By using complex math module And you can put this question on google

I googled it but I could not find solution

what is complex math module?

A math module

Is there an example?

Just put this question and open first or second website You can see examples on google

thank you for your help

formulae for the roots of a quadratic equations are well defined. It's high school mathematics

yes I wanted to solve it without delta command and automatically.

what do you mean automatically? python isn't magic. It'll just use that formula, of course with some optimizations but 🤷‍♂️

😁😁automatically means usng built in procedures or commans

google quadratic solvers and you'd find one 🤔, here's something that will interest you: https://stackoverflow.com/questions/17009774/quadratic-program-qp-solver-that-only-depends-on-numpy-scipy

🙏🙏🙏🌺🌺🌺 thanks a lot infact it is a Quadratic matrix form y^TQy but as I do not know how to solve these types of inequalities I am probing for second order polynomial

oh i just realized that wasn't what you wanted

also sympy has inequality solvers

yes it wasnt the main problem is a quadratic form with two variables as these variables are free I am trying to find out this please consider the arbitrary column vector y=np.array([[?],[?]]) , and this matrix P=np.array([[12137.5, 26.381], [26.381,11438.7]]) (I began with vector y=np.array([[0.1],[0.2]]) as an initial guess) I need to unederstand for which vectors "y" This inequality is valid np.transpose(y)*P*y -8.918847<0.000731 What I have down was that I began with an initial guess y=np.array([[0.1],[0.2]] and randomly I changed y but I could not find suitable y

as I know it just solve one variable inequalities infact my problem is in terms of two variables

i see now what your problem is

Im confused how can I solved it 😔😔

wait a second this is just ytranspose*P*y where is the 2nd variable?

Aha sorry for not explaining y is a 2*1 vector with unknown or free components (e.g. y_1 and y_2)

If u don't Want to spent time trying to understand how libraries works, just do a for loop in range (0, 1000000000) and inside of it generate a random y, and see when your inequality is ok. Its like a Montecarlo optimization, is not ok in term of computation, but iy could works.

thank u so much I do not know how can I relate randome y to index of the loop

hmm, i just reduced that and it solves down to (y_1)²*(12137.5 + 26.381) + (y_2)²*(26.381 + 11438.7) < (8.918847 +0.00731) this is just an equation of a circle 🤔 ax^2 + by^2 < c the inequality represents all points inside circle

come to @pythonofftopic, as this is not python related

there would be a term based on y_1*y_2 : 12137.5y_1^2+2(26.381)y_1y_2+11438.7y_2^2

hmm..come to @pythonofftopic. I'll just how you the reduction i did. You can tell me where i am wrong, if i am

well you have dropped the second term. There can I state the problem?

ok thnx a lot for your help I joined

it is a hard problem

yes it is