Limits of functions of 2 variables

Limits of functions of 2 variables - Сообщения

#1 Опубликовано: 21.02.2017 17:58:54
frapuano

frapuano

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Hi Martin,

this is just to know if it is possible from Smath using Maxima to handle limits of functions of 2 variables.

Thanks in advance for your feedback

Franco

#2 Опубликовано: 21.02.2017 18:39:02
Martin Kraska

Martin Kraska

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this is just to know if it is possible from Smath using Maxima to handle limits of functions of 2 variables.


There is no hint on such capabilities in the maxima handbook.
Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx
#3 Опубликовано: 22.02.2017 13:11:28
Jean Giraud

Jean Giraud

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this is just to know if it is possible from Smath using Maxima to handle limits of functions of 2 variables.



The limit of a function of two variables is the contour limit @ user value.
Maxima X_Y plots by default the 0 level contour. For other 'level(s)'
use the maple solve block.

Jean
#4 Опубликовано: 22.02.2017 14:08:40
Martin Kraska

Martin Kraska

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The limit of a function of two variables is the contour limit @ user value.
Maxima X_Y plots by default the 0 level contour. For other 'level(s)'
use the maple solve block.

Jean



What is a Maxima X_Y plot? Why would you need some solver for other levels if you can plot 0 level?

As I understand, the bivariate limit is a function of the x,y values and of the direction of approach.
It would be helpful to see what you expect to see (examples).
Martin Kraska Pre-configured portable distribution of SMath Studio: https://en.smath.info/wiki/SMath%20with%20Plugins.ashx
#5 Опубликовано: 23.02.2017 13:41:09
Jean Giraud

Jean Giraud

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What is the meaning of: handle limits of functions of 2 variables
Wait for the f(x,y):=
X_Y plots contour of any level in the domain of existence w/o solver.
The solver is for discretising the export.

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#6 Опубликовано: 24.02.2017 05:15:10
frapuano

frapuano

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Joan unlukily doesn't work this way.

For a limit of a function in 2 variables ( or more ) its results may depends on the path used to reach it so the program I guess that needs to use a coordinate conversion or other methods to find it and to check that is independent from the path used .
So it is necessary a specific algorithmic "intelligence" to solve such a type of problems.
In my search have found a Wolfram alpha widget that does this in a very good way ...

http://www.wolframalpha.com/widgets/view.jsp?id=2958433016861a528d6221f5ac88eefd

Best regards

Franco
#7 Опубликовано: 24.02.2017 15:11:27
Jean Giraud

Jean Giraud

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Wolfram is of no help as you can check by yourself: it is ill posed.
"the limit of functions of two variables ..."

read: implict f(x,y) have solutions wrt 'x' or 'y' alternately.

Read the two Smath documents

Jean

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Implicit Wolfram.BMP
#8 Опубликовано: 24.02.2017 15:26:01
Jean Giraud

Jean Giraud

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this is just to know if it is possible from Smath using Maxima to handle limits of functions of 2 variables.



From the previous work sheets, answer is probably "NO"
Maxima will plot many implicit functions.

In the attached:
1. Valery Ochov "ImplicitFunctionGrapher"
2. an example of the CONTOUR matrix extractor

I presume I can exemplify the 'maple' RootOf,
Please, let me know.

Jean

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