Suppose you want to simplify an expression and somehow Wolfram Alpha
seems unable to do it for you. Are there any other ways to do it that
can be relied on to yield an answer if there is one?

For example consider this result:

https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%286%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bsqrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29

short alternative link:

http://tinyurl.com/4ebtaedc

Why is Wolfram Alpha unable to see that this result is simply sqrt(7)/8?

Is there another way to get to that desired result when you're trying to
simplify complicated expressions?

Thx in advance for any feedback on this issue!

On 02/25/2024 05:13 PM, sobriquet wrote:
>
> Suppose you want to simplify an expression and somehow Wolfram Alpha
> seems unable to do it for you. Are there any other ways to do it that
> can be relied on to yield an answer if there is one?
>
> For example consider this result:
>
> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%286%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bsqrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>
>
>
> short alternative link:
>
> http://tinyurl.com/4ebtaedc
>
> Why is Wolfram Alpha unable to see that this result is simply sqrt(7)/8?
>
> Is there another way to get to that desired result when you're trying to
> simplify complicated expressions?
>
> Thx in advance for any feedback on this issue!

I don't know, you might explore Computer Algebra Systems
like "Macsyma" or "Mathematica" or "Maple V", where for
example "Maple V" has licenses and student licenses,
while it's quite controlled, vis-a-vis, more often when
you enter an expression it more or less employs numerical
methods, which lose quite immediately the absolute numerical
or analytical character of the expression, using numerical
methods, approximations, missing their usual error terms,
which given sufficient iterations, given the modeling of
their error terms, result outputs to arbitrary precision,
but not necessarily maintaining the symbolic quantities
nor resolving in the algebraic manipulations the derivations,
the symbolic quantities.

A, "Computer Algebra System", seems what you ask for,
while, "an approximator", perhaps is what you're getting.

https://en.wikipedia.org/wiki/Computer_algebra_system
https://en.wikipedia.org/wiki/List_of_computer_algebra_systems

It's a larger slide-rule.

On Feb 25, 2024, sobriquet wrote on sci.math
(in article <urgojr$264hd$1@dont-email.me>):

>
> Suppose you want to simplify an expression and somehow Wolfram Alpha
> seems unable to do it for you. Are there any other ways to do it that
> can be relied on to yield an answer if there is one?
>
> For example consider this result:
>
> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
> 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
> qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
> 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>
> short alternative link:
>
> http://tinyurl.com/4ebtaedc
>
> Why is Wolfram Alpha unable to see that this result is simply sqrt(7)/8?
>
> Is there another way to get to that desired result when you're trying to
> simplify complicated expressions?
>
> Thx in advance for any feedback on this issue!

I forget my Mathematica and Maple now, but in one of them
you had to enclose the expression to be simplified in
Simplify( ) or Simplify[ ]. Then if that didn’t yield a
result you could try FullSimplify. And I am pretty sure
that Wolfram alpha uses the same syntax as Mathematica.
Maybe check out the help files for Simplify.

This thread started on sci.math but I have added
sci.math.symbolic . I would have added
comp.soft-sys.math.mathematica but it seems
that was abandoned by its moderators in 2014.

--
David Dalton dalton@nfld.com https://www.nfld.com/~dalton (home page)
https://www.nfld.com/~dalton/dtales.html Salmon on the Thorns (mystic page)
“And the cart is on a wheel; And the wheel is on a hill;
And the hill is shifting sand; And inside these laws we stand" (Ferron)

Op 26/02/2024 om 07:30 schreef David Dalton:
> On Feb 25, 2024, sobriquet wrote on sci.math
> (in article <urgojr$264hd$1@dont-email.me>):
>
>>
>> Suppose you want to simplify an expression and somehow Wolfram Alpha
>> seems unable to do it for you. Are there any other ways to do it that
>> can be relied on to yield an answer if there is one?
>>
>> For example consider this result:
>>
>> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
>> 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
>> qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
>> 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>>
>> short alternative link:
>>
>> http://tinyurl.com/4ebtaedc
>>
>> Why is Wolfram Alpha unable to see that this result is simply sqrt(7)/8?
>>
>> Is there another way to get to that desired result when you're trying to
>> simplify complicated expressions?
>>
>> Thx in advance for any feedback on this issue!
>
> I forget my Mathematica and Maple now, but in one of them
> you had to enclose the expression to be simplified in
> Simplify( ) or Simplify[ ]. Then if that didn’t yield a
> result you could try FullSimplify. And I am pretty sure
> that Wolfram alpha uses the same syntax as Mathematica.
> Maybe check out the help files for Simplify.
>
> This thread started on sci.math but I have added
> sci.math.symbolic . I would have added
> comp.soft-sys.math.mathematica but it seems
> that was abandoned by its moderators in 2014.
>

It doesn't seem to yield the desired result in Mathematica (in the
Wolfram Cloud) or Wolfram Alpha:

https://i.imgur.com/npiwqPJ.png

https://www.wolframalpha.com/input?i=FullSimplify%5B%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%286%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bsqrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29%5D

