## Saturday, November 5, 2016

### PowerShell Modulus operator is a remainder operator, not a modulus operator

The percent sign in PowerShell is known as the modulus operator. But it is in fact not a modulus operator. It is a remainder operator.

What’s the difference? Most of the time, nothing.

If both operands are positive, modulus and remainder are equivalent.

16 modulo 7 is 2, and the remainder of 16 divided by 7 is 2.

In some calculations used to find an index in a PowerShell array using negative operands, modulus and remainder are mathematically different, but functionally equivalent.

Sometimes in PowerShell, the “wrong” result works anyway.

For example, given the following function:

 function Get-DayofWeek ( $StartDay = 0,$Offset = 0 ) { $Weekdays = "Sun", "Mon", "Tue", "Wed", "Thu", "Fri", "Sat"$EndDay = ( $StartDay +$Offset ) % 7 return $Weekdays[$EndDay] } Get-DayofWeek -StartDay 0 -Offset  16 Get-DayofWeek -StartDay 0 -Offset -16

We are using % to calculate the index to the correct day of the week in the array. If the starting day (day zero) is on Sunday, day 16 will be on 16 modulo 7, or 2, which points to Tuesday.

If we count backwards 16 days from Sunday, -16 modulo 7 is 5, which points to Friday.

But % doesn’t do modulo, it finds the remainder, and the remainder of -16 divided by 7 is -2.

But it works anyway. In PowerShell, $WeekDays[5] points to the sixth element from the start of the array, and$WeekDays[-2] points to the second element from the end of the array. In an array with 7 elements, both of these point to the same element.

Modulus and remainder handle negative dividends differently

If we need to use the results from negative operands anywhere other than as the index of an array, we need to be aware of the difference between modulus and remainder, and understand that % performs a remainder operation.

For positive operands, modulus and remainder follow the same pattern.

 % Dividend Divisor Modulus Remainder 7 3 1 1 6 3 0 0 5 3 2 2 4 3 1 1 3 3 0 0 2 3 2 2 1 3 1 1 0 3 0 0

The difference is in what happens to that pattern when we carry on past zero.

For modulus, the pattern continues unchanged.

For remainder, the pattern reverses, and becomes negative.

 % Dividend Divisor Modulus Remainder 7 3 1 1 6 3 0 0 5 3 2 2 4 3 1 1 3 3 0 0 2 3 2 2 1 3 1 1 0 3 0 0 -1 3 2 -1 -2 3 1 -2 -3 3 0 0 -4 3 2 -1 -5 3 1 -2 -6 3 0 0 -7 3 2 -1

Changing the sign of the divisor does not change the result of either modulus or remainder.

 % Dividend Divisor Modulus Remainder 7 -3 1 1 6 -3 0 0 5 -3 2 2 4 -3 1 1 3 -3 0 0 2 -3 2 2 1 -3 1 1 0 -3 0 0 -1 -3 2 -1 -2 -3 1 -2 -3 -3 0 0 -4 -3 2 -1 -5 -3 1 -2 -6 -3 0 0 -7 -3 2 -1

## Wednesday, October 12, 2016

### Azure Automation hybrid workers require only outbound port 443

Implementing Azure Automation (AzA) hybrid workers is now easier. While it is a technical improvement that is streamlining implementation, it is mostly the politics of implementation that have been streamlined.

Last year the Azure Automation team introduced so-called hybrid workers. With this feature, the AzA database and management services still reside in the Microsoft cloud, but some or all of the work can be performed on servers in your datacenter (or in a different cloud) and which you control.

One of the original challenges to implementing hybrid workers was all of the ports that had to be opened between the hybrid workers and the management components in the cloud. Much of it was easy. The hybrid worker could be fully configured and reporting to the core of the management system using only port 443. But to actually pick up work, the hybrid workers needed to talk to the Azure Service Bus, which required opening up a whole lot of ports to a whole lot of IP addresses. Some network security teams get cranky when you ask them to do that.

Recent updates modified the network requirements, and radically simplified the port requirements.

Now, the only hole that needs to be opened on the corporate firewall is outgoing TCP on port 443. It is now a simple, well understood, reasonable request to the network security team. And in most companies, that connectivity is already in place.

Much easier.

