You should be able to obtain a parametric Groebner basis to represent the solutions of this system. Whether that leads to an explicit solution in radicals is hard to say without trying.
I would demonstrate how to do this but the code for putting together the equations is incomplete. On Fri, 5 Aug 2022 at 14:01, Chris Smith <[email protected]> wrote: > > If you remove the radicals (`sympy.solvers.solvers.unrad(eq1)`) and replace > `Q1` and `Q2` with `x` and `y` and `Q_dp_1` with a and `s1` with `b` you will > get an expression that is of degree 4 in every variable and can be split into > a term with `a` and `b` and a term with only `b` -- both with `x` and `y`. > > u1 = a*(a**3 - 4*a**2*y*(2 - b) - 2*a*y**2*(-3*b**2 + 8*b - 8) - 4*b**3*x**3 > + 2*b**2*(-x**2*(-3*a + 2*y*(b - 2)) + 2*y**3*(b - 2)) - 4*b*x*(a**2 + a*y*(b > - 2) + y**2*(-b**2 - 8*b + 8))) + \ > b**2*(b*(x**2 + y**2) + 2*x*y*(b - 2))**2 > > Replace a,b with c,d (for `q_dp_2` and `s2`) to get `u2`. I can't imagine > that solving a pair of quartics is going to give a nice solution. But solving > this system with known values for `a` and `b` would be straightforward with > `nsolve`. > > /c > > On Thursday, August 4, 2022 at 11:54:24 PM UTC-5 [email protected] wrote: >> >> And eq1=Q_1*s_1 - Q_2*s_1 + 2*Q_2 - Q_dp_1 - 2*sqrt(Q_2*(Q_1*s_1 - Q_2*s_1 + >> Q_2 + 2*sqrt(Q_1*Q_2*s_1*(1 - s_1)))) + 2*sqrt(Q_1*Q_2*s_1*(1 - s_1)) ... >> sorry, long day! >> >> On Thursday, August 4, 2022 at 9:39:53 PM UTC-7 Kevin Pauba wrote: >>> >>> Sorry, Jeremy. Good suggestion! >>> >>> s1, s2, q_dp1, q_dp2 = sym.symbols('s_1, s_2, Q_dp_1, Q_dp_2') >>> eq1 = equ1.subs({ s: s1 }) - q_dp1 >>> md( "$" + sym.latex(eq1) + " = 0$\n" ) >>> >>> eq2 = equ1.subs({ s: s2 }) - q_dp2 >>> md( "$" + sym.latex(eq2) + " = 0$\n" ) >>> >>> soln = sym.solve([eq1, eq2], q1, q2) >>> print(f"soln = {soln}") >>> >>> I'll set simplify to False and see how it goes ... >>> On Thursday, August 4, 2022 at 8:18:00 PM UTC-7 Kevin Pauba wrote: >>>> >>>> I've attached a portion of a jupyter notebook. I'm attempting to solve a >>>> simultaneous equation using sympy. The sym.solve() in the green input box >>>> doesn't return (well, I waited over night on my macbook pro). Might the >>>> solution be intractable? Is there another way to get a solution? Any >>>> help is greatly appreciated. > > -- > You received this message because you are subscribed to the Google Groups > "sympy" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected]. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/72f1b075-dbe2-41c0-bba6-9305c5960443n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion on the web visit https://groups.google.com/d/msgid/sympy/CAHVvXxT%2Bc_%3DDHBnXdi49fpaPxR9p4prOXUJbQNhqjV878S%2B82g%40mail.gmail.com.
