1. Can anyone tell me if equations of the form illustrated by the following example;

have a name?

In general, I would be inclined to represent them as;

but I am not sure that this would be seen as the most appropriate general expression.

2.

3. ax^2+by^2+cx+dy+e=0
used for circles called the general eqn of a circle
i got x=y^2/y-1

4. Originally Posted by fiveworlds
ax^2+by^2+cx+dy+e=0
used for circles called the general eqn of a circle
i got x=y^2/y-1
Thank you for taking the time to comment, but my question does not refer to any particular function of x and y - the expression I gave was merely an example chosen at random.

I have two questions:

1) is there a name for equations of the type ?

Any such equation will obviously be solved by pairs of values where provided that the function exists for the values chosen.

2) is the appropriate way of denoting the function? My reason for wondering about this is that, usually, the expression does not specify the order in which x and y are written, but in the equation I gave above, the order if clearly important. For example, is there some other way of writing it such as indicating that the value of the function not only depends on the values of x and y but that the order is important? This is a detail that I am not much concerned about. The main question is Q1.

5. unfortunately not jonG the equations f(x,y)=f(y,x) assignment statements probably or just functions they could be anything one function using this can solve riemann one solve for a circle. you have no idea of how something changes between the two points it could be a curve or an alternating waveform or a square wave etc. Anything can be that eqn literally anything .i gave your above equation an attempt im afraid im abit rusty on my maths so ill post it later when i have time.Any eqn of known distance can be rotated through 360 degrees. In any equation x always equals y or r always equals i and one is always 1/2 of the other

6. In physics, an equation where f(x,y) = f(y,x) would be called a symmetric equation, or to be explicit an equation that is symmetric in its arguments. I'm not sure whether this description would be used in mathematics.

7. I have wondered about the term symmetric, but it seems to cover too many options - symmetry about the x-axis and/or symmetry about the y-axis.
The solutions to are symmetric about the line y = x but not about the x or y axes. If is a solution then so is .

My reason for wanting to find a name is simply in an attempt to find out more about equations of this type.

8. According to Wikipedia:
A symmetric function of n variables is one whose value at any n-tuple of arguments is the same as its value at any permutation of that n-tuple. While this notion can apply to any type of function whose n arguments live in the same set, it is most often used for polynomial functions, in which case these are the functions given by symmetric polynomials. There is very little systematic theory of symmetric non-polynomial functions of n variables, so this sense is little-used, except as a general definition.
Symmetric function - Wikipedia, the free encyclopedia

So you may be breaking new ground

9. the thing is i dont know a single non symmetrical eqn. do you?

10. Originally Posted by fiveworlds
the thing is i dont know a single non symmetrical eqn. do you?
To pinch the example from Wikipedia:
Consider now the function

If x and y are interchanged, the function becomes

This function is obviously not the same as the original if , which makes it non-symmetric.
Although, the OP seems to be trying to do something slightly different and make these two equal...

11. graph anything and you always have two points through a distance these points can turn through 360 degrees easy in a different section of this circle f(x,y)=x^2+y would be the exact same as f(y,x)=x+y^2

12. Some punctuation to indicate your sentences might make what you are trying to say a little clearer.

But making a guess at it...

Originally Posted by fiveworlds
graph anything nd you always have two points through a distance these points can turn through 360 degrees
I don't believe the graph of every function is rotationally symmetrical. In fact I know it isn't. (And it has nothing to do with the OP)

13. and if you have a line anything with the x and y axis is there always an x and y coord??

14. Originally Posted by fiveworlds
and if you have a line anything with the x and y axis is there always an x and y coord??
Sorry, I don't know what that means. Do you want to try again with full English sentences.

15. well if you have an x and a y co-ord then changes in x must be proportional to changes in y and therefore there is a symmetry between x and y . Since axis are generally used in maths then your maths must have a symmetry to your axis.

16. Originally Posted by fiveworlds
well if you have an x and a y co-ord then changes in x must be proportional to changes in y and therefore there is a symmetry between x and y .
Here is a simple equation that produces a graph which is not symmetrical:

Graph here: http://www.wolframalpha.com/input/?i=2^%281%2Fx^3%29

17. there is a symmetry there x is getting smaller to infinity

18. Do you know what the word "symmetry" means?

19. yeah a relationship/proportion. and you have the proportions ie function

20. Originally Posted by fiveworlds
yeah a relationship/proportion.
Er, no. Maybe that is why we have been talking at cross purposes.

In it's simplest, symmetry defines operations that you can do to something to leave it unchanged. For example a square is symmetric because you can rotate it through 90 degrees. A rectangle is symmetric because you can flip it horizontally or vertically and it will look the same. But a glove is not symmetric there is no series of rotations or transformations that will give you the same shape.
fig8a.jpg

Beyond that, it gets deeply mathematical.

21. flip 90 degrees 180degrees 24.674367238 degrees same shape. turn your hand to the left does it still look like a hand???

22. Originally Posted by fiveworlds
flip 90 degrees 180degrees 24.674367238 degrees same shape
What is? And, no, not if it not symmetrical.

