[WSG21] Daily Study Group: programming tutorials

Good video! Interestingly, when we touched the "weighting" approach to Pi, and the "atomic precision", it was actually about the atomic plane, similar to a grid displayed in the video. You have to draw a circle in such a plane (How? :)) and them to decide which atoms are in and which are out...sort of. And, funny to say, the Planck constant will likely determine the corresponding precision of Pi. So, it seems to me that the discussion in video has a straight "atomic analogy"...

In physics, this realm of questions was wonderfully outlined by Eugene Wigner (if you did not have a chance, please check it: https://www.maths.ed.ac.uk/~v1ranick/papers/wigner.pdf "THE UNREASONABLE EFFECTIVENSS OF MATHEMATICS IN THE NATURAL SCIENCES". )...

Best regards.

Pi in terms of Gaussian numbers and the distribution of primes (it has the feel of Monte-Carlo without RGNs) :)

https://tinyurl.com/p54hjtee

So it seems that pi is not a good random number generator but the fact that you can generate pi using random number techniques (monte carlo method) still boggles my mind.

OH, GOOD! I was wondering. Thanks, Abrita!

Did anybody get the NB files for the Review III session (August 20)?

We plan to post the notebook from the final review session soon. Sorry for the delay.

I agree that the output is cooler with ListLinePlot3D, but I didn't see how to make it match the expected Output.

I could certainly be wrong, but... In the exercises, #2, I don't think you meant ListLinePlot3D. I got the correct answer (per auto-grader) using another function. Ron

There seem to be two possibilities: either the expected result (the picture) was correct while the proposed function was wrong, or vice versa. In any case, trying to solve under both assumptions was good for learning. The closest I could get under the first scenario (trying to reproduce the original plot using ListLinePLot3D) was by setting "Joined -> False" in ListLinePlot3D , which turned lines into points.

In my humble opinion, the original ( with the dots) picture is clear and instructive, while the second is beautiful, impressionistic and hardly interpretable. In combination with the story, it can make a nice NFT. Any way, thank you for the wonderful brain teaser. The errors like this must be included by design! PS. By the way, while playing with the functions, try using the "plane" version ListLinePlot [list, ColorFunction -> "Rainbow"] (both with "Filling->Bottom", shown below, and without it *), Aren't they nice?! "? :)

There were several unsatisfactory answers (IMO) given in yesterday's session.

I had asked if resetting \ $`Line` erased the history entries, or if they persisted until a new entry was evaluated with the `In[]` number. The instructor didn't really answer the question at all (perhaps he didn't understand what I was asking) and simply reiterated that setting \$Line caused the In[] numbers to start again from that value. In a similar vein, someone had asked (I think) about measuring the amount of memory tied up in history entries and did not get a relevant answer.

In any case, for those who may be interested, experimentation shows that changing \$Line does not immediately erase any history entries. And I think an estimate of the amount of space used by previous results can be obtained by

Total[ByteCount /@ Out[Range[$Line - 1]]]

(Out[\$Line] itself has to be excluded to avoid recursion.) But I couldn't figure out how to find the space occupied by the In[] entries, given that I don't actually want to reevaluate them.

Which leads me to mention the third poor or missing reply yesterday. Someone suggested that the correct answer to Poll question 2 "How would you evaluate a previous input?" was not in fact "d. All of the above", as answers b. and c. merely retrieve a previous result, rather than reevaluating the expression that produced it. I agree completely. As stated, the answer should be "a. In[-k] for the input k lines back". Of course In[n] for the specific line n also works, as does re-evaluating the cell in question as suggested in answer e.

Issue with WorkBench installation ;

For some reason, Eclipse does not show the "Wolfram Workbench webMathematica". I only see the "Wolfram WorkBench core". Tried to add a path to my local Mathematica, but Eclipse does not accept it. Please, advise.

Michael, we have requested Support to get back to you on this over email.

Pursuant to my question during today's session about why Remove[Global`square] and Remove[Global`fun1] were said to be necessary, I experimented with leaving it out. I tried the following extracts from the lesson notebook, starting with a fresh kernel:

In[1]:= Begin["mathOperations`"];
        square[x_] := x^2
        End[];
In[4]:= $Context (* current context *)
        square[10] (* returns unevaluated since the current context is not mathOperations` *)
        mathOperations`square[10]
Out[4]:= Global`
Out[5]:= square[10]
Out[6]:= mathOperations`square[10]
In[7]:= PrependTo[$ContextPath, "mathOperations`"];
In[8]:= square[10]
Out[8]:= 100

Although a Global`square did indeed exist, presumably created by the reference to the undefined square by In[5]:

In[9]:= Names["Global`*"]
Out[9]:= {Global`square}

But as observed, the short name square still refers to the function we created, presumably because mathOperations occurs in $ContextPath before `Globals`. Hence the Remove[] call in the original notebook was just an act of excess caution. Does this seem right?