## Monday, September 12, 2016

### Notes on Parker chains

This is a reponse to one of Matt Parker’s videos on his StandUpMaths YouTube channel at https://www.youtube.com/watch?v=LYKn0yUTIU4

Matt talked about a function defined for non-negative integers wherein the result is the number of letters in the name of the number.

For example,

F(23) = 11 (11 letters in “twenty three”)
F(11) = 6 (6 letters in “eleven”)
F(6) = 3 (3 letters in “six”)
F(3) = 5 (5 letters in “three”)
F(5) = 4 (4 letters in “five”)

And that’s the end of the Parker chain, because F(4) = 4.

In English, all starting points eventually lead to 4.

Matt showed us that 23 is the lowest number that starts a Parker chain with a length of 6.

I am defining C_n as the lowest number starting a Parker chain of length n using the Parker algorithm.

C_6 = 23

Matt challenged us to find C_7, and to find any other interesting information about this algorithm, and to post any such findings as a comment on his video. I got a little bit carried away, and wrote a little more than will fit comfortably in a comment.

Assuming use of the short scale (for now) and not using the word “and”.

The longest number name under 10^30 is 373,373,373,373,373,373,373,373,373,373, or three hundred seventy-three octillion three hundred seventy-three septillion three hundred seventy-three sextillion three hundred seventy-three quintillion three hundred seventy-three quadrillion three hundred seventy-three trillion three hundred seventy-three billion three hundred seventy-three million three hundred seventy-three thousand three hundred seventy-three, with 321 alphabetic characters.

Therefore, in the longest possible Parker chain whose first number is 10^30 or lower, the second number in the chain is 321 or lower. All Parker chains starting with 321 or lower have 6 or fewer numbers in the chain. Therefore, the longest possible Parker chain whose first number is 10^30 or lower has a maximum of 7 numbers.

The first Parker chain of 7 numbers is 323, 23, 11, 6, 3, 5, 4.

C_7 = 323

How strange is that? Out of all of the possible starting numbers 30 digits or less, you only have to try as high as 323 to find an example Parker chain of the maximum possible length in that range.

As others have noted, the first Parker chain of 8 numbers has a starting number of just a bit over 10^30.

C_8 ~~ 10^30

That’s a rather large gap.

Which makes me wonder, how large is the next gap?

Within each power of a thousand, the longest number name is approximately 32 letters longer than the longest number name in the previous power of a thousand. That’s an additional 24 letters for “three hundred seventy-three” and an average of 8 letters for the appropriate “*illion” for that power.

(There are many other, possibly infinite, numbers with the same name length, but a number with “373” repeating will be the lowest number of that name length.)

From that we can derive a simple formula to find the approximate location of the start of the next longer Parker chain.

C_(n+1) has as least C_n letters in its name. The first number with C_(n+1) letters in its name will be approximately

C_(n+1) ~~ 10^(3/32 C_n)

We can see this works for C_7 = 323.

C_8 ~~ 10^(3/32 323)
C_8 ~~ 10^30

And we can use that to estimate the size of the next gap.

At this scale, when C_n in is the form 10^x, we can simplify the approximation.

C_(n+1) ~~ 10^(3/32 10^x)
C_(n+1) ~~ 10^(1/10 10^x)
C_(n+1) ~~ 10^(10^(x-1))

C_9 ~~ 10^(10^(30-1))
C_9 ~~ 10^(10^29)

That’s quite a gap.

Now we’re at a scale where we can simplify the approximation even farther, as our x in 10^x is so large that subtracting one from it is a trivial difference. So for very large numbers:

C_(n+1) ~~ 10^(C_n)

From here on out, the gaps are easy to predict.

C10 ~~ 10^(10^(10^29))
C11 ~~ 10^(10^(10^(10^29)))
C12 ~~ 10^(10^(10^(10^(10^29))))
C13 ~~ 10^(10^(10^(10^(10^(10^29)))))

Now you may have noticed I made an assumption early on that you might take issue with. I am assuming an average of 8 letters for the name of each group of three digits, the so-called illion word. But it is actually reasonable.

As going to C_9 takes us well beyond the range of numbers in any existing number naming system, we need a hypothetical number naming system that can handle these ridiculously large numbers. A reasonable extension of existing systems is possible.

To get up to 10^(10^29), we can’t just keep making up new illion words. We’ll run out of possibilities long before we get there. So we need something different. We already have something that can work, the so-called Long System previously used in Britain and still used in the rest of Europe and parts of Canada. We just need to follow it to a different logical conclusion than was done in the past.

