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Issue Numeric integration boundary assignation - Is it a bug?
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Offline Guy Payeur  
#1 Posted : 20 April 2019 18:05:19(UTC)
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Hello,

I was writing an example and meet a possible issue.

Look at the attached file, is it normal to not being able to assign directly t.1 and t.n to the integral interval?

ISERROR QUESTION MARK.sm (15kb) downloaded 10 time(s).

2019-04-20 11_03_05-SMath Studio - [ISERROR QUESTION MARK.sm_].png

2019-04-20 11_04_01-SMath Studio - [ISERROR QUESTION MARK.sm_].png

Thank you
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Offline PompelmoTell  
#2 Posted : 20 April 2019 18:37:52(UTC)
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attention: you used "t" both as a vector and as an integration variable
integ.png

sergio
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Offline Jean Giraud  
#3 Posted : 20 April 2019 21:04:11(UTC)
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Originally Posted by: Guy Payeur Go to Quoted Post
I was writing an example and meet a possible issue.

Like this ...

Cumul.PNG

ISERROR QUESTION MARK.sm (17kb) downloaded 12 time(s).
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Offline Guy Payeur  
#4 Posted : 23 April 2019 18:45:50(UTC)
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Thank you Jean for your example of cumulative integration. That was my next step :-)

Still, I found that the integration variable is not quite independent (local) to the integral function. Should it be the case?

2019-04-23 11_44_33-SMath Studio - [ISERROR QUESTION MARK_2.sm].png

See the attached file. ISERROR QUESTION MARK_2.sm (17kb) downloaded 6 time(s).
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Offline Razonar  
#5 Posted : 23 April 2019 20:46:43(UTC)
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Originally Posted by: Guy Payeur Go to Quoted Post
Thank you Jean for your example of cumulative integration. That was my next step :-)

Still, I found that the integration variable is not quite independent (local) to the integral function. Should it be the case?


Hi. It isn't in other software, like maple. Usually it must to be an undefined name:

Clipboard01.gif

Best regards
Alvaro.
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Offline Jean Giraud  
#6 Posted : 23 April 2019 22:09:05(UTC)
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Originally Posted by: Guy Payeur Go to Quoted Post
Still, I found that the integration variable is not quite independent (local) to the integral function.

Yes, like in Mathcad, in the wild domain of integration
Doctored in red, attached ... Cheers ... Jean

IntegrateGuy.PNG

ISERROR QUESTION MARK_2.sm (19kb) downloaded 8 time(s).
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Offline Guy Payeur  
#7 Posted : 24 April 2019 06:31:11(UTC)
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Using wild value for x axis brought plots that look a lot better. Thank you Jean.

I guess that integration range meant not to be mixed with the integration variable. That does not disturb the calculation, but was only a bit counter intuitive.

Thanks for all (Jean, Alvaro and Sergio)

ISERROR QUESTION MARK_3.sm (58kb) downloaded 7 time(s).
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Offline Jean Giraud  
#8 Posted : 24 April 2019 14:36:49(UTC)
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Originally Posted by: Guy Payeur Go to Quoted Post
I guess that integration range meant not to be mixed with the integration variable. That does not disturb the calculation, but was only a bit counter intuitive.

Same in Mathcad/Mathsoft. Read more in the attached from Drummondville.
Salut Voisin ! .. Jean

Integrate Compendium_000 Indefinite.sm (11kb) downloaded 9 time(s).
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Offline Guy Payeur  
#9 Posted : 24 April 2019 15:53:25(UTC)
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2019-04-24 08_33_40-SMath Studio - [Integrate Compendium_000 Indefinite.sm_].png

Ok, so this worked because 'x' is the variable name for the vanishing iterator.


2019-04-24 08_35_16-SMath Studio - [Integrate Compendium_000 Indefinite.sm_].png

Also worked because 'z' is a passing variable that will be iterated by 'x' in the plot.


2019-04-24 08_39_00-SMath Studio - [Integrate Compendium_000 Indefinite.sm_].png

Would you explain why [-2..2] is 222 pixels? Should this be correlated to the window resolution? And not being a fixed value?

Thank you
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Offline Jean Giraud  
#10 Posted : 24 April 2019 18:41:41(UTC)
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Originally Posted by: Guy Payeur Go to Quoted Post
Would you explain why [-2..2] is 222 pixels? Should this be correlated to the window resolution? And not being a fixed value?

I copied the plot from another document, as it was then calipered.
Smath native 2D plot are adjustable by pixel in both directions.
Very nice to get pleasant looking side by side up/down plots.
Mathcad used to be not by pixel, rater by ½ pica. Thus not fine
trace and never none two of same size.
The other gorgeous plots are OriginLab. Not a function plotter
but plot XY data joined by spline(s) on pixels.
When you Shift+@ you get the native Smath canvas 232 150
Windows screen resolution is 96 ppi [PixelPerInch].
Thus eye fatigue on long term use because the internal
EyeFourierTransform must convert to the normal eye resolution
"normalized" 1200 ppi.

Read more about indefinite integral plots ... Jean

Integrate Compendium_000 Indefinite.sm (20kb) downloaded 10 time(s).
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Offline Jean Giraud  
#11 Posted : 25 April 2019 05:40:05(UTC)
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Originally Posted by: Guy Payeur Go to Quoted Post
Would you explain why [-2..2] is 222 pixels? Should this be correlated to the window resolution? And not being a fixed value?

Another interesting visit ... It would be on prescribed pixels
if the cumulative would be discretized instead of scalar.
In the attached the f(x) looks monster big to calculates, not so.
f(x) is given in the Smath executable format.

Integrate_00000 [ RECAST Scalar].sm (14kb) downloaded 7 time(s).
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