*x*y*z + 9*x*y + 10*y*z + 11*x*z + 12*x+ 13*y + 14*z == 0
sage: eq3 = 15*x*y*z + 16*x*y + 17*y*z + 18*x*z + 19*x + 20*y + 21*z == 0
sage: solve ([eq1,eq2,eq3],x,y,z)
[x*y*z + 2*x*y + 4*x*z + 3*y*z + 5*x + 6*y + 7*z == 0, 8*x*y*z + 9*x*y +
11*x*z + 10*y*z + 12*x + 13*y + 14*z == 0, 15*x*y*z + 16*x*y + 18*x*z +
17*y*z + 19*x + 20*y + 21*z == 0]
In response to "solve" Sage is returning the original equations with no
numerical results. The actual solutions (from Wolfram Alpha) are:
x=-3, y=-3/4, z=-3 and x=-4/3, y=8, z=-4/3
If I try a simpler system with two variables and two equations, Sage
returns a numerical results as desired:
sage: var ('x y')
(x, y)
sage: eq1 = x*y + x + y == 0
sage: eq2 = 3*x*y + 4*x + 5*y == 0
sage: solve ([eq1,eq2],x,y)
[[x == 1, y == (-1/2)], [x == 0, y == 0]]
What am I doing incorrectly in my first more complex example? Incidentally,
all of the equations in my current project are multivariate polynomials of
the general form shown, but all variable exponents are always one. Also,
there may be many more than just three variables and three unknowns in
actual problems - I am just testing at this point.
Thanks in advance for any help!
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