Polynomial notation (2 Viewers)

[Sanical]

You can use a)...

Really? 100% sure? Do you mean I can use a) flat out, without even having delta or gamma? Or do you mean using a) once I refer to my own roots like you said in your previous reply?

 

[SpiralFlex]

Really? 100% sure? Do you mean I can use a) flat out, without even having delta or gamma? Or do you mean using a) once I refer to my own roots like you said in your previous reply?

100%, unless the person that invented polynomials would come back via a time machine and change his set of notations and destroy this lonesome planet. I would do the second option it is more correct. However if your teacher lets you do the first, then I don't see why you wouldn't. It is shorter.

But I would use

 

[Sanical]

Yay thanks

 

[SpiralFlex]

Yay thanks

Delicious humans.

 

[Sanical]

Ok, so I checked Terry Lee Polynomials. Chapter 3.3 Q14, and he uses method a). So does the cambridge 4U worked solutions. So yeah, a) seems good enough

 

[Bored_of_HSC]

Where'd you get b) and c) from?

 

[SpiralFlex]

Ok, so I checked Terry Lee Polynomials. Chapter 3.3 Q14, and he uses method a). So does the cambridge 4U worked solutions. So yeah, a) seems good enough

Importantly check with your teacher. If your teacher is a migrant like mine they will only accept the use of fancy notations.

 

[Sanical]

Where'd you get b) and c) from?

b) is something I made up
c) is the long way of writing, cambridge uses it

Importantly check with your teacher. If your teacher is a migrant like mine they will only accept the use of fancy notations.

Yeah, I'll check.

How do you write on paper? Do you need to have the two small horizontal strokes at the bottom? Someone draw on paint please

 

[SpiralFlex]

Not to be confused with the constant "pi". This one is the capital letter.

 

[Sanical]

Thanks

 

[cutemouse]

That's new...

 

[Carrotsticks]

Not to be confused with the constant "pi". This one is the capital letter.

lol this is how i write my pi:

 

[largarithmic]

I've come across "Sym" and "Cyc" a lot. They work like this; with a, b, c, d (cbf to type alpha beta gamma delta into latex) you can go:




i.e. the first one you take symmetric sums (i.e. 4 choose 2, etc) whereas in the second the a,b,c,d "cycle".

Also using i, j, k nothing is ambiguous ^^


whereas, where indices are taken mod n (so a_(n+1) = a_1)

 

[seanieg89]

I thought that sym. summation ran over ALL permutations of the variables?

So



Probably just a matter of conventions...it makes Muirhead's inequality look nicer .

 

[Carrotsticks]

I thought that sym. summation ran over ALL permutations of the variables?

So



Probably just a matter of conventions...it makes Muirhead's inequality look nicer .

I think it has to have the 2 in front, since symmetry implies ab and ba will be included in the permutations, but then commutativity kicks in.

 

[seanieg89]

Well largs definition probably just varies by a constant multiple to make it easier to write the elementary symmetric polynomials.

 

[largarithmic]

I thought that sym. summation ran over ALL permutations of the variables?

So



Probably just a matter of conventions...it makes Muirhead's inequality look nicer .

Yeah technically so but pshhhtttt nobody really cared about it when I did that. technically it should actually be a factor of 4, coz you can permute the c^0 and d^0 as well. Like with muirhead notation, all symsums in 4 variables have 24 terms

and yeah I was basing it on symmetric polynomial sum notation

 

[seanieg89]

Yeah technically so but pshhhtttt nobody really cared about it when I did that. technically it should actually be a factor of 4, coz you can permute the c^0 and d^0 as well. Like with muirhead notation, all symsums in 4 variables have 24 terms

and yeah I was basing it on symmetric polynomial sum notation

Ah yes 4, my bad.

 

[largarithmic]

Ah yes 4, my bad.

random thing, you know muirhead has a geometric interpretation?

 

[seanieg89]

random thing, you know muirhead has a geometric interpretation?

Nope, I'm not even sure how it is proven. Its just a useful sledgehammer to know.
What is this geometric interpretation?