milofis's profile - activity

To plot one quantity vs. another you can build a list of coordinates of points on the graph and then plot those points. Use plot for graphing a function of an independent variable. In your graph, neither axis variable is "independent".

sage: coordinates = [ (log(x), log(x^2)) for x in range(1,150) ]
sage: point( coordinates )

Which is just a line with slope 2 since $\log(x^2) = 2 \log(x)$. If you want the points to be connected with lines try:

sage: line(coordinates)

I want to do the plot of: log (y) vs log (x), when y = log (x) and x is between (1,150), so I tried:

sage: var ('x,y') (x, y) sage: y = function ('y',x) sage: y = x^2 sage: plot (log(y), (log(x), 1,150))

but the final result that I found is wrong (I did the real plot using openoffice and gnuplot), so finally someone could you help me to solve this problem?

Your syntax for your function z is badly mangled. Perhaps this is what you want?

sage: z,t = var('z,t')
sage: z = 1/2*sqrt(14644013671875*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3/(14644013671875*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 135618210615234381652297748904336450246503209398960128) - sqrt(214447136422061920166015625*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^6 + 3864549077638520528470870886005025216199885162842192609280000000000*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 54181888058488411888503596938295863676921476134912455624013826749306153335312612762848157900410211283238912)/(14644013671875*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 135618210615234381652297748904336450246503209398960128) - 135618210615234381652297748904336450246503209398960128/(5.20175867244141e25*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 135618210615234381652297748904336450246503209398960128)

You had a lot of missing * operators and mismatched parentheses.

Assuming what I've posted is the correct function, the warning message from plot is because the values of this function on the interval [1, 6000] are non-real. For example:

sage: z(t=300)
1/2*sqrt(14644013671875*(3.55214000000000e13*sqrt(3) + 1.97774000000000e13*300^(1/4))^3/(14644013671875*(3.55214000000000e13*sqrt(3) + 1.97774000000000e13*300^(1/4))^3 - 135618210615234381652297748904336450246503209398960128) - sqrt(214447136422061920166015625*(3.55214000000000e13*sqrt(3) + 1.97774000000000e13*300^(1/4))^6 + 3864549077638520528470870886005025216199885162842192609280000000000*(3.55214000000000e13*sqrt(3) + 1.97774000000000e13*300^(1/4))^3 - 54181888058488411888503596938295863676921476134912455624013826749306153335312612762848157900410211283238912)/(14644013671875*(3.55214000000000e13*sqrt(3) + 1.97774000000000e13*300^(1/4))^3 - 135618210615234381652297748904336450246503209398960128) - 135618210615234381652297748904336450246503209398960128/(5.20175867244141e26*sqrt(3) + 1.97774000000000e13*300^(1/4))^3 - 135618210615234381652297748904336450246503209398960128)
sage: z(t=300).n()
1.12748264420482e10 + 1.84131889290825e26*I

So you may have the wrong function if you expect to be able to plot it on that interval.

what is the meaning of:

verbose 0 (4075: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 121 points. verbose 0 (4075: plot.py, generate_plot_points) Last error message: ''

when I try to do:

sage: var ('z,t')
(z, t)

sage: z = function ('z',t)

sage: z = 1/2*sqrt(14644013671875*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3/(14644013671875*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 135618210615234381652297748904336450246503209398960128) - sqrt(214447136422061920166015625*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^6 + 3864549077638520528470870886005025216199885162842192609280000000000*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 54181888058488411888503596938295863676921476134912455624013826749306153335312612762848157900410211283238912)/(14644013671875*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 135618210615234381652297748904336450246503209398960128) - 135618210615234381652297748904336450246503209398960128/(14644013671875*(3.55214000000000e12*sqrt(t) + 1.97774000000000e13*t^(1/4))^3 - 135618210615234381652297748904336450246503209398960128))

sage:  plot (z, (t, 1,6000))

verbose 0 (4075: plot.py, generate_plot_points) WARNING: When plotting, failed to evaluate function at 121 points.
verbose 0 (4075: plot.py, generate_plot_points) Last error message: ''

Thank you very much for your kind attention and your suggestions. However I need to find z as a function of t, when t vary 1 - 1000 with step of 10. is it possible to do that?

could you tell me,what kind of equation do you think is it?. I found this equation from physical principles of shock wave to describe the temporal evolution of relativistic blastwaves. z is the lorentz factor ( http://en.wikipedia.org/wiki/Lorentz_factor ) and r is the shock radius. Thank you for your comment!

Dear sage user,

Could you help me to find z = z(t)?, if:

((2.867e28) / (sqrt (r^3 - (2.1e13)^3 )) ) == (( (2.121e8)*(sqrt(2*(z^2) -1))) / ( z - sqrt (z^2 - 1)))

with,

r == ((1.97774e13)*(sqrt(sqrt(t)))) + ((3.55214e12)*(sqrt(t)))

1 < t < 6000

z(t= 1) = 100

r (t= 1) = 2.332954e13

thanks!!

I couldn't solve it!!!