#### 7.57 bug in elliptic integral, Maple 6 to Maple 8 (28.8.01)

##### 7.57.1 James R. FitzSimons

What did I do wrong? Maple 6 did not give me an answer.

> evalf(int(327082769*(689*t-sqrt(689*sqrt(6005)/2+23377)-373)/(sqrt(474721*t^2
> +t*(sqrt(654165538*sqrt(6005)+44390211268)-513994)-sqrt(191787284*sqrt(6005)
> +12735814988)+689*sqrt(6005)+139178)*(474721*t^2-t*(sqrt(654165538*sqrt(6005)
> +44390211268)+513994)+sqrt(191787284*sqrt(6005)+12735814988)+689*sqrt(6005)
> +139178)^(3/2))
> +I*(sqrt(73711381928151371729*sqrt(6005)/2
> -2500944811806087978097)-2289579383)/(sqrt(474721*t^2+t*(sqrt(654165538
> *sqrt(6005)+44390211268)-513994)-sqrt(191787284*sqrt(6005)+12735814988)
> +689*sqrt(6005)+139178)*(474721*t^2-t*(sqrt(654165538*sqrt(6005)+44390211268)
> +513994)+sqrt(191787284*sqrt(6005)+12735814988)+689*sqrt(6005)+139178)^(3/2))
> ,t=0..1));

Error, (in int/ellalg/trxstandard/4) int/ellalg/trxstandard/4 uses a 7th
argument, L, which is missing



##### 7.57.2 Robert Israel (29.8.01)

You’ve run into a bug in Maple’s evaluation of elliptic integrals. Note, however, that if you wanted a numerical answer, you should use "Int" instead of "int". The answer I get is -20.69727045+41.02175888*I.

The way it is now, "int" is called ﬁrst to do the integration in closed form, and then (if that didn’t run into the bug) "evalf" would evaluate the result. With evalf(Int(...)), numerical integration would be used with no attempt to integrate symbolically.

Maple 7 didn’t return the error message, but it also didn’t return any answer in a reasonable time, so I’m not sure if the bug has been ﬁxed.

Maple 8 returns: Error, (in gcdex) invalid arguments (U. Klein)

##### 7.57.3 Jim FitzSimons (29.8.01)

Robert, thank you, I did want the closed form solution ﬁrst. Maple usually runs faster that way when the results are 64 digits. George’s algorithms are very good. I have my own algorithms for symbolic and numerical evaluation using symmetric ellpitic integrals.

I did not program them using Maple yet. Maybe somebody better at using Maple will do it.