Axel Vogt

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16 years, 210 days
Munich, Germany

MaplePrimes Activity

These are replies submitted by Axel Vogt

@Mariusz Iwaniuk 

I think that Maple's sign is correct, for k=1 the numerical answer is  - 1.5575878673834*I (one can use MMA online, which does not know the symbolic answer, but finds a numerical result)

What do you mean by that - can you give a specific example for that?

a=0.573179148515927e-1, v = 27.0772299601075 or
a=9.54497166461128*10^14, v = .811477602357159

seem to be the only solutions

I have Maple 2017.3 32 bit and get similar results (5 times faster, 10 times for accuracy)

Neat :-)

I once used William T. Shaw, Nick Brickman,

@Rouben Rostamian  

Yes, simplifying diff(solution)/integrand gives 1.

Note that d=1 (see above) and a=1 (using cNew= c/a instead) can be assumed [and perhaps some of the assumptions can be weakend]

I think it is more clear than it displays with all the parameters:

The 1st means: p = constant1 * q where this constant1 depends on (... what you easily see ...).

The 2nd should be read as constant2 * q = 0 (one has to know that Maple abbreviates a bit here), where this constant2 depends on your parameters).

So you have to discuss for which parameters that constant2 equals 0, if you want solutions beyond q=0=p.

You may post / upload one or two examples for which you have problems.

This equation can be solved 'directly', exact.

For small values (say below 1E-4) the value is approximated by
1.23107661228290 - 0.553095709523571*log(Vzero)

I always try to get rid of denominators (just multiply [and check finally]), here giving the linear system - for which fsolve works without pain.

Yes, for example used by Bourbaki (btw deg <= ... ) for the degree


Guessing you have in mind some compiled version (k=352000000, Digits=18 for presentations of IEEE doubles <-> decimals ):

2*k*Pi 'is' 1159557927732361/2251799813685248 * pow(2,32) and sinus of it (with higher precision) is -0.811500562932876925e-8 or -2452609957903403/4503599627370496 * pow(2,-26)

avoiding any "equation labels"



Testing for "" (Win 7, Maple 32 bit): I do not have Maple 2018, but for Maple 2017 it fails  and for Maple 18 and Maple 2016 it works. For classical sheets *.wms it works in all cases. A crosscheck with the "DOS prompt" shows no unexpected characters (as it sometimes happens for files from an Apple machine)

With some modification "split and symmetry" works to show it is zero:

# using symmetry in Pi/2
2*Int(cos(2*x)/(1+2*sin(3*x)^2), x = 0 .. Pi/2);
Change(%, 2*x=xx,xx): subs(xx=x, %): combine(%);
# split and reduce to common range
Split(%, [Pi/3, 2*Pi/3]);
op(1, %) + Change(op(2, %), x = Pi/3 + w) + Change(op(3, %), x = 2*Pi/3 + w);
combine(%): expand(%): combine(%);
# which is zero by symmetry of the integrand
op(1, %):
'eval(%, w = Pi/6 - w) = -eval(%, w = Pi/6 + w)';
expand(%): is(%);

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