@vv Thanks. That explains why the suggestion of @C_R with the "style = line" works.

@Kitonum Thanks. So the algorithm behind the intersectplot is based on sign changes and that is why in this case it failed to plot the intersection of the first example. The spacecurve workaround is good, but it is possible to use it if one has a aprameterization of the intersection.

@C_R Thanks, I got your point, but since the plot is over real numbers, it is indeed a curve and not a surface. It would be a surface if it was over complex numbers. Compare x^2+y^2=0 over the reals and over the complex numbers. In one of them it is a point (0 dimension) and over the other one it is a curve (1 dimension).

@C_R Thanks. This works. But by any chance, do you know why without calling "style = line", the color option does not work?

@Joe Riel Thanks. This is a really good way, I like it.

@tomleslie You are right. After restarting the worksheet, it gives 6. I couldn't regenerate the 4 again. So I don't have any idea why it was 4 the first time in my worksheet.

@acer Thanks for the detailed explanation and the example.

@acer Thank you for the answer and it solved my issue. I understand the uneval quotes which I had tried before, but alone without the colon-dash it was not working here. Can I ask what the colon-dash is doing in this case? I know that colon-dash can be used for calling a procedure from a package, but what does it do in this scenario?

@Joe Riel Thanks. You're right. That was a mistyping by me and removing the extra 2, both give true ^_^

@Carl Love Thank you for the clarification, that was really educational for me, because now I can design my manually defined objects better.

@Joe Riel Thanks for introducing andseq, but just to be sure I got it right, should it be m = M or m in M? For example

test := MutableSet({ 1, 5, 8 }):
andseq( type( m, posint ), m in test );
andseq( type( m, posint ), m = test2 );

For the second line I get true, but for the third line I get false.

@acer Thanks for the update. Now I can read the previous comment. :)
"it is mot working for all" in fact is "it is not working for all" not what I thought the first time; "it is most working for all".

@acer Thanks for the good suggestion +1

@tomleslie Thanks. I just read the last part of your answer. Indeed the extra whitespaces were causing the error ^_^ Now everything works. It seems yesterday I wrote my usual 4 lines with extra whitespace in the last one, and then I kept copy-pasting them from that worksheet for my next tests.

@tomleslie Thanks, I fixed the typo for the directory, but that doesn't fix the issue. I tried these 4 lines several times for several works yesterday and I got the similar error. The example in the question is just designed for asking the question. So the typo was not the main problem ^_^ The post is edited now so you can see that my problem was not made because of a wrong directory.