1 Feb 2012 02:12

### sqrt(1-x^2)/(2-2*x^2) --/--> 1/(2*sqrt(1-x^2))

```The general simplifier does sqrt(1-x^2)/(1-x^2) --> 1/sqrt(1-x^2), but it doesn't
simplify sqrt(1-x^2)/(2-2*x^2) to 1/(2*sqrt(1-x^2)). Ratsimp, radcan, and rootscontract
don't do this simplification either.

--Barton
```
1 Feb 2012 02:37

### Re: sqrt(1-x^2)/(2-2*x^2) --/--> 1/(2*sqrt(1-x^2))

That's annoying.  A workaround (not a solution) is 1/gfactor(1/expr).

On Tue, Jan 31, 2012 at 20:12, Barton Willis wrote:
sqrt(1-x^2)/(2-2*x^2)

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1 Feb 2012 04:09

### Re: sqrt(1-x^2)/(2-2*x^2) --/--> 1/(2*sqrt(1-x^2))

An even simpler related problem:

How do I get sqrt(1-x^2) to be expressed as sqrt(1-x)*sqrt(x+1) or even %i*sqrt(x-1)*sqrt(x+1)?

All three are simplified according to the general simplifier, but I can't seem to find some combination of factor, gfactor, scanmap, etc. that will get me from the first version to the others....

-s

On Tue, Jan 31, 2012 at 20:37, Stavros Macrakis wrote:
That's annoying.  A workaround (not a solution) is 1/gfactor(1/expr).

On Tue, Jan 31, 2012 at 20:12, Barton Willis wrote:
sqrt(1-x^2)/(2-2*x^2)

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1 Feb 2012 07:54

### Re: references to methods, algorithms behind lsquares

```On 1/31/12, gwpublic <at> wp.pl <gwpublic <at> wp.pl> wrote:

> For lsquares there are no such nice references:
> http://maxima.sourceforge.net/docs/manual/en/maxima_65.html#SEC304
>
> I'd like to cite in my thesis to works behind lsquares, as I use it
> (to be more specific: lsquares_estimates , lsquares_mse ).

Well, lsquares_estimates tries to find an exact minimum of the
mean square error, via the Maxima function "solve".
If solve cannot find a solution, then lsquares_estimates tries
to find an approximate minimum, via the function "lbfgs",
which is an implementation of the LBFGS algorithm, which
is a limited-memory BFGS (quasi-Newton) algorithm.
"?? lbfgs" finds some info in the reference manual.

> One more issue : What's are best terms for lsquares ?
>
> I'd like to call it somehow, I am curious about recommendations for
> "terms" describing lqaures, like :
> Optimization Search Routine ?
> Optimisation in Symbolic Mathematics ?
> Data fitting of parametrised symbolic mathematics ?

I think it's what's commonly called "estimation" or
more specifically "least squares estimation".

best,

Robert Dodier
```
1 Feb 2012 09:36

### sqrt(1-x^2)/(2-2*x^2) --/--> 1/(2*sqrt(1-x^2))

Barton Willis willisb at unk.edu
Tue Jan 31 19:12:08 CST 2012

The general simplifier does sqrt(1-x^2)/(1-x^2) --> 1/sqrt(1-x^2), but it doesn't
simplify sqrt(1-x^2)/(2-2*x^2) to 1/(2*sqrt(1-x^2)). Ratsimp, radcan, and rootscontract
don't do this simplification either.

--Barton

*****************************************************************************************

(%i1) S:sqrt(1-x^2)/(2-2*x^2)\$
(%i2) subst(2-2*x^2=2*(1-x^2),S);
(%o2) 1/(2*sqrt(1-x^2))

Aleksas

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1 Feb 2012 11:40

### Re: sqrt(1-x^2)/(2-2*x^2) --/--> 1/(2*sqrt(1-x^2))

```Maxima calls inte to do integrate((sqrt(1-x^2)*(x^2+1))/(2-2*x^2),x,0,1). If I recall,
inte is one of the last functions integrate tries. Some other method (not sure which one)
handles integrate((x^2+1)/(2*sqrt(1-x^2)),x,0,1).

integrate((sqrt(1-x^2)*(x^2+1))/(2-2*x^2),x,0,1) is in the testsuite.

--Barton
```
1 Feb 2012 13:04

### integrate bug

Integrate bug:

(%i1) integrate(acos((x-1/2)/sqrt(1-x^2)), x, 0, 1/2);
(%o1) -%pi/4
(%i2) float(%), numer;
(%o2) -0.78539816339745

(%o3) [0.9161228399914,1.0171006703434392*10^-14,21,0]

Aleksas D

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1 Feb 2012 13:48

```Dear Aleksas,

I sent a private message to you a month or so ago. At the moment, your
emails are getting held in the moderation queue until someone approves
them.

I'm sure you'd like your emails to get through in a timely fashion. I'm
also sure that I'd rather not approve them quite so often. The solution
to both problems is to sign up to the mailing list. If you don't want
mail delivery (because you use GMane or the like), you can turn it off.

Also, words and sentences in emails are always nice. But that's a
different problem.

Rupert
```
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1 Feb 2012 14:05

### Re: integrate bug

```On 02/01/2012 12:04 PM, Aleksas Domarkas wrote:
> Integrate bug:
>
> (%i1) integrate(acos((x-1/2)/sqrt(1-x^2)), x, 0, 1/2);
> (%o1) -%pi/4
> (%i2) float(%), numer;
> (%o2) -0.78539816339745
>
> (%i3) quad_qags(acos((x-1/2)/sqrt(1-x^2)), x, 0, 1/2);
> (%o3) [0.9161228399914,1.0171006703434392*10^-14,21,0]

And:

(%i2) integrate (acos ((x-1/2)/sqrt (1-x^2)), x);
(%o2) -%pi*x/2

which is obviously wrong.

Jaime
```
1 Feb 2012 14:14

### simplification problem

```Dear Maxima users

3^0.5/(2-3^0.5) - (2*3^0.5+3)/(4-3)

is simplified to

-2.664535259100376e-15

How can I simplify it to 0?
```

Gmane