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What does it mean when solving equation and only brackets come back in maxima?

I tried to solve for phi and it keeps phi on both sides. I try to solve for A and it comes back with brackets Any ideas why?

Here's the equation

eq2:acos(A*cos((2*%pi*f*t+phi)/A) -2*%pi*f*t)=phi;

enter image description here

wxWidgets: 3.0.0 Unicode support: yes Maxima version: 5.32.1

Even when I add values in it still refuses to get phi onto one side

enter image description here

Rick T
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2 Answers2

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Maxima cannot solve every equation. Have you tried simple ones? Are the results right? Maybe you could check the help document for some samples on the syntax of equations like yours.

Lei Yang
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because this is transcendent equation.

  • you can not solve native transcendent equations algebraically
  • if they can be changed by some math trick/substitution to non transcendent form
  • then they are not native transcendent equations.

This type of equations are solvable numerically

  • so for that you have to know the A or phi value and get the other one
  • there are many numerical solutions to it
  • most cases use some iteration process to improve accuracy
  • but you can not get result as function
  • you find only solution points per specific known input points
  • here an example of one similar equation: solving Kepler`s equation just look at bullet 3 there
  • you can use such iterative process only if your equation meet some conditions
  • like the signum and monotonicity of first/second derivations etc ...

If you need functional output at some finite interval

  • you can approximate equation by polynomial, Taylor/Furrier series, or whatever else
  • and get the algebraic solution for such form instead
Community
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Spektre
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  • I do know A, F, and t. I was just trying to get phi on one side before I subst them in. Thanks – Rick T Oct 27 '14 at 12:57