This is about the question 8 of the Test 2: Which attribute of Plot causes it to return an error when the following expression is evaluated? Plot[Integrate[x,x],{x,-10,10}]: (a) HoldRest, (b) HoldFirst, (c) HoldAll, (d) Hold Pattern

To avoid the error, the function Integrate[x,x] can be evaluated to 0.5 x^2 before x is allowed to vary. This can be done, e.g., by switching to Plot[Evaluate[Integrate[x,x]], {x,-10,10}]. However, the question suggests to focus on the (alleged) attribute(s) of the Plot. Attributes[Plot] does not include any of the suggested choices (a)-(d). I would appreciate any possible hints that won't compromise the integrity of the Test.

The documentation for Plot should help https://reference.wolfram.com/language/ref/Plot.html Look under "Details and Options".

Hi Peter

A location within

EntityValue[Entity["GeographicRegion", "World"], "Polygon"]

can be below sea level. e.g. Death Valley, Dead Sea, ... An alternative approach is in the attached notebook - to avoid spoiler.

Quiz 1, Problem 8. None of the answers seem to be correct. Am I missing something?

In an earlier version of the quiz, the quotes were missing around ""too bee or not". The correctly formatted expressions should be:

StringCases["too bee or not", x_ ~~ x_]

StringCases["too bee or not", ("o" | "e") ..]

StringReplace["too bee or not", x_ ~~ x_ :> StringJoin[x, x]]

StringCases["too bee or not", ("o" || "e") ..]

Is there a relation between the attributes of a user-built function f (if none of attributes have been assigned to it), to the attributes of built-in functions included in f? And specifically, why Attributes[f3] returns {} if it does exactly what the Sum does?

f3[x_, y_] := Sum[x, y];
Attributes[f3] ={}..

Probably, the answer should be obvious: when M evaluates Sum, it deals with the attributes of Sum. But this still may trigger some extra question (say, about a possible conflicts between attributes assigned to f3, and the existing attributes of built in functions). Hence, I would appreciate your take on this issue. Thank you. M

Attributes[f3] returns an empty list {} because f3 itself has no attributes permanently set for it. If within the definition of f3, there are calls to some built-in functions, the attributes of the built-in functions will work independently on the inputs being provided to the built-in function itself, regardless of the original inputs to the user-defined function. Within the function definition everything will get evaluated according to the "Standard Evaluation Procedure" which will take into account the attributes of the built-in function. (This tutorial on "Evaluation of Expressions" may explain some of the process, and the concept of assigning attributes, a little more https://reference.wolfram.com/language/tutorial/EvaluationOfExpressions.html).

Thank you! This is a great help.

You can add the definition(s) to $UserBaseDirectory/Kernel/init.m.

The yellow box with the italic print is just one way of representing entity properties. Entity properties are also represented as plain strings within quotes. These string names for the properties are accessible from the auto-completion menu that comes up when you type in [" immediately following the entity. For example:

You can also get to the entire Wolfram Language interpretation of both Entity and the EntityProperty by typing in a natural language query after the = sign in an input cell:

and then hit enter to see the following:

An EntityProperty is always associated with an Entity. So if you are interested in a property, look at the documentation for the Entity you think it will be associated with. If I am interested in a property like "Literacy Rate", it would be a property I would associate with an Entity like a "country". So I could look within the "Properties" section at https://reference.wolfram.com/language/ref/entity/Country.html

Similarly "Elevation" sounds like a property associated with a mountain. So I could look for it at http://reference.wolfram.com/language/ref/entity/Mountain.html or type in :

Hope this helps.

I believe the author wrote out:

EntityProperty["City", "Area"]

and evaluated using Shift+Enter to get the output in a separate cell (to copy and paste) or selected the code snippet and evaluated in place from the menu Evaluation -> Evaluate in Place or shortcut keys Shift+Ctrl+Enter (Windows) or Cmd+Return (Macintosh).

If you hover over a formatted EntityProperty, it will show you the InputForm that you could write out in full, in the tootip.

How can I type the yellow-box form of a property? They appear italic in the example notebook, like "electric charge".

