Nownuri1's profile - activity

I appreciate for your answer. It works perfectly. But could you please let me know what the code means? The 'parent()()' and 'x.full_simplify()'?

Could anyone please tell me how to solve a matrix equation? In the following code I have an extremely complicated matrix O. But I know that the matrix O equals to P. (I'm deriving what textbook didn't and the textbook said that they are same.)

var('theta, phi, psi, omega_1, omega_2, omega_3, t, f, g, h') #Variables are defined. 

theta=function('theta')(t); phi=function('phi')(t); psi=function('psi')(t);

R1=matrix([[cos(phi), sin(phi),0],[-sin(phi), cos(phi), 0],[0, 0, 1]])

R2=matrix([[1,0,0],[0, cos(theta), sin(theta)],[0, -sin(theta), cos(theta)]])

R3=matrix([[cos(psi),sin(psi),0],[-sin(psi),cos(psi),0],[0,0,1]])

P=matrix([[0,omega_3,-omega_2],[-omega_3, 0, omega_1],[omega_2, -omega_1, 0]])

R=R3*R2*R1

R_T=R.T; R_dev=R.derivative(t)

O=R_dev*R_T

view(O)

assuming that O==P, How can I obtain the omega_1, omega_2, omega_3 as function of theta, phi, psi, t?

But could you please tell me what the D[0] (theta) (x) means?

Thank you so much!

Could anyone let me know how you can define a variable as some function of another variable without specific definition? For example, how can you define theta as some function of x and then differentiate the 'sin(theta)' by x?

The following is my code that doesn't work. I couldn't find how to fix it in reference manuals. Any help will be appreciated.

var('theta, y, f')

y=sin(theta) ; theta=f(x);

y.derivative(x)

Thank you for the answer. It means that the reason why I couldn't see dashed lines in the legend was just the small size of legend box. Is it correct?

Could anyone let me know how you can change the style of the line in the legend box? I'm struggling with this for 2 hours. I can only change the fontsize of legend_label and color and etc. Please help me!

This is a part of my code for the plot

Lg1=plot(f1, (x, 1, 100),  ticks=[None, [0.000005, 1/5, 10^-5, 10^-4, 10^-3, 10^-2, 10^-1]], scale=('loglog', 10), ymin=0, ymax=1, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=None, axes_pad=False, legend_label='$I=2cd$, $L_s=50m$', frame=True, color='blue');

Thank you for such a nice code and advices. I would learn with this code.

I solved this problem with the followings. axes=None axes_pad=False

Would you please let me now how to modify min value of this plot? I want to make x axis begin from 13, but I can't modify the minimum value of the frame. Now I have no idea what to do....

var('I, r, L_s, z, g, f1, f2, f3, f4, c1, c2, c3, g1, g2, g3, Lg1, Lg2, Lg3, Lg4, Lg5, cp1, cp2, cp3')
f1=1/r^2*exp(-r/50);
f2=2.4/r^2*exp(-r/50);
f3=4/r^2*exp(-r/50);
f4=5/r^2*exp(-r/50);
f5=15/r^2*exp(-r/50);


Lg1=plot(f1, (x, 13, 200),  ticks=[[log(13)/log(10), 10^2],[0.000005, 1/5, 10^-5, 10^-4, 10^-3, 10^-2, 10^-1]], scale=('loglog', 10), ymin=0, ymax=0.1, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=True, legend_label='I=1 cd', frame=True, color='blue', title='L_s(scattering length)=50m');
Lg2=plot(f2, (x, 13, 200), ymin=10^-4, ymax=0.3, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, legend_label='I=2.4 cd', frame=True, color='black');
Lg3=plot(f3, (x, 13, 200), ymin=10^-4, ymax=0.3, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, legend_label='I=4 cd', frame=True, color='red'); 
Lg4=plot(f4, (x, 13, 200), ymin=10^-4, ymax=0.3, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, legend_label='I=5 cd', frame=True, color='green'); 
Lg5=plot(f5, (x, 13, 200), ymin=10^-4, ymax=0.3, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, legend_label='I=15 cd', frame=True, color='violet'); 
cp4=plot(0.000001, (x, 13, 200), ymin=10^-4, ymax=0.3, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, frame=True, color='gray', linestyle='dashed'); 
cp5=plot(0.0005, (x, 13, 200), ymin=10^-4, ymax=0.3, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, frame=True, color='gray', linestyle='dashed'); 
Lg1.set_legend_options(loc=1);
cp6=plot(0.00008, (x, 13, 200), ymin=10^-4, ymax=0.3, axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, frame=True, color='gray', linestyle='dashed'); 
cp3=plot(0.2, (x, 13, 200), ymin=0, ymax=0.1,  axes_labels=['Distance between led and camera [m]','Illuminace on camera sensor[lux]'],axes=False, frame=True, color='red', linestyle='dashed'); 

g=line([(20,0), (20, 0.1)], color='black')
z= g + Lg1 + Lg2 + Lg3 + Lg4 + Lg5 + cp3 + cp4 + cp5 + cp6;