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How to I get Maple to spit out 1?

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  How to I get Maple to spit out 1? Salmon Egg <SalmonEgg@sbcglobal.net> - 2011-07-13 16:27 -0700
    Re: How to I get Maple to spit out 1? Axel Vogt <&noreply@axelvogt.de> - 2011-07-14 09:24 +0200
      Re: How to I get Maple to spit out 1? "G. A. Edgar" <edgar@math.ohio-state.edu.invalid> - 2011-07-14 06:20 -0600
      Re: How to I get Maple to spit out 1? Salmon Egg <SalmonEgg@sbcglobal.net> - 2011-07-14 05:23 -0700
        Re: How to I get Maple to spit out 1? Axel Vogt <&noreply@axelvogt.de> - 2011-07-14 21:48 +0200
      Re: How to I get Maple to spit out 1? Evan24 <ha15@earthlink.net> - 2011-07-14 15:19 +0000
      Re: How to I get Maple to spit out 1? clicliclic@freenet.de - 2011-07-14 22:30 +0200

#207 — How to I get Maple to spit out 1?

I already know the answer.

If I get to an expression

 z := x*exp(-(1/2)*x)/(2*sinh((1/2)*x))*((exp(x)-1)/x)

How do I get Maple to spit out 1? implify does not do it.

I looked at the help for simplify, and looked up convert and then See 
Also. That looked promising, so I went to help on Convert. Convert had a 
bus load of optional arguments. exp looked promising and worked, much to 
my pleasant surprise.

If I were even less knowledgeable than I am, how could I go about 
finding a correct approach? Is it merely an empirical search? Is there a 
guidebook? Suppose I had a much more complicated expression, say with 
radicals and Bessel functions. Us there a cookbook approach to 
simplification?

-- 

Sam

Conservatives are against Darwinism but for natural selection.
Liberals are for Darwinism but totally against any selection.

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#208

On 14.07.2011 01:27, Salmon Egg wrote:
> I already know the answer.
>
> If I get to an expression
>
>   z := x*exp(-(1/2)*x)/(2*sinh((1/2)*x))*((exp(x)-1)/x)
>
> How do I get Maple to spit out 1? simplify does not do it.
>
> I looked at the help for simplify, and looked up convert and then See
> Also. That looked promising, so I went to help on Convert. Convert had a
> bus load of optional arguments. exp looked promising and worked, much to
> my pleasant surprise.
>
> If I were even less knowledgeable than I am, how could I go about
> finding a correct approach? Is it merely an empirical search? Is there a
> guidebook? Suppose I had a much more complicated expression, say with
> radicals and Bessel functions. Us there a cookbook approach to
> simplification?

For guessing I often just plot as a first step ...

Difficult to say, though I would expect that Maple would try
to convert hyperbolics to exp, as we would do, since other
exp terms are present.

The simplification problem is not specific for Maple, but it
is a problem in any symbolic software system (thus I included
sci.math.symbolic)

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#209

> > I already know the answer.
> >
> > If I get to an expression
> >
> >   z := x*exp(-(1/2)*x)/(2*sinh((1/2)*x))*((exp(x)-1)/x)
> >
> > How do I get Maple to spit out 1? simplify does not do it.
> >
> > I looked at the help for simplify, and looked up convert and then See
> > Also. That looked promising, so I went to help on Convert. Convert had a
> > bus load of optional arguments. exp looked promising and worked, much to
> > my pleasant surprise.
> >
> > If I were even less knowledgeable than I am, how could I go about
> > finding a correct approach? Is it merely an empirical search? Is there a
> > guidebook? Suppose I had a much more complicated expression, say with
> > radicals and Bessel functions. Us there a cookbook approach to
> > simplification?
> 
> For guessing I often just plot as a first step ...
> 
> Difficult to say, though I would expect that Maple would try
> to convert hyperbolics to exp, as we would do, since other
> exp terms are present.
> 
> The simplification problem is not specific for Maple, but it
> is a problem in any symbolic software system (thus I included
> sci.math.symbolic)

As noted, in this case convert(r,exp); works.  But also as noted, there
is no algorithm that always works!

-- 
G. A. Edgar                              http://www.math.ohio-state.edu/~edgar/

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#210

In article <987jtmF301U1@mid.individual.net>,
 Axel Vogt <&noreply@axelvogt.de> wrote:

> The simplification problem is not specific for Maple, but it
> is a problem in any symbolic software system (thus I included
> sci.math.symbolic)

To my mind, one of the big advantages of something like Maple is to 
simply complicated expressions. At least, I would hope that you could 
tell if expression A is equivalent to expression B. That is, Maple would 
be able to tell if A=B is true or false. Unfortunately, that will 
require simplification to happen automatically in most cases.

