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Re: elliptic integrals

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  • Subject: [mg636] Re: [mg602] elliptic integrals
  • From: Richard Mercer <richard at>
  • Date: Mon, 03 Apr 1995 14:11:37 -0400

>  first, load package <<Calculus`EllipticIntegrate`

>  Then:  Integrate[1/Sqrt[(a + b x + x^2)(a - b x + x^2)],
>  x]

>  I get an expression that includes the symbol
>  "Calculus`EllipticIntegrate`Private`a$24".  What is this?

The technical term is "bug". 

>  What do I do with it?  Things get even more complicated
>  when I put some limits on my integral (as I will need to
>  do).

Open your package Calculus`EllipticIntegrate` and search for

{a, c} = -Map

There are two such locations. At the end of each such line (but before the  
semicolon) type 


and save the package. This seems to fix the problem. The problem was the code  
was written under the assumption that exactly two roots would result from  
solving certain equations. In your example each root was listed twice, which is  
fixed by the //Union. An even better fix might be 

Take[#,2]& @ -Map .... //Union

to guarantee more than two roots will not screw up the calculation.

Richard Mercer

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