The equations you are attempting to solve lead to a very complicated Groebner basis that is slow to compute (I'm not sure how long it takes) and probably gives quite a complicated expression for the solution.
It might be better if you can derive the equations without introducing radicals i.e. to work with the quadrances rather than square rooting them to get lengths. I'm not sure how you derived this but I imagine the intention of rational geometry is to avoid things like square roots. On Sat, 6 Aug 2022 at 16:22, Kevin Pauba <[email protected]> wrote: > > That might be another approach but this represents an applied geometry > problem (mechanics). The segment DP (along with s) is an input measure that > is easy to determine/specify. > > On Saturday, August 6, 2022 at 4:45:13 AM UTC-7 [email protected] wrote: >> >> >> Kevin, I took a look at some of the rational geometry links -- it makes me >> wonder if you might approach the relationship between Q1 and Q2 and the area >> of the triangle extending past the line instead of simply the length DP. >> >> /c >> On Friday, August 5, 2022 at 9:11:39 PM UTC-5 [email protected] wrote: >>> >>> Hi Oscar, >>> >>> That very well may be (as you've noticed, I'm not well versed in math as I >>> once was). This is an applied geometry problem (see attached diagram) >>> where the triangle rotates about point A. I am solving for the >>> relationships between q1 and q2, the perpendicular distance from P to the >>> base of the triangle (segment DP) and the angular measure s using rational >>> trigonometry (see https://stijnoomes.com/laws-of-rational-trigonometry/). >>> I have a solution using sin, cos but I'm interested in this alternative >>> method. >>> >>> equ1 in my working example solves for the segment DP given q1, q2 and s >>> (and angular measure). The problem presented here is to determine q1 and >>> q2 given two known segments and angular measures (q_dp1, s1) and (q_dp2, >>> s2). >>> >>> I hope this makes sense and that the information might help you help me. >>> >>> Thanks for taking the time looking into it! >>> >>> On Friday, August 5, 2022 at 4:50:09 PM UTC-7 Oscar wrote: >>>> >>>> I just had a quick look and I think that maybe this has a positive >>>> dimensional solution set. >>>> >>>> On Fri, 5 Aug 2022 at 16:08, Kevin Pauba <[email protected]> wrote: >>>> > >>>> > Here's the minimal working example (except for it hanging on solve()): >>>> > >>>> > import sympy as sym >>>> > from sympy import sqrt >>>> > >>>> > q1, q2, s, s1, s2, q_dp1, q_dp2 = sym.symbols('Q_1, Q_2, s, s_1, s_2, >>>> > Q_dp_1, Q_dp_2') >>>> > >>>> > equ1 = q1*s - q2*s + 2*q2 - 2*sqrt(q2*(q1*s - q2*s + q2 + >>>> > 2*sqrt(q1*q2*s*(1 - s)))) + 2*sqrt(q1*q2*s*(1 - s)) >>>> > >>>> > eq1 = equ1.subs({ s: s1 }) - q_dp1 >>>> > print(f"{eq1} = 0") >>>> > >>>> > eq2 = equ1.subs({ s: s2 }) - q_dp2 >>>> > print(f"{eq2} = 0") >>>> > >>>> > soln = sym.solve([eq1, eq2], (q1, q2), simplify=False) >>>> > print(f"soln = {soln}") >>>> > >>>> > On Friday, August 5, 2022 at 7:47:07 AM UTC-7 Oscar wrote: >>>> >> >>>> >> 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/54eddcdc-a42e-4ebc-87b8-b6aaea1e2d0an%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/357f1ceb-d50f-484f-ae1e-0c82a1414a62n%40googlegroups.com. -- You received this message because you are subscribed to the Google Groups "sympy" group. 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