Here is the Short System, used in the US, Britain and parts of Canada.

Short system
1000^010^0
1000^(2^0)1000^110^3thousand
1000^(2^1)1000^210^6million
1000^310^9billion
1000^(2^2)1000^410^12trillion
1000^510^15quadrillion
1000^610^18quintillion
1000^710^21sextillion
1000^(2^3)1000^810^24septillion
1000^910^27octillion
1000^1010^30nonillion

Compare that to the Long System. I like the long system. Mathematically it is more logical, with major names based on powers of one million. And we can use it for much larger numbers without needing to add new words.

Short systemLong system
1000^010^0
1000^(2^0)1000^110^3thousandthousand
1000^(2^1)1000^210^6millionmillion
1000^310^9billionthousand million
1000^(2^2)1000^410^12trillionbillion
1000^510^15quadrillionthousand billion
1000^610^18quintilliontrillion
1000^710^21sextillionthousand trillion
1000^(2^3)1000^810^24septillionquadrillion
1000^910^27octillionthousand quadrillion
1000^1010^30nonillionquintillion
1000^1110^33thousand quintillion
1000^1210^36sextillion
1000^1310^39thousand sextillion
1000^1410^42septillion
1000^1510^45thousand septillion
1000^(2^4)1000^1610^48octillion
1000^1710^51thousand octillion
1000^1810^54nonillion
1000^1910^57thousand nonillion
1000^2010^60

But that only gets us twice as far, and we need to go much, much farther. Here is my hypothetical Really Long System. It starts the same as the long system, but more than one pattern can start from there, and I took the one less traveled by.

Short systemLong systemReally long system
1000^010^0
1000^(2^0)1000^110^3thousandthousandthousand
1000^(2^1)1000^210^6millionmillionmillion
1000^310^9billionthousand millionthousand million
1000^(2^2)1000^410^12trillionbillionbillion
1000^510^15quadrillionthousand billionthousand billion
1000^610^18quintilliontrillionmillion billion
1000^710^21sextillionthousand trillionthousand million billion
1000^(2^3)1000^810^24septillionquadrilliontrillion
1000^910^27octillionthousand quadrillionmillion trillion
1000^1010^30nonillionquintillionthousand trillion
1000^1110^33thousand quintillionmillion trillion
1000^1210^36sextillionthousand million trillion
1000^1310^39thousand sextillionbillion trillion
1000^1410^42septillionthousand billion trillion
1000^1510^45thousand septillionmillion billion trillion
1000^(2^4)1000^1610^48octillionthousand million billion trillion
1000^1710^51thousand octillionquadrillion
1000^1810^54nonillionthousand quadrillion
1000^1910^57thousand nonillionmillion quadrillion
1000^2010^60thousand million quadrillion
1000^2110^63billion quadrillion
1000^2210^66thousand billion quadrillion
1000^2310^69million billion quadrillion
1000^2410^72thousand million billion quadrillion
1000^2510^75thousand trillion quadrillion
1000^2610^78million trillion quadrillion
1000^2710^81thousand million trillion quadrillion
1000^2810^84billion trillion quadrillion
1000^2910^87thousand billion trillion quadrillion
1000^3010^90million billion trillion quadrillion
1000^3110^93thousand million billion trillion quadrillion
1000^(2^5)1000^3210^96quintillion
vdots
1000^(2^6)1000^6410^99sextillion
1000^(2^7)1000^12810^102septillion
1000^(2^8)1000^25610^768octillion
1000^(2^9)1000^51210^1536nonillion

In the short system, with every new illion term added, we can count up through another power of a thousand.

In the long system, with every new illion term added, we can count up through another 2 powers of a thousand.

In the really long system, it’s an exponential growth rate. With every new illion term added, we can count up through the square of the previous word. That is, we double the number of powers of a thousand we can count through.

With this system, we only need 95 illion words (and a really long time) to count all the way up to 10^(10^29).

So this is a system that hypothetically would work.

