@NYK Ah, what exactly do you mean by "type in a subspace"? The canonical representation of a subspace is a basis. Most subspaces cannot be represented by a single (scalar) equation. If you want to work directly with the equation, there's this:

Student:-LinearAlgebra:-NullSpace(
     Student:-LinearAlgebra:-GenerateMatrix(
          [2*x-3*y+6*z], [x,y,z]
     )[..,1..-2]
);

@Chia Matrices can use a very large amount of memory. Making a copy of a Matrix necessarily doubles that memory usage. In-place operation avoids that.

@Chia The print commands print the four numbers. The output of the map command is the last line only.

@Chia Since an expression sequence cannot contain NULLs, the four NULLs which are the outputs of the print commands collapse to a single NULL expression sequence. When this expression sequence is turned into a list, it is the empty list, represented as [].

@Chia I am not getting your point. What is the inconsistency? Note that the numbers printed are the side-effect results of the four print commands, and the Vector of NULLs is the output of the map command. Also note that a Vector can contain NULL entries but an expression sequence cannot. The expression sequence can be NULL, but it cannot contain NULLs.

@lemelinm I notice that the first value in your dataset is 100404, which is an extreme outlier, more than 60 standard deviations from the mean of the others. My guess is that this was transcribed wrong, and it should be 100484. If I make that change, then the standard deviation is 1.289, which may have been incorrectly rounded to 1.28. So, please check whether you entered the first datum correctly.

Note that there is a difference between RMS and RMS deviation. You have used both terms in this post. I am certain that you mean RMS deviation.

@JEBland When dsolve({sys1, inits}) gives NULL output, it usually means that it was unable to find a symbolic solution; it is not usually an indication of user error.

@lemelinm I did not try the worksheet.

To cut and paste: Select the column of data from the post with the mouse. Hit Control-C (that's the "cut"). Place your cursor in a Maple (Standard) worksheet. Hit Control-V. That's all there is to it.

@Thomas Richard Yes, that's what I was refering to.

Please don't change a Question after an Answer has been given! Make a new Question instead. I have an answer to your question about the error plot, but I won't give it until you put back the original Question.

@lemelinm According to the Wikipedia page "Root-mean-square deviation", for a dataset it is the same as the standard deviation. But the standard deviation of your dataset is 10.906, not 1.28. So what is your formula for RMS deviation?

Note that you can cut and paste your dataset directly into a Maple worksheet, and it thus becomes a 55x1 Matrix. There's no need to use file I/O for such a small dataset.

@casperyc Yes, a seq is usually a little faster than the corresponding for loop.

@mehdi jafari Since the stats package is deprecated, you might as well use Statistics:-QuadraticMean.

What do you mean by exporting? Do you want the data written a file in two columns: the first coordinate value and the second coordinate value? Note that your plot data exists in tabular form before you plot it, so you don't need to "extract" it from the plot. The data is simply

[seq([k[i],cos_phi2[i]],i=0..number_of_points)]

@mehdi jafari evalr is surely the correct thing to use. Indeed, the vote up is mine. If you use lprint to look at the internal structure of the objects generated by the Tolerances package, you will see that they are all of the of the form INTERVAL(........), which are precisely the things that evalr is for. I just find it amazing that there is no example of this on the page ?Tolerances and no mention of the use of INTERVAL.

For example, using the code in the original Question, take a look at lprint(Phi). Then look at lprint(evalr(Phi)).