David Dalton schrieb:
>
> On Feb 25, 2024, sobriquet wrote on sci.math
> (in article <urgojr$264hd$1@dont-email.me>):
>
> >
> > Suppose you want to simplify an expression and somehow Wolfram Alpha
> > seems unable to do it for you. Are there any other ways to do it
> > that can be relied on to yield an answer if there is one?
> >
> > For example consider this result:
> >
> > https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
> > 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
> > qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
> > 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
> >
> > short alternative link:
> >
> > http://tinyurl.com/4ebtaedc
> >
> > Why is Wolfram Alpha unable to see that this result is simply
> > sqrt(7)/8?
> >
> > Is there another way to get to that desired result when you're
> > trying to simplify complicated expressions?
> >
> > Thx in advance for any feedback on this issue!
>
> I forget my Mathematica and Maple now, but in one of them
> you had to enclose the expression to be simplified in
> Simplify( ) or Simplify[ ]. Then if that didn't yield a
> result you could try FullSimplify. And I am pretty sure
> that Wolfram alpha uses the same syntax as Mathematica.
> Maybe check out the help files for Simplify.
>
> This thread started on sci.math but I have added
> sci.math.symbolic . I would have added
> comp.soft-sys.math.mathematica but it seems
> that was abandoned by its moderators in 2014.
>

Assuming that "%CF%80" in the URL represents the imaginary unit #i,
your symbolic input expression reads:

1/SQRT(2)*SIN((1/8
- 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
+ SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
+ 82*SQRT(21/(7 + 4*SQRT(3)))))/#i)*2*pi)

in Derive notation.

I suspect that Alpha's atan() function ranges from -pi/2 to +pi/2 on
the real axis and usually should not be multiplied by 2*pi.

Numerical evaluation of my reading of your expression gives:

46.63320401 + 46.63052344*#i

whereas SQRT(7)/8 equals:

0.3307189137

Martin.

> Assuming that "%CF%80" in the URL represents the imaginary unit #i,
> your symbolic input expression reads:

I haven't followed this thread closely, but that got me curious.
cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.

-JimC
--
James Cloos <cloos@jhcloos.com>
OpenPGP: https://jhcloos.com/0x997A9F17ED7DAEA6.asc

James Cloos schrieb:
>
> > Assuming that "%CF%80" in the URL represents the imaginary unit #i,
> > your symbolic input expression reads:
>
> I haven't followed this thread closely, but that got me curious.
> cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.
>

Thanks. Now we need to know if the GREEK SMALL LETTER PI is supposed to
equal the ASCII string "pi" appearing a few characters later in the
URL. If the two are equal, the expression becomes:

1/SQRT(2)*SIN((1/8
- 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
+ SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
+ 82*SQRT(21/(7 + 4*SQRT(3)))))/pi)*2*pi)

and evaluates numerically to:

-0.5445033022

which still does not equal SQRT(7)/8 though. Why should it?

Martin.

Op 26/02/2024 om 22:24 schreef clicliclic@freenet.de:
>
> David Dalton schrieb:
>>
>> On Feb 25, 2024, sobriquet wrote on sci.math
>> (in article <urgojr$264hd$1@dont-email.me>):
>>
>>>
>>> Suppose you want to simplify an expression and somehow Wolfram Alpha
>>> seems unable to do it for you. Are there any other ways to do it
>>> that can be relied on to yield an answer if there is one?
>>>
>>> For example consider this result:
>>>
>>> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%2
>>> 86%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bs
>>> qrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%
>>> 2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>>>
>>> short alternative link:
>>>
>>> http://tinyurl.com/4ebtaedc
>>>
>>> Why is Wolfram Alpha unable to see that this result is simply
>>> sqrt(7)/8?
>>>
>>> Is there another way to get to that desired result when you're
>>> trying to simplify complicated expressions?
>>>
>>> Thx in advance for any feedback on this issue!
>>
>> I forget my Mathematica and Maple now, but in one of them
>> you had to enclose the expression to be simplified in
>> Simplify( ) or Simplify[ ]. Then if that didn't yield a
>> result you could try FullSimplify. And I am pretty sure
>> that Wolfram alpha uses the same syntax as Mathematica.
>> Maybe check out the help files for Simplify.
>>
>> This thread started on sci.math but I have added
>> sci.math.symbolic . I would have added
>> comp.soft-sys.math.mathematica but it seems
>> that was abandoned by its moderators in 2014.
>>
>
> Assuming that "%CF%80" in the URL represents the imaginary unit #i,
> your symbolic input expression reads:
>
> 1/SQRT(2)*SIN((1/8
> - 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
> + SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
> + 82*SQRT(21/(7 + 4*SQRT(3)))))/#i)*2*pi)
>
> in Derive notation.
>
> I suspect that Alpha's atan() function ranges from -pi/2 to +pi/2 on
> the real axis and usually should not be multiplied by 2*pi.
>
> Numerical evaluation of my reading of your expression gives:
>
> 46.63320401 + 46.63052344*#i
>
> whereas SQRT(7)/8 equals:
>
> 0.3307189137
>
> Martin.

