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Polynomial coefficient vector to symbolic polynomial

asked 2013-11-14 09:36:07 -0600

gundamlh gravatar image

updated 2013-11-14 09:36:34 -0600

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matlab: poly2sym([1 3 2])
ans =
x^2 + 3*x + 2

I couldn't find a similar function in SAGE. Fortunately this small function is quite easy, consisting of only one loop.

Thanks in advance!

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answered 2013-11-14 09:48:31 -0600

tmonteil gravatar image

updated 2013-11-14 23:32:34 -0600

I am not sure that Sage shoud contain a function for each such feature, it will lead to a huge global namespace, making tab completion unusable. Here is a quick proposition:

sage: L = [1, 3, 2]
sage: sum([b*x^a for a,b in enumerate(reversed(L))])
x^2 + 3*x + 2

Or, if you want a function, define:

sage: poly2sym = lambda L : sum([b*x^a for a,b in enumerate(reversed(L))])
sage: poly2sym([1, 3, 2])
x^2 + 3*x + 2

Now, if you want genuine polynomials (not symbolic functions), you can define the polynomial ring you want and build a polynomial from a list as follows:

sage: R.<x> = PolynomialRing(QQ)
sage: R
Univariate Polynomial Ring in x over Rational Field

sage: R([1, 3, 2])
2*x^2 + 3*x + 1

As you can see, the order is not the one you wanted, so you can do:

sage: R(list(reversed([1, 3, 2])))
x^2 + 3*x + 2

And again:

poly2sym = lambda L : R(list(reversed(L)))

But then, you should understand that the prouced object are genuine polynomials, not symbolic expressions as before.

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Thanks! The type "polynomial" is better than "symbolic expression", from my point of view. It has methods such "smith_form()", "roots()", ...

gundamlh gravatar imagegundamlh ( 2013-11-14 23:45:53 -0600 )edit

Yep, i definitely agree with that, you know where your objects live :) The same difference between `sqrt(2)` and `sqrt(QQbar(2))`.

tmonteil gravatar imagetmonteil ( 2013-11-14 23:58:27 -0600 )edit

:) I am a control Eng. student, and trying to build my own robust control toolbox using SAGE and MATLAB.

gundamlh gravatar imagegundamlh ( 2013-11-15 00:09:14 -0600 )edit

Well, Sage is far from being robust or certified. I am not an expert at all, but aren't tools like `coq` more adapted ?

tmonteil gravatar imagetmonteil ( 2013-11-15 00:21:15 -0600 )edit

Coq http://en.wikipedia.org/wiki/Coq .. I have not ever heard about it before.. it seems to be a genius software.. "functional programming". In fact my control toolbox is only a kind of "toy" box.

gundamlh gravatar imagegundamlh ( 2013-11-22 05:04:21 -0600 )edit

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Asked: 2013-11-14 09:36:07 -0600

Seen: 604 times

Last updated: Nov 14 '13