In the table above, it looks like some of those names are quite a bit longer than 8 letters, but they are only used for a single group like that when talking about round numbers. For example, this number 1,000,000,000,000,000,000,000 would “one thousand million billion” but this number 1,002,003,004,005,006,007,008 would be “one thousand two million three thousand four billion five thousand six million seven thousand eight”

So with this system we do maintain an average of eight letters per power of a thousand group into very, very large numbers. Eventually we will be forced to start using longer illion words that will drive the average above 8 letters, but by then the approximate numbers we are describing will be so monstrous in size that the increase will be relatively trivial.

## Saturday, June 18, 2016

### Getting the current time from an NTP service using PowerShell

Recently I needed to be able to query the current time from an NTP service using PowerShell. I was surprised to find out that it wasn’t going to be easy.

There isn’t a simple-to-call way to do it. With modern Windows computers, you tell the operating system which NTP server to sync with, or let it sync with a domain controller or a Hyper-V host, and Windows does all of the doing automatically and invisibly.

But I was automating minimal configuration of thousands of brand new physical machines with a generic OS installed. My script needed to prepare them to successfully and securely talk to the system that would handle all of the configuration, domain join, etc. The challenge was the occasional new machine which, for whatever reason, had an internal clock that was far enough off that secure communications were being rejected. I wanted to add a simple piece of code that would query a corporate NTP service and set the system time, without modifying the machine’s NTP configuration.

After some searching, I found a script in the PowerShell Gallery name Get-NTPTime, written by Chris J Warwick. https://gallery.technet.microsoft.com/scriptcenter/Get-Network-NTP-Time-with-07b216ca

It’s a great script, but it outputs a lot more than I need, does a lot of work to create that output, is more precise than I need, and at over 500 lines (mostly comments) a bit too large to comfortably drop into my script.

So I heavily modified his script, ripping out everything I didn’t need, ripping out the high level of accuracy, and simplifying some of the syntax to make it easier for future engineers to support my script. The result is the reasonably concise function below.

There is no error handling in the function. It is presumed that error handling, if needed, will be handled at a higher level.

Our only parameter is a string with the (resolvable) name or IP address of the NTP service to query. We will assume the service is listening on port 123.

 Function Get-NtpTime ( [String]$NTPServer ) { We create an array of 48 bytes which we will use to hold our NTP request packet, and then reuse to hold the response packet. $NTPData    = New-Object byte[] 48

We populate the first byte with the request header.

 $NTPData[0] = 27 # Request header: 00 = No Leap Warning; 011 = Version 3; 011 = Client Mode; 00011011 = 27 We open a connection to the NTP service, setting timeouts so it doesn’t hang. $Socket = New-Object Net.Sockets.Socket ( 'InterNetwork', 'Dgram', 'Udp' ) $Socket.SendTimeOut = 2000 # ms$Socket.ReceiveTimeOut = 2000  # ms $Socket.Connect($NTPServer, 123 )

Then we send the request and receive the results. Both of the .Send() and .Receive() methods output the number of bytes sent or received. We don’t need that output, so we’ll send those to $Null. Setting$Null equal to the result is much faster than piping to Out-Null, as PowerShell doesn’t have to waste the time and resources creating and handling a pipeline to nowhere.

 $Null =$Socket.Send(    $NTPData )$Null = $Socket.Receive($NTPData )

Close the connection.

 $Socket.Shutdown( 'Both' )$Socket.Close()

The date/times in the response packet are in a weird epoch-based format. 4 bytes hold the number of seconds which passed between midnight of January 1, 1900, and the UTC time* represented. An additional 4 bytes hold a number which, when divided by 2^32, is an additional fraction of a second to a ridiculous precision.

In his version of this script, Chris uses two date/times in the response packet in conjunction with local times captured immediately before and after the query to calculate an extremely precise offset between the local system time and the NTP service time which even accounts for network latency.

I don’t need that level of accuracy; I just need to get it reasonable close. So instead of working with four time stamps, I am going to just use the first one in the response packet. And I am going to ignore the fraction of a second and any network latency. Most of the time, this will give me a time within one second of the NTP service time.

We can use the static .Net class [System.BitConverter] to convert the relevant 4 bytes into a single integer. We convert to UInt32 (unsigned integer) instead of Int32, because in this case the highest bit is set to one, and Int32 would interpret that as indicating a negative number rather than as part of the number itself. This gives us the number of seconds since 1/1/1900. (Who designs this stuff? Engineers are weird.)**

 $Seconds = [BitConverter]::ToUInt32($NTPData[43..40], 0 )

Lastly, we convert the number of seconds elapsed to the correct date time by creating a datetime object for 1/1/1900 and adding the seconds to it. Then we convert it from UTC to whatever the local time zone is, and return the result.

