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Yes, that is what happened when I was on M. Why is that happening?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

This may be simplistic but you are obviously doing something wrong. Let's concentrate for a minute on my graph. What do you observe and how do you fix it?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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I would subtract 0.3 frommy curve

*Last edited by Agnishom (2014-02-22 02:40:02)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

That suggests that you computed a[0], the constant term wrong.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Hmm

```
(%i10) f(x) := if x>0 then sin(x) else 0$
(%i11) a(n) := (1/%pi)*(integrate(f(x)*cos(n*x),x,-%pi,%pi))$
(%i12) b(n) := (1/%pi)*(integrate(f(x)*sin(n*x),x,-%pi,%pi))$
(%i13) s(x,y) := a(0)/2 + sum((a(n)*cos(n*x)+b(n)*sin(n*x)),n,1,y)$
(%i14) plot2d([f(x),s(x,10)],[x,-%pi,%pi],[box, false]);
```

Why am I getting so many 'too many context' errors after that? Is it a bug?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

I do not know very much about Maxima and its error codes.

I do know that you are not computing a[0] right.

`a0 = 1/(2 \[Pi]) Integrate[f[x], {x, -\[Pi], \[Pi]}]`

Replace a[0] with a0.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Sorry, that is not possible right now.

f[x] is a piecewise function.

`f[x_] := If [x>0, Sin[x],0]`

How can M know what the following evaluates to without knowing if x is > 0?

```
a[0] + a[1] Cos[x] + a[2] Cos[2 x] + a[3] Cos[3 x] +
a[4] Cos[4 x] + a[5] Cos[5 x] + a[6] Cos[6 x] + a[7] Cos[7 x] +
b[0] + b[1] Sin[x] + b[2] Sin[2 x] + b[3] Sin[3 x] + b[4] Sin[4 x] +
b[5] Sin[5 x] + b[6] Sin[6 x] + b[7] Sin[7 x]
```

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

Hi;

That is not the correct way to enter the piecewise function.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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bobbym wrote:

Why didn't you tell me sooner?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

About the piecewise function? This was a question to you, not to me.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Hm, how does a normal M user enter a piecewise function?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

`Piecewise[{{0, -\[Pi] <= x <= 0}, {Sin[x], \[Pi] >= x > 0}}]`

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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How is it different from mine?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

1) You asked how an M programmer would do it.

2) Yours defines the function passed π, mine does not.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Agnishom wrote:

How can M know what the following evaluates to without knowing if x is > 0?

`a[0] + a[1] Cos[x] + a[2] Cos[2 x] + a[3] Cos[3 x] + a[4] Cos[4 x] + a[5] Cos[5 x] + a[6] Cos[6 x] + a[7] Cos[7 x] + b[0] + b[1] Sin[x] + b[2] Sin[2 x] + b[3] Sin[3 x] + b[4] Sin[4 x] + b[5] Sin[5 x] + b[6] Sin[6 x] + b[7] Sin[7 x]`

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

The piecewise function declares that x is sin(x) when x is between 0 and π.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Yes, so what?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

The formulas produce an expression that will closely approximate the given function between -π and π.

Look at the answer. Notice how closely the blue line ( Fourier series ) covers the red line ( original function ).

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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That is not my question

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

I am not following you. Do you mean about the context error?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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No, not that. I have now figured out the answer myself.

For now, I am integrating numerically.

```
(%i1) f(x) := if x>0 then sin(x) else 0$
(%i2) a(n) := (1/%pi)*(first(quad_qags(f(x)*cos(n*x),x,-%pi,%pi)))$
(%i3) b(n) := (1/%pi)*(first(quad_qags(f(x)*sin(n*x),x,-%pi,%pi)))$
(%i4) s(x,y) := a(0)/2 + sum((a(n)*cos(n*x)+b(n)*sin(n*x)),n,1,y)$
(%i5) plot2d([f(x),s(x,10)],[x,-%pi,%pi],[box, false]);
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
***MESSAGE FROM ROUTINE DQAGS IN LIBRARY SLATEC.
***INFORMATIVE MESSAGE, PROG CONTINUES, TRACEBACK REQUESTED
* ABNORMAL RETURN
* ERROR NUMBER = 2
*
***END OF MESSAGE
(%o5)
```

Yields the attached image

The polynomial is the following

```
(%i6) s(x,10);
1.3877787807814457E-16 sin(10 x) 0.02020202020202 cos(10 x)
(%o6) -------------------------------- - --------------------------
%pi %pi
3.3219954564955856E-16 sin(9 x) 1.3877787807814457E-17 cos(9 x)
+ ------------------------------- - -------------------------------
%pi %pi
4.163336342344337E-17 sin(8 x) 0.031746031746032 cos(8 x)
+ ------------------------------ - --------------------------
%pi %pi
3.2265856653168612E-16 sin(7 x) 5.7245874707234634E-17 cos(7 x)
- ------------------------------- - -------------------------------
%pi %pi
3.9091435841719085E-16 sin(6 x) 0.057142857142857 cos(6 x)
- ------------------------------- - --------------------------
%pi %pi
4.8572257327350599E-17 sin(5 x) 1.6653345369377348E-16 cos(5 x)
- ------------------------------- + -------------------------------
%pi %pi
2.0816681711721685E-16 sin(4 x) 0.13333333333333 cos(4 x)
- ------------------------------- - -------------------------
%pi %pi
3.2612801348363973E-16 sin(3 x) 1.9081958235744878E-17 cos(3 x)
+ ------------------------------- + -------------------------------
%pi %pi
1.6653345369377348E-16 sin(2 x) 0.66666666666667 cos(2 x)
- ------------------------------- - -------------------------
%pi %pi
1.570796326794897 sin(x) 1.1102230246251565E-16 cos(x) 1.0
+ ------------------------ - ----------------------------- + ---
%pi %pi %pi
```

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

There are a lot of error messages in that calculation. Also, many of those coefficients are just fungi.

But that is the correct answer. Very good.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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fungi?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 105,709

A number that is very, very tiny so it is obviously 0.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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All tiny numbers are essentially zero? Why?

There are a lot of error messages in that calculation.

Not the calculation, its just the plotting part.

*Last edited by Agnishom (2014-02-22 15:50:39)*

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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