ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Tue, 16 Aug 2011 00:53:23 +0200unsolved equationhttps://ask.sagemath.org/question/8265/unsolved-equation/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!!!
Mon, 08 Aug 2011 12:48:57 +0200https://ask.sagemath.org/question/8265/unsolved-equation/Comment by milofis for <p>Dear sage user,</p>
<p>Could you help me to find z = z(t)?, if: </p>
<pre><code>((2.867e28) / (sqrt (r^3 - (2.1e13)^3 )) ) == (( (2.121e8)*(sqrt(2*(z^2) -1))) / ( z - sqrt (z^2 - 1)))
</code></pre>
<p>with,</p>
<pre><code>r == ((1.97774e13)*(sqrt(sqrt(t)))) + ((3.55214e12)*(sqrt(t)))
1 < t < 6000
z(t= 1) = 100
r (t= 1) = 2.332954e13
</code></pre>
<p>thanks!! </p>
<p>I couldn't solve it!!!</p>
https://ask.sagemath.org/question/8265/unsolved-equation/?comment=21407#post-id-21407could 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!Mon, 08 Aug 2011 21:37:44 +0200https://ask.sagemath.org/question/8265/unsolved-equation/?comment=21407#post-id-21407Comment by benjaminfjones for <p>Dear sage user,</p>
<p>Could you help me to find z = z(t)?, if: </p>
<pre><code>((2.867e28) / (sqrt (r^3 - (2.1e13)^3 )) ) == (( (2.121e8)*(sqrt(2*(z^2) -1))) / ( z - sqrt (z^2 - 1)))
</code></pre>
<p>with,</p>
<pre><code>r == ((1.97774e13)*(sqrt(sqrt(t)))) + ((3.55214e12)*(sqrt(t)))
1 < t < 6000
z(t= 1) = 100
r (t= 1) = 2.332954e13
</code></pre>
<p>thanks!! </p>
<p>I couldn't solve it!!!</p>
https://ask.sagemath.org/question/8265/unsolved-equation/?comment=21408#post-id-21408This isn't a system of linear equations, nor a system of ordinary differential equations, unless you've made a typo. Try rephrasing your question, or looking at the Sage documentation about solving linear or differential equations.Mon, 08 Aug 2011 14:16:59 +0200https://ask.sagemath.org/question/8265/unsolved-equation/?comment=21408#post-id-21408Answer by benjaminfjones for <p>Dear sage user,</p>
<p>Could you help me to find z = z(t)?, if: </p>
<pre><code>((2.867e28) / (sqrt (r^3 - (2.1e13)^3 )) ) == (( (2.121e8)*(sqrt(2*(z^2) -1))) / ( z - sqrt (z^2 - 1)))
</code></pre>
<p>with,</p>
<pre><code>r == ((1.97774e13)*(sqrt(sqrt(t)))) + ((3.55214e12)*(sqrt(t)))
1 < t < 6000
z(t= 1) = 100
r (t= 1) = 2.332954e13
</code></pre>
<p>thanks!! </p>
<p>I couldn't solve it!!!</p>
https://ask.sagemath.org/question/8265/unsolved-equation/?answer=12563#post-id-12563A differential equation would involve the derivative `z'(t)` which you don't have in your equation(s).
If you substitute the value of `r` into the first equation you would have a single non-linear equation relating `z` and `t`. You may be able to solve this equation using the `solve` command. You don't have any unknown parameters in the expression for `r` or the equation involving `z` so you might not be able to solve the equation and have the values at `t=1` that you specify be true.
You might try something like:
r,z,t = var('r,z,t')
equation = ((2.867e28) / (sqrt (r^3 - (2.1e13)^3 )) ) == (( (2.121e8)*(sqrt(2*(z^2) -1))) / ( z - sqrt (z^2 - 1)))
equation = equation.subs(r == ((1.97774e13)*(sqrt(sqrt(t)))) + ((3.55214e12)*(sqrt(t))))
solve(equation, t)
When I tried this I got:
Is (2*z^2-1)*(z-sqrt(z^2-1)) positive, negative, or zero?
meaning that Maxima (the solver underneath Sage) can't solve the equation without more information.
Mon, 08 Aug 2011 23:09:38 +0200https://ask.sagemath.org/question/8265/unsolved-equation/?answer=12563#post-id-12563Comment by milofis for <p>A differential equation would involve the derivative <code>z'(t)</code> which you don't have in your equation(s).</p>
<p>If you substitute the value of <code>r</code> into the first equation you would have a single non-linear equation relating <code>z</code> and <code>t</code>. You may be able to solve this equation using the <code>solve</code> command. You don't have any unknown parameters in the expression for <code>r</code> or the equation involving <code>z</code> so you might not be able to solve the equation and have the values at <code>t=1</code> that you specify be true.</p>
<p>You might try something like: </p>
<pre><code>r,z,t = var('r,z,t')
equation = ((2.867e28) / (sqrt (r^3 - (2.1e13)^3 )) ) == (( (2.121e8)*(sqrt(2*(z^2) -1))) / ( z - sqrt (z^2 - 1)))
equation = equation.subs(r == ((1.97774e13)*(sqrt(sqrt(t)))) + ((3.55214e12)*(sqrt(t))))
solve(equation, t)
</code></pre>
<p>When I tried this I got:</p>
<pre><code>Is (2*z^2-1)*(z-sqrt(z^2-1)) positive, negative, or zero?
</code></pre>
<p>meaning that Maxima (the solver underneath Sage) can't solve the equation without more information.</p>
https://ask.sagemath.org/question/8265/unsolved-equation/?comment=21366#post-id-21366Thank 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?Tue, 16 Aug 2011 00:53:23 +0200https://ask.sagemath.org/question/8265/unsolved-equation/?comment=21366#post-id-21366