Hi,

Is this OK ? I am not sure.

Matrix exponential is not implemented.

You can replicate in SMath what the Maxima engine does with the vecotrize() function (otherwise by default SMath tries to perform a scalar operation and fails).

But still the SMath result is not the same as the Mathcad result...

Wrote

But still the SMath result is not the same as the Mathcad result...

I think it's because as Davide said, Matrix exponential is not implemented in SMath. But then how to calculate the Matrix exponential in SMath? There is a way somehow?

Wrote

Hi,

This is the answer via wolfram alpha:



Is the same obtained via vectorize function on SMath. Maybe your file or configuration on Mathcad have some parameters you are not mentioning?

Hi Cornel. The exponential function is a well-defined function from the complex plane into the complex plane. A possible extension to its domain and range being square matrices analogous to the ordinary exponential function can be defined as e^A = sum(A^k, k=1...infinity). And notice that this is valid only for square matrices, not for the general case.

In general, the other CASs have special functions for this extension of the exponential function: expm in matlab, MatrixExp in wolfram mathematica, exponential in maple and matrixexp in maxima, which you can access from SMath:



mat-exp.sm (13 KiB) downloaded 68 time(s).

So I guess if it is right for the developers of maxima, maple, mathematica and matlab to distinguish between both functions and to have specific instructions for each of them, then doing so in SMath is right, regardless of what the developers of mathcad think.

Best regards.
Alvaro.

Wrote

Hi Cornel. The exponential function is a well-defined function from the complex plane into the complex plane. A possible extension to its domain and range being square matrices analogous to the ordinary exponential function can be defined as e^A = sum(A^k, k=1...infinity). And notice that this is valid only for square matrices, not for the general case.

In general, the other CASs have special functions for this extension of the exponential function: expm in matlab, MatrixExp in wolfram mathematica, exponential in maple and matrixexp in maxima, which you can access from SMath:



mat-exp.sm (13 KiB) downloaded 68 time(s).

So I guess if it is right for the developers of maxima, maple, mathematica and matlab to distinguish between both functions and to have specific instructions for each of them, then doing so in SMath is right, regardless of what the developers of mathcad think.

Best regards.
Alvaro.

Ok, understood. This was the thing I was looking for. Thank You.

Wrote

In general, the other CASs have special functions for this extension of the exponential function: expm in matlab, MatrixExp in wolfram mathematica, exponential in maple and matrixexp in maxima, which you can access from SMath:

It seems there is also MatrixExponential in newer maple versions.
I tried to solve this problem using maple plugin by its library with(LinearAlgebra) command in maple, but couldn't prevail.
Old LinearAlgebra library lacks this particular command. Then you posted this solution.

Regards

If it were possible to update from maple 6 to the latest version of maple...then would be great to stay up to date with the latest maple engine and with his latest available capabilities, but i understood that this is not possible..right?

It's possible, but not as part of a plugin. I don't use maple often, so I'm too lazy to spend time on it.

Wrote

It's possible, but not as part of a plugin. I don't use maple often, so I'm too lazy to spend time on it.

But how to use then the latest maple engine If it's possible?

From my point of view If someone can make possible to use every time the latest version of maple engine in SMath then it would rise a lot SMath


And If You dont use often maple 6, then what you use? Maxima?

@uni there is also wolfram engine for developers FREE to use...but how to integrate this in SMath?

See below:

https://writings.stephenwolfram.com/2019/05/launching-today-free-wolfram-engine-for-developers/

And this wolfram engine for developers it's updated as latest wolfram mathematica engine, even though the article is from 2019

Maybe someone can announce, call or tell somehow to the SMath owner to integrate wolfram engine in SMath..