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1answer
29 views

How to draw cubic plane curve?

In Python, using MatPlotLib, given [vector] parameters $a$ and $b$ and [scalar] parameter $c$, I want to draw a general cubic plane curve in 2-dimensional space (regular plane with $x$ and $y$ axes): $...
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1answer
50 views

Generalized Hermite Function as eigenfunction of a differential operator

I'm going through this paper. The article defines function function $\phi_n^\mu(x)$ that is orthonormal on $L^2$ with measure $dm = dx$: \begin{equation} \phi^\mu_n =\left(\frac{\gamma_\mu(n)}{\...
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28 views

Tensor Eigenstates

I have the following equation: $$f_i^´(t+1)=\sum_{jk}R_{i|jk}\tilde{f_j}(t)\tilde{f_k}(t)$$ It is about evolution of a population. I use this equation in my python program in the following way: <...
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0answers
44 views

Finite field and its element with symbols [Sage / Python / …]

I have a finite field $T=GF(2^3)$, normal basis $(a, a^2, a^4)$ and polynomial $f$ from field $T$, which contains unknown variables / symbols. Is it possible to get vector with coordinates of f in ...
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0answers
23 views

Finding equilibrium points of a system of nonlinear differential equations

I am currently working on a spatially explicit ODE model with dispersion to study the population dynamics of mosquitoes. I wish to compute the equilibrium values of the populations as functions of the ...
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4 views

What should be expected values of weights in statistics (specifically a set of biweight weightings)

I am working on a project that involves taking the biweight sample variance of a velocity dataset. This is defined as $\sigma_{BI}^2 = N\dfrac{\sum_{|u_i|<1}(1-u_i^2)^4(v_i-\bar{v})}{D(D-1)}$ ...
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24 views

Orthogonality of spherical Bessel functions

Please consider the following toy function $$ k_{i}\int^{\infty}_{0}j_{l}(k_{i}*x)*j_{l}(k*x)dx $$ where $j_{l}$ are spherical Bessel functions (sbf) and $k_{i}$ and $k$ are positive constants. It ...
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14 views

How to change position of the axes values of a Sage plot.

I am plotting 2D functions on Sage, and I would like to move the values displayed along the $y$ axis (the ticks) from the left of the axis to the rigth, because they bother me there. I had a look and ...
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20 views

Computationally check for roots/positiveness of a big polynomial in a given interval

For a proof, I need to check that given a little interval $(0, 0.28)$ some concrete polynomials $\in \mathbb{Q}[w]$ (polynomials in one variable ranging over the real numbers, with degrees around 50) ...
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24 views

Discretization of nonlinear system for using extend Kalman filter in python

I have a continuous nonlinear system which includes three differential equations: $\dot{x}=f(x, u)+\omega_k$ Now I wanna use numerical method to make discretization of it. Then I can use it in a ...