5 ms·

“Fixing” the rules of division

13 points by memorable 4y ago

Joker_vD 4y ago
> Long division makes my head hurt! Well, I suspect it has something to do with writing out the process of 5772 / 37 as 156 ______ 37 | 5772 37 --- 207 185 ---- 222 222 --- 0 because it a) reverses the order of dividend and divisor for no good reason; b) the result goes up instead of to the right or down. Why not write it like this 5772 | 37 37 +---- --- 156 207 185 ---- 222 222 --- 0 instead? In fact, I think we could replace the corner with just normal slash, "/", write = to the right of the divisor and spell out the digits of the result to the right of it; the substraction chain will still go down the page.
- nh23423fefe 4y ago
  you can't extend the numerator to get more places like this unless you do it upfront 5772.00000000 | 37 also polynomial division works better the other way too, i think.
  - Joker_vD 4y ago
    Sure you can: 5772 / 36 = 160,33... 36 --- 217 216 ---- 120 108 ---- 120 108 ---- ...
- gloria_mundi 4y ago
  > In fact, I think we could replace the corner with just normal slash, "/", write = to the right of the divisor and spell out the digits of the result to the right of it; the substraction chain will still go down the page. That's exactly the way I was taught long division (in Germany).
  - skyde 4y ago
    same this is how i learned it in Canada public school
eesmith 4y ago
Ahh, so Ruby doesn't - and can't[1] - support constant folding. In CPython, because monkey-patching like this isn't supported, the byte compiler turns a "0/2" into a "0.0", as you can see with: >>> def f(): ... return 0 / 2 ... >>> import dis >>> dis.dis(f) 2 0 LOAD_CONST 1 (0.0) 2 RETURN_VALUE [1] EDIT: except through something like whole-program analysis.
- languageserver 4y ago
  > Ahh, so Ruby doesn't - and can't[1] - support constant folding. it is because most "OOP" languages are not really "object" languages. Ruby is a "proper" everthing is an object language, which is why everyone loves it so much even if they do not think about it.
  - Spivak 4y ago
    Huh? Python is an everything-is-an-object language too. Supporting monkey-patching is a separate thing.
    - nomel 4y ago
      I didn't realize this. I thought things like int's were special. I just tried x = 5 dir(x) Output: ['__abs__', '__add__', '__and__', '__bool__', ...
      - eesmith 4y ago
        Some Python objects are open for modification, and some are closed. Closed objects don't support this sort of monkey-patching. Integers, strings, and other class objects defined in C are closed for modification. >>> x = 5 >>> x.__add__ = lambda x, y: x*y Traceback (most recent call last): File "<stdin>", line 1, in <module> AttributeError: 'int' object attribute '__add__' is read-only In that sense they are "special" (or class objects defined in Python are special). But that doesn't make a language with closed classes non-OO.

13 points by memorable 4y ago

> Long division makes my head hurt! Well, I suspect it has something to do with writing out the process of 5772 / 37 as 156 ______ 37 | 5772 37 --- 207 185 ---- 222 222 --- 0 because it a) reverses the order of dividend and divisor for no good reason; b) the result goes up instead of to the right or down. Why not write it like this 5772 | 37 37 +---- --- 156 207 185 ---- 222 222 --- 0 instead? In fact, I think we could replace the corner with just normal slash, "/", write = to the right of the divisor and spell out the digits of the result to the right of it; the substraction chain will still go down the page.

nh23423fefe 4y ago
you can't extend the numerator to get more places like this unless you do it upfront 5772.00000000 | 37 also polynomial division works better the other way too, i think.
- Joker_vD 4y ago
  Sure you can: 5772 / 36 = 160,33... 36 --- 217 216 ---- 120 108 ---- 120 108 ---- ...
gloria_mundi 4y ago
> In fact, I think we could replace the corner with just normal slash, "/", write = to the right of the divisor and spell out the digits of the result to the right of it; the substraction chain will still go down the page. That's exactly the way I was taught long division (in Germany).
- skyde 4y ago
  same this is how i learned it in Canada public school

eesmith 4y ago

Ahh, so Ruby doesn't - and can't[1] - support constant folding. In CPython, because monkey-patching like this isn't supported, the byte compiler turns a "0/2" into a "0.0", as you can see with: >>> def f(): ... return 0 / 2 ... >>> import dis >>> dis.dis(f) 2 0 LOAD_CONST 1 (0.0) 2 RETURN_VALUE [1] EDIT: except through something like whole-program analysis.

languageserver 4y ago
> Ahh, so Ruby doesn't - and can't[1] - support constant folding. it is because most "OOP" languages are not really "object" languages. Ruby is a "proper" everthing is an object language, which is why everyone loves it so much even if they do not think about it.
- Spivak 4y ago
  Huh? Python is an everything-is-an-object language too. Supporting monkey-patching is a separate thing.
  - nomel 4y ago
    I didn't realize this. I thought things like int's were special. I just tried x = 5 dir(x) Output: ['__abs__', '__add__', '__and__', '__bool__', ...
    - eesmith 4y ago
      Some Python objects are open for modification, and some are closed. Closed objects don't support this sort of monkey-patching. Integers, strings, and other class objects defined in C are closed for modification. >>> x = 5 >>> x.__add__ = lambda x, y: x*y Traceback (most recent call last): File "<stdin>", line 1, in <module> AttributeError: 'int' object attribute '__add__' is read-only In that sense they are "special" (or class objects defined in Python are special). But that doesn't make a language with closed classes non-OO.