## 170 Reputation

7 years, 269 days

## Another problem with EllipticPi...

There is another problem with EllipticPi:

For example, EllipticPi(-0.73771460993642198, -631.31663697556753, 25.0196489560624613*I) just freezing

## Re:...

> Maple uses the conventions in Abramowitz & Stegun or DLMF, https://dlmf.nist.gov/

Not really.

https://dlmf.nist.gov/19.2

Maple uses sin(phi) instead of phi as input in elliptic integrals.

And Maple doesn't support properties 19.2.10.

To recover them one should use something like

(-1)^floor(z/Pi + 1/2)*EllipticF(sin(z), k) + 2*floor(z/Pi + 1/2)*EllipticK(k)

Mathematica does 19.2.10.

Mathematica has another advantage in conventions - uses k^2 instead of k. It's useful when you have integral with + sign before k^2. So in Maple you need to put imaginary k*I parameter and then get complex answer with -0.*I imaginary part. Answer that completely real:

In Mathematica you just put real -k^2 and get real answer.

The same issue with some Jacobi functions in Maple.

## Re:...

> As you see, now the result is the same as in Maple's real part.

Yeah, I did the same yesterday.

Seems a bug because the integrand is staying real with arbitrary nu

## Re:...

Yeah, I missed that dot. I fixed this and updated t_LL.mw:

t_LL.mw

However the value function again leads to the appearance of explicit metric components.

And I tried to define tensors using the Define function. But it didn't help. Is that what you mean?

I stiil think that key in convert function. Convert should "crack" formulas with implicit determinants. And then Simplify should reduce second derivatives of metric with those from Einstein tensor.

## Re:...

UPD:

t_LL.mw

As you can see convert function didn't converting terms with determinants. And value function is leading to appearing of explicit metric components. It's difficult to get 96.8 from result of value fucntion. The key of 96.8 is that second derivatives of metric should disappear.

And after simplification we get some index issue.

## Re:...

I mean 96.8 can be product of some Maple's converting from 96.7. It's awful to input 96.8 directly)

## Re: Yes....

It's really amazing.

What about formula 96.8 from Landau-Lifshitz? Can you derive it for arbitrary metric from 96.2-7 in Maple?

## Re:...

Oh, great!)

Physics package even can handle formulas 86.9-10 from Landau-Lifshitz vol. 2 for arbitrary implicit metric when simplify tensorial expressions?

## Re: Physics Updates for Maple 2021 v.928...

Thank you. I impressed how quickly you fixed this.

## Re:...

It ssems like modp1(Embed(a,p)) convert polynomial a with arbitrary modulo to the given modulo p.

## Re: Use animate()...

How I can set custom value of fps for animated plot?

## Re: There is an issue in int, triggered ...

Thank you.

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