Hey,

I might have a bug in the sine function. It's minorily out of course...


My calculator gives
sin(0) -> 0
sin(pi) -> 0
sin(2 pi) -> 0

Options are set to radians.

I have found a significant reason for this 'error'...

It seams, that smath doesn't take into account, PI, as symbol behind the scenes.
It calculates it as a decimal value with 'only' (I think) 15 decimals...

Please make PI a symbol until absolutely necessary to show as a decimal

Wrote

I have found a significant reason for this 'error'...

It seams, that smath doesn't take into account, PI, as symbol behind the scenes.
It calculates it as a decimal value with 'only' (I think) 15 decimals...

Please make PI a symbol until absolutely necessary to show as a decimal

If you use symbolic SMath engine, here is the result:
[MATH]sin(π)—0[/MATH]
[MATH]sin(2*π)—sin(2*π)[/MATH]

EDIT:On the other hand there is no decimal treshold in SMath where the small numbers should be represented as zero.

How does one use this symbolic engine?

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How does one use this symbolic engine?

Instead of regular equal to (numeric) press symbolic equal to (right arrow on the Arithmetic palette) or CTRL+. as shortcut.

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How does one use this symbolic engine?

Instead of regular equal to (numeric) press symbolic equal to (right arrow on the Arithmetic palette) or CTRL+. as shortcut.

Like this?:

Wrote

Wrote

Wrote

How does one use this symbolic engine?

Instead of regular equal to (numeric) press symbolic equal to (right arrow on the Arithmetic palette) or CTRL+. as shortcut.

Like this?:

Yes, you are right. The symbolic result will give symbols and numbers as fractions, numeric result will give you floats (with fixed decimal point, or scientific format - number of decimals can be set by Tools=>Options=>Decimal places)

EDIT:some functions (like solve) will give you only numerical values (you will not have PI in this case). Therefor, you will not have the "symbolic" answer. The same is with integration f.e.

We do then agree, that working with PI as a number, is stupid.
F.ex, when setting it into the sine function, as such: sin(pi).

When I then do this:


I'd prefer if it showed 0 both places. Given the fact that behind the scenes, it *should* work symbolically.

EDIT: (omorr edited)
Hmm.. That's not practical. Seriously...

Wrote

EDIT: (omorr edited)
Hmm.. That's not practical. Seriously...

I agree Mike, but at the moment SMath is working this way. Andrey is doing his best to improve it. Xcas as a symbolic engine and plugin will make solving equations and integration real symbolically. Maybe some other symbolic engines as plugins will be included in the future.

EDIT: Hmm... Did I make a mistake - it is different than yours?
[MATH]solve(-sin(x)≡0;x;0;2*π)=mat(0;3,142;2;1)[/MATH]
[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);1))=0[/MATH]
[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);2))=-5,787*10^{-12}[/MATH]

or setting 10 decimal places

[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);2))=3,2310851043*10^{-15}[/MATH]

Wrote

Wrote

EDIT: (omorr edited)
Hmm.. That's not practical. Seriously...

I agree Mike, but at the moment SMath is working this way. Andrey is doing his best to improve it. Xcas as a symbolic engine and plugin will make solving equations and integration real symbolically. Maybe some other symbolic engines as plugins will be included in the future.

EDIT: Hmm... Did I make a mistake - it is different than yours?
[MATH]solve(-sin(x)≡0;x;0;2*π)=mat(0;3,142;2;1)[/MATH]
[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);1))=0[/MATH]
[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);2))=-5,787*10^{-12}[/MATH]

or setting 10 decimal places

[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);2))=3,2310851043*10^{-15}[/MATH]

I had 3 decimal places... Dunno what you had on the first one ...

EDIT:
10 decimal spaces:
-1.0206823939*10^{-11}

Wrote

Wrote

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EDIT: (omorr edited)
Hmm.. That's not practical. Seriously...

I agree Mike, but at the moment SMath is working this way. Andrey is doing his best to improve it. Xcas as a symbolic engine and plugin will make solving equations and integration real symbolically. Maybe some other symbolic engines as plugins will be included in the future.

EDIT: Hmm... Did I make a mistake - it is different than yours?
[MATH]solve(-sin(x)≡0;x;0;2*π)=mat(0;3,142;2;1)[/MATH]
[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);1))=0[/MATH]
[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);2))=-5,787*10^{-12}[/MATH]

or setting 10 decimal places

[MATH]sin(el(solve(-sin(x)≡0;x;0;2*π);2))=3,2310851043*10^{-15}[/MATH]

I had 3 decimal places... Dunno what you had on the first one ...

EDIT:
10 decimal spaces:
-1.0206823939*10^{-11}

Have no explanation about this, sorry ????
EDIT: I think I found it. It seems the release v0.85_3531 (the official one) gives your result. I think that some fixes are applied in the meantime. My results are from the recent ones v0.85_3545 and v0.85_3578.Alpha.

Will check at home.

In stable version 0.87 I still have this:

degree setting:
a=0
b=90
cos a =1
cos b =2,9371118168*10^{-14}

radians seems correct.

Thanks in advance.