I am trying to solve some algebraic (polynomial) equations. In the first
approximation, I have 4 equations in 4 variables, and it is very easy to
solve them manually. In the second approximation, I have 8 equations in 8
variables, and I am trying to solve them. At the beginning, the equations
are linear or quadratic in the variables. After solving one equation for
one variable and substituting the result into the other equations, the
complexity grows very fast.
One very naive attempt I made was to give all 8 equations and 8 variables
to solve. That has been running for over 3 weeks and I don't know if it
will succeed.
Then I started using solveset and solving the equations one by one. After
one call to nonlinsolve and one substitution, I tried giving this
expression (Latex form)
2 \(-1\) b_{-1} \left( - \frac{\(1\) b_{-1}^{2} + 2 \(1\) b_{-2} + \[1,-1\]
b_{-1} b_{-2} + \[1\]}{\[1,2\] b_{2} + 2 \[1\] b_{-1} - 1}\right) + \(-1\)
+ \[-1,-2\] b_{-1} b_{-2} + \[-1,1\] b_{2} \left( - \frac{\(1\) b_{-1}^{2}
+ 2 \(1\) b_{-2} + \[1,-1\] b_{-1} b_{-2} + \[1\]}{\[1,2\] b_{2} + 2 \[1\]
b_{-1} - 1}\right) + \[-1\] b_{-1}^{2} + 2 \[-1\] b_{-2} - b_{-1}
to solveset as
solbm1 = solveset([exbm1], [bm1])
and I got the error
[2b_{-1}b_{-1}2 + 2*(1)*b_{-2} + [1,-1]*b_{-1}*b_{-2} + [1])/([1,2]*b_2 +
2*[1]*b_{-1} - 1),) + (-1) + [-1,-2]*b_{-1}*b_{-2} +
[-1,1]*b_2*(-((1)*b_{-1}2 + 2b_{-2} + [1,-1]b_{-2} +
[1])/([1,2][1]b_{-1}**2 + 2b_{-2} - b_{-1}] is not a valid SymPy expression
When I use nonlinsolve instead, I get the error
'Tuple' object has no attribute '_eval_is_polynomial'
When I use solve instead, I get the error
Can't multiply sequence by non-integer of type '<class
'sympy.core.mul.Mul'>'
The complex expression came from solving one equation and using subs to put
the result into a second equation. If it helps, I could try calling expand
before trying to solve the resulting equation.
Basically, I am looking for advice about the best strategy for solving
multiple polynomial equations. Is it better to try to solve them all at
once, or one equation at a time (but with multiply substitutions and
multiple calls to solve/solveset/nonlinsol), or all equations but one
variable at a time?
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