Numeric integration boundary assignation

Numeric integration boundary assignation - Is it a bug? - Сообщения

#1 Опубликовано: 20.04.2019 12:05:19
Guy Payeur

Guy Payeur

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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?

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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
#2 Опубликовано: 20.04.2019 12:37:52
sergio

sergio

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attention: you used "t" both as a vector and as an integration variable
integ.png

sergio
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frapuano 20.04.2019 14:49:00
#3 Опубликовано: 20.04.2019 15:04:11
Jean Giraud

Jean Giraud

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Wrote

I was writing an example and meet a possible issue.


Like this ...

Cumul.PNG

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sergio 20.04.2019 15:40:00
#4 Опубликовано: 23.04.2019 12:45:50
Guy Payeur

Guy Payeur

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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

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#5 Опубликовано: 23.04.2019 14:46:43
Alvaro Diaz Falconi

Alvaro Diaz Falconi

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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?



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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frapuano 23.04.2019 15:20:00
#6 Опубликовано: 23.04.2019 16:09:05
Jean Giraud

Jean Giraud

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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

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#7 Опубликовано: 24.04.2019 00:31:11
Guy Payeur

Guy Payeur

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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)

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#8 Опубликовано: 24.04.2019 08:36:49
Jean Giraud

Jean Giraud

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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

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#9 Опубликовано: 24.04.2019 09:53:25
Guy Payeur

Guy Payeur

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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
#10 Опубликовано: 24.04.2019 12:41:41
Jean Giraud

Jean Giraud

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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

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#11 Опубликовано: 24.04.2019 23:40:05
Jean Giraud

Jean Giraud

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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.

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