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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

That is not correct. With respect to t, 2pi*n is a constant, so it vanishes. You should have dt=dx.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

It does not vanish, multiplicative constants go to the front.

t = 2 n π x

dt/dx = 2 n π

dt = 2 n π dx

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

You do not multiply x by it. You add it to x!

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

Oh brother, I am doing the wrong problem. You said t=x+n*2pi and I am doing t=x*n*2pi

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Yes. t=x+2pi*n.

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

Okay thank you, I think I understand what he did there now.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Great! So, do you think you will be able to expand it to 1000 digits with that?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

Hi;

Nope, objection 2 and 3 still apply.

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Have you found any other ways?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

Nothing that could exceed about 100 digits. I used my idea with a few more bells and whistles.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Have you had other propositions about finding more digits?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

I am not following you. Propositions? Do you mean other ideas?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Have you had other propositions about finding more digits?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

Other problems like this one?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

No. Did anyone tell you of another way to solve the integral problem?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

I am afraid not.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Too bad. Be sure to tell me if you find something new.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

If I were to find something new I would tell immediately but every new idea just evaporates.

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

Great then!

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

bobbym wrote:

To start, although any CAS known will gag on this problem they are able to do pieces of so it is to our advantage to split the integral like this.

The first integral is not too difficult and any CAS can do it to 100 digits.

Hi bobbym

I wanted to ask you about this bit. How do I get Maxima to evaluate this?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

What does maxima provide for numeric integration that is built in?

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
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I don't think there is anything built in.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

There are numeric integration routines I think they are call quad_gags.

Also there is romberg and nint.

*Last edited by bobbym (2013-03-04 07:02:50)*

**In mathematics, you don't understand things. You just get used to them.**

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,673

I tried loading nint, but it won't load!

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,886

Does this run?

```
(%i1) f(x) := (mode_declare (n, integer, x, float), n:n+1, exp(-x))$
(%i2) translate(f)$
Warning-> n is an undefined global variable.
(%i3) block ([rombergtol: 1.e-6, romberabs: 0.0], n:0, romberg (f, 0, 50));
(%o3) 1.000000000488271
(%i4) n;
(%o4) 257
```

**In mathematics, you don't understand things. You just get used to them.**

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