# Order of polynomial display: increasing order of powers?

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Alasdair McAndrew 2016 年 10 月 26 日
コメント済み: Bilal Akbana 2021 年 4 月 29 日
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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Bilal Akbana 2021 年 4 月 29 日
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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### 採用された回答

Walter Roberson 2016 年 10 月 26 日
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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Alasdair McAndrew 2016 年 10 月 27 日
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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### その他の回答 (1 件)

Robert 2016 年 10 月 26 日
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 2016 年 10 月 26 日
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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