When I press ctrl+= and type elevation for example, I sometimes get a gray box that when confirmed turns into a string "Elevation". Sometimes I get "No Wolfram Language translation found." Never do I get a property that looks like what's in the example notebook.

An instructor answered that if you type EntityProperty["River", "Length"], then the property is printed in italic-yellow-box form like in the example notebook. Does that mean that the example notebook was written by evaluating EntityProperty and copy/pasting? What about "fertilizer production" which was used in the last example today, for which I don't know the entity class it applies to?

You can view the recordings on the series signup page here.

The link to the notebooks will be included in the reminder email.

UnitConvert would work as follows:

In[19]:= UnitConvert[Quantity[1, "SpeedOfLight"], "PlanckLength/second"]
Out[19]= Quantity[1.8549*10^43, ("PlanckLength")/("Seconds")]

In[18]:= UnitConvert[Quantity[1, "UniverseMass"], "PlanckMass"]
Out[18]= Quantity[7.*10^60, "PlanckMass"]

TargetUnits is an option available for use with visualization functions e.g. ListPlot

Symbolic computations can definitely be performed with Quantity expressions as described here: http://reference.wolfram.com/language/tutorial/SymbolicCalculationsWithUnits.html

The reason you get an empty list is because the == condition is failing. EntityValue[#,"Countries"] comes back as a list and so you never find a match for the list against the single entity of Entity["Country", "UnitedStates"]

Try instead:

Select[EntityList[EntityClass["NuclearReactor", All]], 
     MemberQ[EntityValue[#, "Countries"], 
       Entity["Country", "UnitedStates"]] &]

or

EntityList[
 FilteredEntityClass["NuclearReactor", 
  EntityFunction[c, 
   MemberQ[c["Countries"], Entity["Country", "UnitedStates"]]]]]

How do choose not as a condition with patterns? For example,

mylist={1,1.5,2,3,3.14,2.718}
list /. _! Integer :> "Real"

I was also wondering how to replace all integers with "Int" and all reals with "Real" in one line. I think there is a way to use replace with lists

mylist /. {_Integer, _Real} :> {"Integer", "Real"}

The previous code does not work. How would I use conditions and patterns to replace each element of string list equal to False with Style[False, Red] and each element of string list equal to True with Style[True, Green]?

stringlist={True,False,False,True,False,False,True,False,True,True,False}

Example Notebook->

Re-read your last question. I think this is what you were looking for

Style[#, If[#, Green, Red]] & /@ stringlist

I didn't see a recording for Day 2. Is there one?

Here is something to get you started:

Graph[{1 -> 2, 2 -> 3, 3 -> 1}, 
 EdgeShapeFunction -> 
  Function[{coord, edge}, 
   Tooltip[
    Triangle[{First[coord], Last[coord] + {0, 0.04}, 
      Last[coord] - {0, 0.04}}], {First@coord, Last@coord}]]]

The EdgeShapeFunction needs to be set to a pure function that will take the coordinates of the edge line and create something closer to your requirements. In the above example I created a triangle. The Tooltip is only intended to show what the inputs to the pure function look like when it tries to draw the edge.

Part of the answer to my question is that the trapezoid elements in GraphElementData are set up for use with vertices as shown here:

Table[EdgeTaggedGraph[{1 \[UndirectedEdge] 2, 2 \[UndirectedEdge] 3, 
   3 \[UndirectedEdge] 1}, VertexShapeFunction -> s, 
  VertexSize -> 0.2, PlotLabel -> Style[s, 9]], {s, 
  GraphElementData["VertexShapeFunction", "Rounded"]}]

https://wolfram.com/xid/0cpsizfbsjq8gq-lsz53w

The weekly quizzes will be announced on Fridays, and the exercises will be announced during the final week of the Study Group. Watch your email notifications for direct links to recordings, the quizzes and exercises, and additional resources.

Here is the series landing page, where you can see details and from where all session recordings will be linked: https://www.bigmarker.com/series/daily-study-group-programming-tutorials/series_details

The weekly quizzes will be announced on Fridays, and the exercises will be announced during the final week of the Study Group. Watch your email notifications for direct links to recordings, the quizzes and exercises, and additional resources.

For this Study Group, the certification refers to Wolfram Technology Certified Level 1 for proficiency in using the Wolfram Language. This Level 1 certification is equivalent to the one you can earn by taking the Wolfram Language Level 1 exam on the Wolfram U website.

I have never participated in a webinar like this. The study materials .nb downloads. Don't look familiar or readable. What am I supposed to do with them?

Right! Sorry for the error.