 ( [datetime]'1/1/1900' ).AddSeconds( $Seconds ).ToLocalTime() } Using our function to set the system time can be as simple as this.  Set-Date ( Get-NTPDateTime$NTPServiceIPAddress )

Here is how it looks all together.

 Function Get-NtpTime ( [String]$NTPServer ) { # Build NTP request packet. We'll reuse this variable for the response packet$NTPData    = New-Object byte[] 48  # Array of 48 bytes set to zero $NTPData[0] = 27 # Request header: 00 = No Leap Warning; 011 = Version 3; 011 = Client Mode; 00011011 = 27 # Open a connection to the NTP service$Socket = New-Object Net.Sockets.Socket ( 'InterNetwork', 'Dgram', 'Udp' ) $Socket.SendTimeOut = 2000 # ms$Socket.ReceiveTimeOut = 2000  # ms $Socket.Connect($NTPServer, 123 ) # Make the request $Null =$Socket.Send(    $NTPData )$Null = $Socket.Receive($NTPData ) # Clean up the connection $Socket.Shutdown( 'Both' )$Socket.Close() # Extract relevant portion of first date in result (Number of seconds since "Start of Epoch") $Seconds = [BitConverter]::ToUInt32($NTPData[43..40], 0 ) # Add them to the "Start of Epoch", convert to local time zone, and return ( [datetime]'1/1/1900' ).AddSeconds( $Seconds ).ToLocalTime() } * Irrelevant bonus fact: We use the abbreviation UTC because it is wrong in two different languages. In English, it should be CUT for “coordinated universal time”. In French, it should be TUC for “temps universel coordonné”. We compromised by agreeing to be universally uncoordinated with our time abbreviations. ** Irrelevant bonus fact 2: Storing date/times by using an Epoch-based system has been a common solution. For example, the .Net datetime objects we use in PowerShell store the number of ten millionths of a second since midnight of January 1 of the year 1. We lost a space probe to a short-sighted epoch-based system. On August 11, 2013, shortly after midnight, NASA's Deep Impact space probe, travelling between comets, stopped talking to us, because it was 2^32 tenths of a second after 1/1/2000. The clock rolled over, the probe thought it was suddenly 13 years earlier and it wasn’t due to check in again for over a decade. ## Thursday, April 14, 2016 ### Call for a Microsoft PowerShell Czar This is an open plea to Microsoft for the creation of the internal position of PowerShell Czar. There is a PowerShell UserVoice suggestion to open source the AD module that is quickly accumulating votes. https://windowsserver.uservoice.com/forums/301869-powershell/suggestions/13350033-open-source-the-activedirectory-powershell-module This is not users requesting a feature or a fix. This is exasperated users giving up hope that Microsoft will make basic improvements to the product. There are too many teams at Microsoft that years ago came out with a reasonable (for the time) first version of the PowerShell module for their product, but have never followed up with v2. When they release a new version of their product, they make some minor changes to the PowerShell module that are related to new features in the core product. But they don’t understand that the PowerShell module is an integral part of their product, deserving of and requiring the same continuous improvement as the rest of their product, and it never matures past the level of barely good enough for a first release. It has been ten years now, and too many teams at Microsoft have demonstrated that left to their own devices, they are not willing or able to produce the quality of PowerShell integration that we need. Microsoft needs to create a PowerShell Czar. They can, of course, replace that silly title with one of the standard Microsoft silly titles, but the role would be the same. The Czar would have the power to write and enforce PowerShell standards across the organization. The Czar would prevent releases from releasing if the PowerShell isn’t ready. The Czar would require teams to fill gaps in the PowerShell interface. The Czar would prevent desktop teams from locking in a pre-release version of PowerShell. The Czar would prevent teams from using non-standard parameter names and cmdlet names that are so long they wrap around the screen. The Czar would require implementations that are intuitive to PowerShell scripters, rather than to product architects. The Czar would require all MSDN articles about .Net objects to have PowerShell examples. The Czar would require MSDN articles about PowerShell .Net object be as complete as articles about other .Net objects. The Czar would require fixes to .Net objects that break PowerShell functionality that depends on them. If Microsoft has another, less authoritarian way of accomplishing the same goals, fine, do it that way. But the current way is not working. This needs to be fixed. Microsoft, please make it happen. ## Monday, March 28, 2016 ### Sorting IP addresses in PowerShell, part 1, IPv4 Sorting IP v4 addresses is a pain. If they are strings, they sort typographically rather than numerically. $IPAddresses = @( '10.11.12.13' '10.11.102.3' '10.11.10.26' '10.11.10.252' ) $IPAddresses | Sort  10.11.10.252 10.11.10.26 10.11.102.3 10.11.12.13 If they are [ipaddress] objects, they do the same thing. The [ipaddress] does not have the built in methods that PowerShell would use to sort it, so PowerShell converts it to a string, and then sorts it typographically. $IPAddresses = @( [System.Net.IPAddress]'10.11.12.13' [System.Net.IPAddress]'10.11.102.3' [System.Net.IPAddress]'10.11.10.26' [System.Net.IPAddress]'10.11.10.252' ) $IPAddresses | Sort | Select IPAddressToString  IPAddressToString ----------------- 10.11.10.252 10.11.10.26 10.11.102.3 10.11.12.13 I have in the past come up with a variety of complex ways to do it. Here’s one.  # Function to convert dotted decimal notation to integer64 (e.g. - "255.255.255.0" to 4294967040) function ConvertDottedDecimalToInt64 ($DottedDecimal )     {     $DecimalParts =$DottedDecimal.Split( "." )     $Result = [int64]0 0..3 | ForEach {$Result += [int64]$DecimalParts[$_] * [math]::pow( 256, 3 - $_ ) } return$Result     } $IPAddresses = @( '10.11.12.13' '10.11.102.3' '10.11.10.26' '10.11.10.252' )$IPAddresses | Sort { ConvertDottedDecimalToInt64 $_ }  10.11.10.26 10.11.10.252 10.11.12.13 10.11.102.3 There is an easier way There is an object which can look like an IP address, which needs to be sorted like an IP address, and whose creators had the foresight to endow it with a .CompareTo() method, which is what PowerShell uses when it sorts things. The [System.Version] object is used to represent file and application versions, and we can leverage it to sort IP addresses simply. We sort on a custom calculation, converting the IP addresses to version objects. The conversion is just for sorting purposes. The output is the original input objects. $IPAddresses = @( '10.11.12.13' '10.11.102.3' '10.11.10.26' '10.11.10.252' ) $IPAddresses | Sort { [System.Version]$_ }