Here's what it looks like (screenshot) when I open the link in Wolfram
Alpha:

https://i.imgur.com/JwsKuic.png

"clicliclic@freenet.de" <nobody@nowhere.invalid> writes:

> James Cloos schrieb:
>>
>> > Assuming that "%CF%80" in the URL represents the imaginary unit #i,
>> > your symbolic input expression reads:
>>
>> I haven't followed this thread closely, but that got me curious.
>> cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.
>>
>
> Thanks. Now we need to know if the GREEK SMALL LETTER PI is supposed to
> equal the ASCII string "pi" appearing a few characters later in the
> URL. If the two are equal, the expression becomes:
>
> 1/SQRT(2)*SIN((1/8
> - 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
> + SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
> + 82*SQRT(21/(7 + 4*SQRT(3)))))/pi)*2*pi)
>
> and evaluates numerically to:
>
> -0.5445033022

If I take what the OP passed to Wolfram Alpha and add in the missing
operators I get this:

(1/sqrt(2))*sin((1/8-((6*(atan(1/4*(-20-12*sqrt(3))-sqrt(7*(7+4*sqrt(3)))+sqrt(102+58*sqrt(3)+142*sqrt(7/(7+4*sqrt(3)))+82*sqrt(21/(7+4*sqrt(3)))))))/pi))*2*pi)

Passing that to a calculator program I get:

~0.33071891388307382398

which is pretty close to SQRT(7)/8.

--
Ben.

Ben Bacarisse schrieb:
>
> "clicliclic@freenet.de" <nobody@nowhere.invalid> writes:
>
> > James Cloos schrieb:
> >>
> >> > Assuming that "%CF%80" in the URL represents the imaginary unit
> >> > #i, your symbolic input expression reads:
> >>
> >> I haven't followed this thread closely, but that got me curious.
> >> cf 80 is the utf8 for U+03C0 GREEK SMALL LETTER PI.
> >>
> >
> > Thanks. Now we need to know if the GREEK SMALL LETTER PI is supposed
> > to equal the ASCII string "pi" appearing a few characters later in
> > the URL. If the two are equal, the expression becomes:
> >
> > 1/SQRT(2)*SIN((1/8
> > - 6*ATAN(1/4*(-20 - 12*SQRT(3)) - SQRT(7*(7 + 4*SQRT(3)))
> > + SQRT(102 + 58*SQRT(3) + 142*SQRT(7/(7 + 4 + SQRT(3)))
> > + 82*SQRT(21/(7 + 4*SQRT(3)))))/pi)*2*pi)
> >
> > and evaluates numerically to:
> >
> > -0.5445033022
>
> If I take what the OP passed to Wolfram Alpha and add in the missing
> operators I get this:
>
> (1/sqrt(2))*sin((1/8-((6*(atan(1/4*(-20-12*sqrt(3))-sqrt(7*(7+4*sqrt(3)))+sqrt(102+58*sqrt(3)+142*sqrt(7/(7+4*sqrt(3)))+82*sqrt(21/(7+4*sqrt(3)))))))/pi))*2*pi)
>
> Passing that to a calculator program I get:
>
> ~0.33071891388307382398
>
> which is pretty close to SQRT(7)/8.
>

Yes, that's because in my rendering of the original URL, I
misrepresented one of the denominators (7 + 4*SQRT(3)) as (7 + 4 +
SQRT(3)). With this mistake is corrected, I get 0.3307189137 as
required for SQRT(7)/8. Even better, Derive 6.10 now succeeds in
symbolically simplifying the trigonometric expression to SQRT(7)/8.

Case closed.

Martin.

Op 26/02/2024 om 02:13 schreef sobriquet:
>
> Suppose you want to simplify an expression and somehow Wolfram Alpha
> seems unable to do it for you. Are there any other ways to do it that
> can be relied on to yield an answer if there is one?
>
> For example consider this result:
>
> https://www.wolframalpha.com/input?i=%281%2Fsqrt%282%29%29sin%28%281%2F8-%28%286%28atan%281%2F4%28-20-12sqrt%283%29%29-sqrt%287%287%2B4sqrt%283%29%29%29%2Bsqrt%28102%2B58sqrt%283%29%2B142sqrt%287%2F%287%2B4+sqrt%283%29%29%29%2B82sqrt%2821%2F%287%2B4sqrt%283%29%29%29%29%29%29%29%2F%CF%80%29%292pi%29
>
>
> short alternative link:
>
> http://tinyurl.com/4ebtaedc
>
> Why is Wolfram Alpha unable to see that this result is simply sqrt(7)/8?
>
> Is there another way to get to that desired result when you're trying to
> simplify complicated expressions?
>
> Thx in advance for any feedback on this issue!

I guess one option would be to enter the pattern in the continued
fraction to see if that yields a simplified answer.

https://www.wolframalpha.com/input?i=continued+fraction+%5B0%3B+3%2C%7B42%2C6%7D%5D

continued fraction [0; 3,{42,6}]