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.Thu, 05 Oct 2017 17:20:34 +0200convert parametric equations to a normal onehttps://ask.sagemath.org/question/39028/convert-parametric-equations-to-a-normal-one/I solved my problem into parametric equations as shown below:
x == 3/4*sqrt(2*m^2 + 2)*m/(m^2 + 1), y == 1/4*sqrt(2*m^2 + 2)/(m^2 + 1)
But I meet difficult on how to convert into a normal one, I want to get an equation with `x, y` only. For another general description: is there any function will help solve parametric equations into a normal one like solve: `x == cos(theta), y == sin(theta)` into `x ^ 2 + y ^ 2 == 1`. I learned how to solve it with my pen, but I want a solution with Sage code.
Thanks.Wed, 04 Oct 2017 07:53:59 +0200https://ask.sagemath.org/question/39028/convert-parametric-equations-to-a-normal-one/Comment by lancaster for <p>I solved my problem into parametric equations as shown below:</p>
<pre><code>x == 3/4*sqrt(2*m^2 + 2)*m/(m^2 + 1), y == 1/4*sqrt(2*m^2 + 2)/(m^2 + 1)
</code></pre>
<p>But I meet difficult on how to convert into a normal one, I want to get an equation with <code>x, y</code> only. For another general description: is there any function will help solve parametric equations into a normal one like solve: <code>x == cos(theta), y == sin(theta)</code> into <code>x ^ 2 + y ^ 2 == 1</code>. I learned how to solve it with my pen, but I want a solution with Sage code. </p>
<p>Thanks.</p>
https://ask.sagemath.org/question/39028/convert-parametric-equations-to-a-normal-one/?comment=39038#post-id-39038I have edited my question, hope it is clearer now. I mean "normal" to be something like a Conic Curve equation like ellipse is `x^2/a^2 + y^2/b^2 = 1`Thu, 05 Oct 2017 17:20:34 +0200https://ask.sagemath.org/question/39028/convert-parametric-equations-to-a-normal-one/?comment=39038#post-id-39038Comment by dan_fulea for <p>I solved my problem into parametric equations as shown below:</p>
<pre><code>x == 3/4*sqrt(2*m^2 + 2)*m/(m^2 + 1), y == 1/4*sqrt(2*m^2 + 2)/(m^2 + 1)
</code></pre>
<p>But I meet difficult on how to convert into a normal one, I want to get an equation with <code>x, y</code> only. For another general description: is there any function will help solve parametric equations into a normal one like solve: <code>x == cos(theta), y == sin(theta)</code> into <code>x ^ 2 + y ^ 2 == 1</code>. I learned how to solve it with my pen, but I want a solution with Sage code. </p>
<p>Thanks.</p>
https://ask.sagemath.org/question/39028/convert-parametric-equations-to-a-normal-one/?comment=39034#post-id-39034Please give a clear sense to
*But I meet difficult on how to convert into a normal one.*
What should be converted into a "normal one"? Note that the (non-algebraic!) parametrization works for
$$x^2+9y^2 = 9/8$$
and **not** for $x^2+y^2=1$:
sage: var('m');
sage: x = 3/4*sqrt(2*m^2 + 2)*m/(m^2 + 1)
sage: y = 1/4*sqrt(2*m^2 + 2)/(m^2 + 1)
sage: (x^2+9*y^2).canonicalize_radical()
9/8
Do we really need the $m$-parametrization for the further question with parameter $\theta$?
Note also that $\theta$ appears in the *transcendental* functions $x,y$, which live in a domain outside algebra. So the suggested question asks for finding an algebraic relation between non-algebraic objects?Wed, 04 Oct 2017 20:28:02 +0200https://ask.sagemath.org/question/39028/convert-parametric-equations-to-a-normal-one/?comment=39034#post-id-39034