To go back the the glove example. There is no way to change a left hand glove to a right hand glove: any set of rotations and transformations will not do it. Because it does not have symmetry.

23. so if you take your shoe and turn it to your left is it not a shoe?ps a left hand glove and right hand glove are different functions you cant make radius = plane

24. Originally Posted by Strange
According to Wikipedia:
A symmetric function of n variables is one whose value at any n-tuple of arguments is the same as its value at any permutation of that n-tuple. While this notion can apply to any type of function whose n arguments live in the same set, it is most often used for polynomial functions, in which case these are the functions given by symmetric polynomials. There is very little systematic theory of symmetric non-polynomial functions of n variables, so this sense is little-used, except as a general definition.
Symmetric function - Wikipedia, the free encyclopedia

So you may be breaking new ground
Thank you Strange - the link is the sort of thing I am looking for, but I didn't expect "symmetric function" to find it. As for breaking new ground - I have done it often - it's called gardening.

25. oh i love gardening we may exchanges ideas sometime gardenening lots of fun and you get veg out of it and study biology and cook (chemistry). im sure strange would like it.

26. Originally Posted by Strange
To pinch the example from Wikipedia:
Consider now the function

If x and y are interchanged, the function becomes

This function is obviously not the same as the original if , which makes it non-symmetric.
Although, the OP seems to be trying to do something slightly different and make these two equal...

Yes - that is right. The symmetry I have referred to is symmetry related to the solutions of , not the symmetry of the function itself.

27. Originally Posted by JonG

Yes - that is right. The symmetry I have referred is symmetry related to the solutions of not the symmetry of the function itself.
Oh. As a physicist I am more familiar with the solutions of f(x,y) given that f(x,y) = f(y,x). My immediate reaction to your problem is thus to write

F(x,y) = f(x,y) - f(y,x)

in which case the solutions you are talking about are identically the solutions of F(x,y) = 0, since that is your equation rewritten. Now notice that

F(y,x) = - F(x,y)

i.e. F is antisymmetric under interchange of x and y. So the solutions you are seeking are antisymmetric under this exchange. I doubt that they have any additional, independent properties until you say something about f .

As a side note, if f(x,y) is symmetric under interchange of x and y, the equation for F becomes

F(y,x)=0 identically

and you have no information at all.

28. if the function itself is symmetrical does this not imply that the solutions are too i would imagine so you view something as anti symmetric but how if you take blocks out of a container in a certain order you can also replace them in the same or an alternate order.

29. Yes, if f(x,y) is symmetrical under interchange of x and y, all solutions of f(x,y) = 0 are also, and similarly if f(x,y) is antisymmetrical.

30. Originally Posted by mvb

i.e. F is antisymmetric under interchange of x and y. So the solutions you are seeking are antisymmetric under this exchange. I doubt that they have any additional, independent properties until you say something about f .

Yes, that is right. The solutions can be antisymmetric. If (x,y) = (a,b) is a solution, then so is (x,y) = (-a,-b). However, as you also indicate, one needs to be more specific about f(x,y) - for example, is it well-defined for negative values of x or y?

31. mvb if you take the blocks in your container and upturn it making a jenga stack then magnetise each of the blocks so its suspended in midair can you now remove any block keeping shape?

32. Originally Posted by JonG
Originally Posted by mvb

i.e. F is antisymmetric under interchange of x and y. So the solutions you are seeking are antisymmetric under this exchange. I doubt that they have any additional, independent properties until you say something about f .

Yes, that is right. The solutions can be antisymmetric. If (x,y) = (a,b) is a solution, then so is (x,y) = (-a,-b). However, as you also indicate, one needs to be more specific about f(x,y) - for example, is it well-defined for negative values of x or y?
That wasn't what I meant by antisymmetric, sorry I missed the ambiguity. What I was talking about was f(x,y) = - f(y,x)

33. Originally Posted by fiveworlds
mvb if you take the blocks in your container and upturn it making a jenga stack then magnetise each of the blocks so its suspended in midair can you now remove any block keeping shape?
Sorry, I don't understand this at all. In any event, I don't know of any useful analogies between blocks in a container and solutions of a function.

34. thats okay i know all about jenga. though i know sometimes its good to keep a container

35. Originally Posted by mvb
Sorry, I don't understand this at all. In any event, I don't know of any useful analogies between blocks in a container and solutions of a function.
Not even knapsack functions ?

36. Originally Posted by mvb
That wasn't what I meant by antisymmetric, sorry I missed the ambiguity. What I was talking about was f(x,y) = - f(y,x)
It can become confusing - I had to look at what I had written more than once - and even then, wasn't sure that it said what I intended.
Just to be clear as to what I mean by the solutions being antisymmetric: - imagine a graph of for both positive and negative values of x. Half of the graph will be in the upper right quadrant and the other half in the lower left quadrant. If is a point on the part in the upper right quadrant, then will be a point in the lower left quadrant. Changing the sign of x, changes the sign of y. The solutions of can be points on a plot with the same general shape as the graph of . It won't be exactly the same graph, of course, but it can have the same topology.

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