-- 

Sam

Conservatives are against Darwinism but for natural selection.
Liberals are for Darwinism but totally against any selection.

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#212

On 14.07.2011 14:23, Salmon Egg wrote:
> In article<987jtmF301U1@mid.individual.net>,
>   Axel Vogt<&noreply@axelvogt.de>  wrote:
>
>> The simplification problem is not specific for Maple, but it
>> is a problem in any symbolic software system (thus I included
>> sci.math.symbolic)
>
> To my mind, one of the big advantages of something like Maple is to
> simply complicated expressions. At least, I would hope that you could
> tell if expression A is equivalent to expression B. That is, Maple would
> be able to tell if A=B is true or false. Unfortunately, that will
> require simplification to happen automatically in most cases.

My knowledge is quite limited (thus cross-posted), but practically:

- you have to measure 'simple' and that may not result in s.th. you
expect (say: you want a fraction, but the algo leads to s.th. else)

- you want the system to try 'all' ways - but that may be quite
expensive in general (just not in your situation), thus the coders
decided not to implement that (with/out specific demand). That will
lead to terrific many options - or that one CAS will do a specific
task quite easily, while for others it is a mess (need to provide
many hints/commands)

- there are situations, where it will too complicated to find good
answers, examples are long or nested expressions of 'roots' or the
nasty trigonometric expressions

There are situations, where Maple finds A=B, sometimes it is more
easy to simplify A - B and do the rest by hand. And sometimes it
is better to look at A/B.

Moreover - if I remember correctly - it has a general switch to
instruct it to invest a lot of time to test for zero.

I would not hope (in general) that it could 'prove' equivalence
without guidance (however in your case: yes, I would expect).

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#211

On Thu, 14 Jul 2011 09:24:08 +0200, Axel Vogt wrote:

> On 14.07.2011 01:27, Salmon Egg wrote:
>> I already know the answer.
>>
>> If I get to an expression
>>
>>   z := x*exp(-(1/2)*x)/(2*sinh((1/2)*x))*((exp(x)-1)/x)
>>
>> How do I get Maple to spit out 1? simplify does not do it.
>>
>> I looked at the help for simplify, and looked up convert and then See
>> Also. That looked promising, so I went to help on Convert. Convert had
>> a bus load of optional arguments. exp looked promising and worked, much
>> to my pleasant surprise.
>>
>> If I were even less knowledgeable than I am, how could I go about
>> finding a correct approach? Is it merely an empirical search? Is there
>> a guidebook? Suppose I had a much more complicated expression, say with
>> radicals and Bessel functions. Us there a cookbook approach to
>> simplification?
> 
> For guessing I often just plot as a first step ...
> 
> Difficult to say, though I would expect that Maple would try to convert
> hyperbolics to exp, as we would do, since other exp terms are present.
> 
> The simplification problem is not specific for Maple, but it is a
> problem in any symbolic software system (thus I included
> sci.math.symbolic)

For what is worth, im Maxima 5.23.2, trigrat(z) gives 1.

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#213

Axel Vogt schrieb:
> On 14.07.2011 01:27, Salmon Egg wrote:
> >
> > I already know the answer.
> >
> > If I get to an expression
> >
> >   z := x*exp(-(1/2)*x)/(2*sinh((1/2)*x))*((exp(x)-1)/x)
> >
> > How do I get Maple to spit out 1? simplify does not do it.
> >
> > [...]
> 
> For guessing I often just plot as a first step ...
> 
> Difficult to say, though I would expect that Maple would try
> to convert hyperbolics to exp, as we would do, since other
> exp terms are present.
> 
> [...]

Derive 6.10 handles this automatically. Here is the stepwise
simplification:

x*EXP(-1/2*x)/(2*SINH(1/2*x))*((EXP(x)-1)/x)

" SINH(z) -> #e^z/2-#e^(-z)/2 "

x*#e^(-x/2)*(#e^x-1)/(2*x*(#e^(x/2)/2-#e^(-x/2)/2))

" e^(z)*#e^(w) -> #e^(z+w) "

(x*#e^(x/2)-x*#e^(-x/2))/(2*x*(#e^(x/2)/2-#e^(-x/2)/2))

" one final step "

1

Martin.

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