MATLAB: Puzzling syntax: 2:4:6:8:10:12

puzzlersyntax

Dear Matlab-profis and beginners,
What do you expect as result of this:
a = 2:3:4:5:6:7
And this:
b = 2:3:4:5:6:7:8
What reasons do you have for your assumptions?
Letting Matlab find the results is too easy. But even if you do, do you have good arguments for the results? Btw, The results are equal for 6.5, 2009a and 2011b.

Best Answer

The documentation lists the colon operator as having the 6th highest precedence and says that
Within each precedence level, operators have equal precedence and are evaluated from left to right
What is not clear from the precedence documentation is if a:b:c has one or two colon operators. The documentation for the colon operator says
To generate a series that does not use the default of incrementing by 1, specify an additional value with the colon operator (first:step:last).
which suggests to me that a:b:c is a single colon operation (I think this is probably the weakest aspect of the documentation).
The documentation of the colon function says
COLON(J,K) is the same as J:K and COLON(J,D,K) is the same as J:D:K.
I interpret "the same" to me that the converse is also true and that J:K is the same as colon(J,K) and J:D:K is the same as colon(J,D,K).
Based on this I would assume a left to right substitution of triplets.
a = 2:3:4:5:6:7
  = colon(2,3,4):5:6:7
  = 2:5:6:7
  = colon(2,5,6):7
  = 2:7
  = colon(2,7)
  = [2,3,4,5,6,7]
b = 2:3:4:5:6:7:8
  = colon(2,3,4):5:6:7:8
  = 2:5:6:7:8
  = colon(2,5,6):7:8
  = 2:7:8
  = colon(2,7,8)
  = 2
For the additional case given in the comment to IA's answer of 2:3:6:7 we need a little more of the documentation
If you specify nonscalar arrays, MATLAB interprets j:i:k as j(1):i(1):k(1).
a = 2:3:6:7
  = colon(2,3,6):7
  = [2, 5]:7
  = colon(2, 7)
  = [2,3,4,5,6,7]
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