 10.11.10.26 10.11.10.252 10.11.12.13 10.11.102.3

The System namespace is the default namespace PowerShell searches for things, so we can leave that out and write it more simply.

 $IPAddresses | Sort { [version]$_ }

Or if we want to go the other way, and avoid aliases and positional parameters, we can say it this way.

 $IPAddresses | Sort-Object -Property { [System.Version]$_ }

## Wednesday, February 17, 2016

### Codependent simultaneous variable updates in PowerShell

I recently rediscovered the comma. There is always something more to learn in PowerShell. And not just the new big things. There are always little things that get missed or forgotten. I think I may have known about commas at one time, but did not find them of immediate use, so I forgot about them.

Specifically, I was reading an advance copy of chapter 1 of PowerShell in Action, Third Edition, by Bruce Payette and Richard Siddaway, and read that you can assign values to multiple variables at the same time in a single line by separating both the variable names and the values by commas.

 $A = 1$B = 2

You can do this:

 $A,$B = 1, 2

Most of the time, you would never do that. The first syntax is much more clear.

But there are two situations where this is useful. One is when a command naturally results in the multiple values you are looking to assign.

 $FQDN = "Server1.HQ.contoso.com"$FQDNArray = $FQDN.Split( ".", 3 )$ComputerName = $FQDNArray[0]$ChildDomain = $FQDNArray[1]$RootDomain = $FQDN[2] You can do this: $FQDN = "Server1.HQ.contoso.com" $ComputerName,$ChildDomain, $RootDomain =$FQDN.Split( ".", 3 )

Where it becomes really useful, is when you have to make simultaneous codependent changes to your values.

