Coding Period Week 9

Some points regarding trigonometric and inverse trigonometric functions in solveset :

• There are many issues in solveset solve_trig.More inverse trigonometric formula and trigonometric identities should be defined/added or improved. Also simplify, trigsimp and in solveset _invert methods should be improved accordingly.

• Some links, that is helpful to improve these functions.

  • https://en.wikipedia.org/wiki/Inverse_trigonometric_functions
  • https://en.wikipedia.org/wiki/Proofs_of_trigonometric_identities
  • https://owlcation.com/stem/List-of-Inverse-Trig-Function-Identities-Integrals-and-Derivatives

• trigsimp must be more powerful so that solve_trig get simplified eq. (which solves trig equation by converting them into its exp form).

• solve_trig solves the trig eq. using its exp form. There may be cases when that exp form is complicated and solveset fail to handle that form. There should be technique to convert that complicated form to simpler form(if possible) and then call the solveset_complex. That may help to improve the solve_trig method.

• We can use _osbornei, hyper_as_trig methods defined in simplify/fu.py to convert hyperbolic function to trigonometric function, then we can use trigsimp (we can’t use trigsimp for hyperbolic functions).

• First need to improve basic concepts and add more identities. I opened a new PR to improve rewrite for trigonometric functions , PR is #11424.

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eliminate() :

• issue #2720 : We need some kind of eliminate function, like http://reference.wolfram.com/mathematica/ref/Eliminate.html. See also http://stackoverflow.com/q/20826969/161801

• It looks something related to substitution function. But they are not same. Using eliminate() we will try to remove the variable(s) from the each equations(not solving the eq).

• Plan : First choose eq that have min. variables and get the value of the variable, to be eliminated. Go further and subs the value to next min. variable eq., and so on.

• Work in progress.

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Meanwhile :

• I found some basic issues in ComplexInfinity and trying to solve them in this PR #11409.

• there may be many things to be added about ComplexInfinity, one can refer this link to implement them : http://reference.wolfram.com/language/ref/ComplexInfinity.html.

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continue..

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