MKS's profile - activity

A circle is a section of a sphere by a plane, the equation \begin{equation} x^2+y^2+z^2+2gx+2fy+2hz+d=0\tag{1} \end{equation} and \begin{equation} ax+by+cz=p\tag{2} \end{equation} together represent a circle. How do I plot like these diagram for given $g,f,h,a,b,c,p$. How to input by using @interact for the parameter $a,b,c,p$ to move the plane through the sphere ?

Yes $k$ is fixed.

How to solve this system of equations in sage?

$x_1+l_1x_2+l_1^2x_3+\dots+l_1^{k-1}x_k=c_1+r $.

$x_1+l_2x_2+l_2^2x_3+\dots+l_2^{k-1}x_k=c_2+r^2$

$\dots $

$x_1+l_kx_2+l_k^2x_3+\dots+l_k^{k-1}x_k=c_k+r^k$

where $l_i$'s are different positive integers and $c_i,r$ are integers in $[0,256]$

In particular, we can solve with sage. Here is the code :

a0, a1,a2,b3,b4, b5,r,l1,l2,l3 = var('a0,a1,a2,b3,b4,b5, r,l1,l2,l3')

X=solve([a0+l1*a1+l1^2*a2==b3+r^3, a0+l2*a1+l2^2*a2==b4+r^2,a0+l3*a1+l3^2*a2==b5+r^1], a0,a1, a2)

Error in lines 1-1 Traceback (most recent call last): File "/cocalc/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 1013, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "<string>", line 1 | Sage Version RealNumber('4.7').gen(2), Release Date: Integer(2011)-Integer(10)-Integer(29) | ^ SyntaxError: invalid syntax

I would like to draw geometrical figures with coordinate axes. suppose I want to draw a sphere with three coordinate axes x,y,z. How can I do this?