# Order of polynomial display: increasing order of powers?

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Alasdair McAndrew le 26 Oct 2016
Commenté : Bilal Akbana le 29 Avr 2021
A symbolic polynomial will be displayed in order of decreasing powers:
>> taylor(sin(x),x,'Order',11)
ans =
x^9/362880 - x^7/5040 + x^5/120 - x^3/6 + x
Is there a preference value I can set which will display such polynomials in increasing order of powers? Like this:
x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880
Thank you!
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HiWave le 18 Fév 2020
I find this extremely annoying as well. It is as if they anticipate no practical use of the output.
Bilal Akbana le 29 Avr 2021
Following command works and gives result as shown below;
syms x
sympref('PolynomialDisplayStyle','ascend');
sinTaylor = taylor(sin(x),x,'Order',11);
disp(sinTaylor)
x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880

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### Réponse acceptée

Walter Roberson le 26 Oct 2016
No, there is no preference for adjusting the order of expressions. The symbolic engine is permitted to return expressions in any order, and is permitted to change the order during different executions.
There might be a rule, but it is not easy to figure out what it is. For example,
>> y*k*x
ans =
k*x*y
>> k*x*k+x*y*x*x*x + y*x*k + k^2
ans =
k^2*x + k^2 + y*k*x + y*x^4
>> k*x*k+x*y*x*x*x + y*x*k + k^2*y
ans =
k^2*x + y*k^2 + y*k*x + y*x^4
The first of those suggests possibly alphabetical order, k coming before x coming before y. But the second of those has y*k*x -- why did it choose that in the larger expression? It has not ordered the expression by powers of x -- if it did then k^2 would have to be first or last. The third shows k^2*x and y*k^2 which has equal powers of k but sorts differently, non-alphabetically. But
>> x*k^2 + y*k^2
ans =
k^2*x + k^2*y
so sometimes it does put them in alphabetical order.
It is not sorting alphabetically. It is not sorting by total power.
But it is influenced by those things. For example if you replace k by the other single-letter names in k^2*x + k^2 + y*k*x + y*x^4 (excluding x and y) then the same order is used in each case, except for z:
y*x^4 + x*z^2 + y*x*z + z^2
When I was testing last week, I found cases where the order changed completely if a constant was added to the expression.
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Walter Roberson le 26 Oct 2016
I understand why you want to do this... Unfortunately there just does not appear to be any way to control it.
By the way, Live Script calls pretty() to format the expression and pretty() does an undocumented call into the mupad engine to turn on pretty formatting and then calls into the engine to ask for the character representation of the expression (and then makes an undocumented call to turn off pretty formatting). The formatting is all done within the engine not at the MATLAB level.
Alasdair McAndrew le 27 Oct 2016
The crazy thing is that, as I pointed out above, you can create a polynomial, and then 'coeffs' will display the coefficients in increasing order of powers. But the polynomial itself will be displayed in decreasing order of powers. I find this very annoying.

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### Plus de réponses (1)

Robert le 26 Oct 2016
Hey there
So this is a bug in matlab I found the bug a few weeks ago and it should be fixed in the next release
It turns out with the addition of a tilda you can change the order in which the coeffs function returns values.
Try the following code and please don't forget to accept the answer so i can get the credit for helping. Thanks!
syms x
y = x - x^3/6 + x^5/120 - x^7/5040 + x^9/362880
[High_Order , ~] = coeffs(y) % Use this to get the higher order first
Coefficient_Low_first = coeffs(y)
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Walter Roberson le 26 Oct 2016
You can extract the coefficients in one order or the reverse but the user needs the symbolic expression itself to be displayed in a different order
Walter Roberson le 26 Oct 2016
Consider for example sin() around the expression. coeffs() would not work because that would not be a multinomial, but you might still have an interest in the order that the expression displays.

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