In the lecture, you show the full local names on a few occasions. How is that done? For instance x=1; y=3, Plot{ x, {x,0,y}; x might show as x=1; y=3, Plot{ x$12345, {x$12345,0,y}; x clearly showing the localize, temporary definition of the x inside the Plot... How do you switch between the two views of the cell?

No, mostly made up, it was in the live presentation, but I don't think shows in the notebook. I assume it a front end maybe cell type or something. The presenter switch back and forth but I didn't hear if he indicated how. I was thinking it was a plot, but not sure - just some expression that had a mixture of localized and global in the expression.

In the last session, I mentioned that Alternatives (a pattern object) and Or (a function) are not interchangeable. Here's an example to demonstrate how they differ.

Consider trying to extract all of the cases from a list that are either 2 or True. Using Alternatives (|) gives the correct result:

Cases[{1, 2, 3, True, 4}, 2 | True]
(* {2, True} *)

However, using Or (||) gives an incorrect result:

Cases[{1, 2, 3, True, 4}, 2 || True]
(* True *)

This is because Or immediately evaluates if any of its arguments resolve to True or False. In this case, 2||True evaluates to True, so Cases only picks out the items that match True.

Wow! Note that it needs 13.3 to evaluate PlotHighlighting -> None, If you delete that statement it works with 13.2

Hi Hubert, your questions can be answered with overloading – something we will be covering in today's session (Extending Capability).

To solve (c), you can use OrderlessPatternSequence, and to solve (b), you can use Condition (/;). Both of these were covered in the first session (The Basics). To solve (a), you can use Message, which will be covered in the fourth session (Error Handling).

Here's some code to get you started:

ClearAll[getClass];

getClass::orderTooLow = "The order you have provided (`1`) is too low. It must be an integer greater than 2.";
getClass::badArgs = "Bad arguments. getClass takes exactly 2 arguments: an 'order' and a 'cycle'. The order must be an integer greater than 2 and the cycle must be a valid permutation cycle.";

(* Main definition: *)
getClass[
    OrderlessPatternSequence[
     order_?IntegerQ,
     cycle_?PermutationCyclesQ
     ]
    ] /; order > 2 := (* Your function *);

(* Order provided is too low: *)
getClass[
   OrderlessPatternSequence[
    order_?IntegerQ,
    cycle_?PermutationCyclesQ
    ]
   ] := (
   Message[getClass::orderTooLow, order];
   $Failed
   );

(* Arguments provided are either invalid, too numerous or too few: *)
getClass[badArgs___] := (
   Message[getClass::badArgs];
   $Failed
   );

You can add more definitions / error messages to handle more cases.

P.S. – you seem to have a lonely p in your function definition.

Any reference of how to order/place the functions in a mathematica packages , context etc, will be useful.

Thanks! That's interesting. Just curious: Where in the vast warehouse of Documentation files would I find this little factoid?

Carl

Thanks for first lecture. I am interested in learning more about sequences. Your introduction is difficult for me to apply to a sequence of mathematical operations. I want to write a function to accept pullback metrics and compute the sequence as a parameter varies. Any guidance/suggestion would be appreciated. Larry

Excellent first session!