For example, if you need to swap two values, instead of this

 $Temp =$A $A =$B $B =$A

You can do this:

 $A,$B = $B,$A

Or let’s say you are working on a script for calculating Mandelbrot’s set. You will have a function that sets complex number Z to Z squared plus C. As a complex number, Z has both a real component and an imaginary component. In your calculation, you need to use the old value of the real component to calculate the new value of the imaginary component, and you need the old value of the imaginary component to calculate the new value of the real component.

 $Newr =$Zr * $Zr -$Zi * $Zi +$Cr $Newi = 2 *$Zr * $Zi +$Ci $Zr =$Newr $Zi =$Newi

You can do this:

 $Zr,$Zi = ( $Zr *$Zr - $Zi *$Zi + $Cr ), ( 2 *$Zr * $Zi +$Ci )

(And yes, I know there are .Net object that will let you work with complex numbers even more easily than that, but this is the conceit of the example, so deal with it.)

## Tuesday, January 19, 2016

### Answer to PowerShell riddle 2

Spoilers below! Obviously. Go here for the posing of the two riddles.

Riddle 2

 If ( $y.$y($y,$y.$y($y)) -eq 0 ) { <# What is $y? #> } It is a true equality; no type conversion is performed for the comparison. Answer to riddle 2 In PowerShell, when calling a method or property of an object, the name of the method or property can be represented by any expression that evaluates to be the name of the method or property.$y is a string and the name of a string method. We call it twice, so let’s simplify and pull out the nested call.

 $z =$y.$y($y ) $y.$y( $y,$z ) –eq 0

So we can see that it must be a method that returns a number. It must be able to take a single string as a parameter, or a string and number.

There are a couple string methods that meet those requirements, but only one that results in the full equation being true, that is, only one that results in a zero in our usage.

 $y = 'IndexOf' The index (location) of the string ‘IndexOf’ within the string ‘IndexOf’ is 0. The index of the string ‘IndexOf’ within the string ‘IndexOf’ starting the search at location 0 is 0. $z = 'IndexOf'.IndexOf( 'IndexOf' ) 'IndexOf'.IndexOf( 'IndexOf', 0 ) –eq 0

All together:

 'IndexOf'.IndexOf( 'IndexOf', 'IndexOf'.IndexOf( 'IndexOf' ) ) -eq 0

### Answer to PowerShell riddle 1

Spoilers below! Obviously. Go here for the posing of the two riddles.

Riddle 1

 If ( $x.$x($x,$x) –eq $x ) { <# What is$x? #> }

It is a true equality; no type conversion is performed for the comparison.

In PowerShell, when calling a method or property of an object, the name of the method or property can be represented by any expression that evaluates to be the name of the method or property.

$x is a string and the name of a string method. It must be a method that can take two string parameters. And we are looking specifically for one that would leave$x essentially unchanged.

 $x = 'Replace' If we replace the string ‘Replace’ with the string ‘Replace’ anywhere it appears in the string ‘Replace’, we get the string ‘Replace’.  'Replace'.Replace( 'Replace', 'Replace' ) -eq 'Replace' Riddle 2 So with that as big hint, can you figure out the second riddle?  If ($y.$y($y,$y.$y($y)) -eq 0 ) { <# What is$y? #> }

Again, it is a true equality; no type conversion is performed for the comparison.

### PowerShell riddles

PowerShell riddle 1

 If ( $x.$x($x,$x) –eq $x ) { <# What is$x? #> }

It is a true equality; no type conversion is performed for the comparison.

PowerShell riddle 2

 If ( $y.$y($y,$y.$y($y)) -eq 0 ) { <# What is $y? #> } Again, it is a true equality; no type conversion is performed for the comparison. Big hint to both riddles. ### Big hint to both PowerShell riddles PowerShell riddle 1  If ($x.$x($x,$x) –eq$x ) { <# What is $x? #> } It is a true equality; no type conversion is performed for the comparison. PowerShell riddle 2  If ($y.$y($y,$y.$y($y)) -eq 0 ) { <# What is$y? #> }

Again, it is a true equality; no type conversion is performed for the comparison.

Big hint

In PowerShell, when calling a method or property of an object, the name of the method or property can be represented by any expression that evaluates to be the name of the method or property.

These all result in 3.

 @( 1, 2, 3 ).Count @( 1, 2, 3 ).'Count' @( 1, 2, 3 ).\$( [char]67 + 'ou' + "NT".ToLower() )

Answer to riddle 1, which is a hint to riddle 2.