Symbol math error?

[ValeryOchkov]

Is it an error in Mathcad (and Maple) symbolic math or I do not understand something? (See please the attached Mathcad 15 file)

[LucMeekes]

That does not seem like Maple output (the roots are written with the square root symbol, rather than using a power of 1/2), I guess you're using Mathcad 15, not 13 or before.

Anyway, the same problems occur in Mathcad 11, with Maple, as soon as r is set enough below 3:

Luc

[ValeryOchkov]

Thanks, Luc!

No error by using the implicit plot in Maple - we have no false branch of the curve

We can not plot the implicit function in Mathcad. But if you can not, but really want, then you can

We have no false branch of the curve in Mathcad too!

[ValeryOchkov]

Maple without Explicit plot

[ViktorKorobov]

ВФ! Я "отсек" физически бессмысленные решения. Вот что получилось.

[ViktorKorobov]

[ValeryOchkov]

Thanks, Viktor!

But we are talking (толкуем) not about sizes one body - real or fiction, but about the symbolic math of Mathcad and Maple. What is it - a bug or our not understanding this powerful tool. 

[ValeryOchkov]

[ValeryOchkov]

Viktor, thanks for the picture.

See please the animation-solution:

[ValeryOchkov]

One more solution - a systen of equations!

What curves are false?

[ViktorKorobov]

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@ValeryOchkov wrote:

What curves are false?

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In what sense? Mathematical? Physical?

[ValeryOchkov]

Все кроме двух замкнутых!

All curves are false except two closed! The red for L and blue for H!

[ValeryOchkov]

Same error in Mathematica too

[ValeryOchkov · Accepted solution]

It seems to me that I know the reason for this error.
The engine of symbolic mathematics reduces the solution of a complex equation to the solution of a quadratic equation. Here we have two roots, one of which is correct, and the other is false.

[ValeryOchkov]

See please about this bug

The article "Symbolic Computation to Solving an Irrational Equation on Based Symmetric Polynomials Method"