That's Abstract Algebra, Holden. Yep, in fact, that is exactly what they meant by "Modern Algebra". It was condemned as "New Math".
I am very interested in that kind of thing. It's as though, if you wanted, you might invent your own field ...
I am going to upload another text version I completed before moving on to the next stage, where I alter the output.
I really like it the way it is, and I suppose I will have to give each version special names.
This version I really like even as I am doing the problems by hand. The way I have the output for different sections of the code gives me a great feeling when the form stands out, when the subtrahends all add up to nearly the original number.
Have you pasted any of this and run it online?
Do you still have that Mac? I'm sure, since it is Unix, it would have a GNU g++ compiler or could easily be installed via some kind of internal software manager of the OS.
You would rename the file to Sqrt_work.cpp, then
g++ -g Sqrt.cpp -o Sqrt
Then, to run, from that directory: ./Sqrt 7720.17 4
If you place Sqrt in your path, you can just type the command and arguments.
Eventually, if I ever think others might be interested in using this to teach themselves or others, I could make the version request the needed input rather than being command line driven.
Myself, I prefer typing the command with the parameters. If I were to leave it around for someone to inspect or explore, perhaps it would be better if the program took the initiative and requested the input, explaining to the user what it will do.
if a@b=a+b/2, a#b=a^2-b^2, (a!b)=a-b/2
Given this info,I found out what (4#3)@(2!3) would be.I sort of liked it.
Hmmm. Yes, that is a cool problem, very much like what they wanted to teach just before or when I was born into this realm. I also like such problems since they are novel, and, well, to put it plainly, WEIRD.
Let's see. Since a#b = a^2-b^2, 4#3 = 16 - 9 = 7
Since (a!b)=a-b/2, 2!3 = 2 - 3/2 = 4/2 - 3/2 = 1/2
Since a@b=a+b/2, (4#3)@(2!3) = 7@(1/2) = 7 + 1/4 = 7.25
Is this the result you came up with. I am sleepy so my brain might be fried.
That's kind of similar to the composite functions you were looking at a few days ago.
Oh well, I am actually getting sleepy earlier than usual tonight, so I'm going to see if I can step away from the machines and leave my math books alone for a second.
Believe it or not, I just pulled a book on Abstract Algebra off the shelf and was going to read a couple pages in the intro before switching gears and reading a few pages of philosophy before hopefully dozing off.