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Polynomial derivative causes Prime to Crash?
07-13-2016, 05:05 PM
Post: #1
Polynomial derivative causes Prime to Crash?
Hello!

Perhaps just trying to save some time while finding the derivative of this polynomial function:
d/dx(5x^(3/5)+4x^(3/4)) ... using the Prime Virtual Calculator, it failed causing the Emulator to crash, then I tried to solve it separating each term to find out the symbolic results are no the ones I expected.
   
   
I noticed that evaluating the derivative numerically it returns correct values... but symbolically I'm not sure, what do you think?

Thank you.

Spybot.
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07-13-2016, 05:16 PM
Post: #2
RE: Polynomial derivative causes Prime to Crash?
Well, the answer is correct, you got to simplify yourself.
Arno
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07-13-2016, 06:19 PM
Post: #3
RE: Polynomial derivative causes Prime to Crash?
I don't think it crashes (at least it does not inside Xcas), but you would have to wait much too long, I will change some parameters to avoid that (maximum degree for common algebraic extension built for simplifications).
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07-13-2016, 10:56 PM
Post: #4
RE: Polynomial derivative causes Prime to Crash?
In xcas diff(5*x^(3/5)+4*x^(3/4),x) returns:

3/(x^(1/5))^2+3*1/(x^(1/4))^3*sqrt(x)

However, simplify(diff(5*x^(3/5)+4*x^(3/4),x)) returns:

Code:
rootof([[1849290596989009920*x^3-144653156352000000*x^2+21432560400000000000*x+76904296875000,3178468213574860800​*x^3+7094037381120000000*x^2+2440993500000000000*x-116729736328125,9635845027921920000*x^3-386546688000000000*x^2+229471875000000000*x,7879278565785600000*x^3-1874283840000000000*x^2-22113281250000000*x,(-9423782220272762880)*x^4+1713490624512000000*x^3-107266723200000000000*x^2+1757812500000000*x,(-23106632681898639360)*x^4-34563695837184000000*x^3-98018458200000000000*x^2+71411132812500*x,(-62818287878563430400)*x^4-25623209410560000000*x^3-10937965500000000000*x^2+487518310546875*x,(-72469455631810560000)*x^4+9139958784000000000*x^3-886802343750000000*x^2,19445417291078959104*x^5-40962633184051200000*x^4+223432480800000000000*x^3+86163574218750000*x^2,(-449515361885057187840)*x^5+101669760663552000000*x^4-5546714328000000000000*x^3-29462585449218750*x^2,(-708857389430907863040)*x^5-1855984556261376000000*x^4-502953623550000000000*x^3+31589813232421875*x^2,(-2431921742405015961600)*x^5+130928497781760000000*x^4-44452603406250000000*x^3-796508789062500*x^2,(-20610723694661074944)*x^6-1971674608293642240000*x^5+265932066816000000000*x^4+7454288671875000000*x^3,(-1129025475352763301888)*x^6-157730966234726400000*x^5-13308929464680000000000*x^4-767644409179687500*x^3,(-2769378177893825249280)*x^6-4396264306606080000000*x^5-8788632003900000000000*x^4+115511627197265625*x^3,(-6561699281264726507520)*x^6-2377594621145088000000*x^5-1056820966931250000000*x^4+32634887695312500*x^3,12198562540686409728*x^7-9550672312568433868800*x^6+1825856668567680000000*x^5-57416284212890625000*x^4+711822509765625*x^3,(-156421643493552685056)*x^7-2674904881032069120000*x^6-2496402776412000000000*x^5+2680500750732421875*x^4,(-138243318795485577216)*x^7-1439651046187008000000*x^6+2043538964595000000000*x^5-236938568115234375*x^4,(-298436070998016000000)*x^7+493404453398016000000*x^6-194979280837500000000*x^5+10898437500000000*x^4],[1,0,0,0,-5*x,-4*x,0,0,10*x^2,-260*x^2,6*x^2,0,-10*x^3,-620*x^3,-340*x^3,-4*x^3,5*x^4,-140*x^4,110*x^4,-20*x^4,-x^5+x^4]])

with these warnings:

Warning, choice of an algebraic branch for root of a polynomial with parameters might be wrong. The choice is done for parameters value=0 if 0 is regular, otherwise randomly. Actual choice is Vector [92]
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Warning, replacing 92 by 92.0, a substitution variable should perhaps be purged.
Evaluation time: 66.129

What am I doing wrong?

-road
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07-14-2016, 12:21 AM
Post: #5
RE: Polynomial derivative causes Prime to Crash?
Thank you Parisse, I appreciate you will do that for us.

Spybot.
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07-14-2016, 01:57 AM (This post was last modified: 07-14-2016 02:12 AM by compsystems.)
Post: #6
RE: Polynomial derivative causes Prime to Crash?
3*x^(-2/5) == diff(5*x^(3/5)) [enter] returns 1 (true)

[up] [up] [copy] => 3*x^(-2/5) == 5*x^(3/5)' [enter] returns 1 (true) ok, but shifted the single quotation mark out of the entire expression, in this case not fails, because 5 is taken as constant

should be
[up] [up] [copy] =>3*x^(-2/5) == (5*x^(3/5))'

in the following case fails
diff(x/y) [enter] returns 1/y ok
but
[up] [up] [copy] => x/y' [enter] returns ±∞. BUG CONFIRMED

should be
[up] [up] [copy] => (x/y)' [enter] 1/y ok

FOR HP-PRIME TEAM

solution to bug

diff(expr) => parser as (expr)' and not as expr'


---------------------------------

for Bernard, we would see the solution as we make to naturally

diff(5*x^(3/5) => 3*x^(-2/5) or 3/x^(2/5) and not 3*(x^(1/5))^3/x (is not so simplified superficially)

as you can improve the simplifier?
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07-14-2016, 05:15 AM
Post: #7
RE: Polynomial derivative causes Prime to Crash?
roadrunner: nothing is wrong. You get the result as rootof(P,Q) i.e. P(alpha) where Q(alpha)=0. This is because the simplifier rewrite all algebraic extensions in a unique one, in order to certify that it will not miss a simplification, the analog as when you add fractions like 1/2+1/3+1/6 you can get a simplification to an integer. However here it requires heavy computations.
I would recommend not to run simplify on expressions with fractional powers, by the way the title of the topic is misleading, this is not a polynomial derivative.

Regarding fractional powers, the CAS rewrites them as polynomials over simpler intermediate variables, here x^(3/5) as x^(1/5)^3.
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