vv

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restart;
ex := sqrt( RootOf((1 - sqrt(_Z^3 + _Z^2 - _Z + 1))) ):
radnormal(ex);
# Error, (in RootOf) _Z occurs but is not the dependent variable

 

@JAMET Maybe this will give you an idea for future posts. Your undocumented and unexplained problem received an undocumented and unexplained answer. It seems that you do not like it (even if it should be easy to fix).

@janhardo Not necessarily a=a. The expressions are evaluated [+ automatic simplifications], but not simplified.

restart;
a:=x+1; b:=a+8; c:=a-9+b-x;
evalb(a=c);    # true

 

@JAMET These type of questions are better  to be presented mathematically and followed by the worksheet with your approach. Otherwise, the math can be skewed by errors in your code and it takes more time for someone to help you. Many people here will not waste their time just because you refuse a proper presentation of the problem.

@sand15  I do not see what is the numerical benefit of using r[i] >= - eps, with eps =1e-8.
It is obvious that mathematically the conditions r[i] >=0  or  r[i] >= +eps  are equivalent (i.e.  S is exactly the same).

@minhthien2016 Denote by S the max of the sum of the radii for n=14.

The sum of the radii in Maple is SMaple = 1.886... > SMma = 1.880..., so, SMaple is better.
It is easy to check the constraints and see that Maple configuration is valid, so: S >= SMaple > SMma.

Note that actually S >= 1.897 and Maple can easily obtain this.
I will probably post this later.

If you have an Answer but want it be labeled as  Comment, the readers could be confused. I'd prefer to see an answer be presented as such.

@sursumCorda  Is convert(..., simplifier=F)  documented?

@Axel Vogt  Only under some assumptions, e.g. real.

@aroche  If was chosen the branch  diff(y(x), x) = (x-2)^(2/3)  instead of diff(y(x), x) = ((x-2)^2)^(1/3).
But then y(x) is complex for x<2, which is probably not wanted.

@nm It is 2 only because you want to be so. For the exponent 2, Maple says 4 (as you have complained).

But note that y(x) + x = 0 ==> y'(x)=-1, so you have:

(x + y(x)) * (1+diff(y(x),x)) = 0  <==> (1+diff(y(x),x)) = 0 <==>  y(x) = -x+c (for some constant c). 

@nm Mathematica is not the supreme authority.

P.S. With your statement,  (x + y(x))^7 * (1+diff(y(x),x)) = 0  has 8 solutions.

@nm It's not in the standard form (or reducible to)  d/dx y(x) = F(x, y(x)).

The reason is obvious. Anyway, I see ODESteps as designed for standard simple ODEs. 

@nm No bug without Physics updates.

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