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2013-11-04 08:35:13 +0100 marked best answer How to factor polynomials in var('x') over the semi-ring of polynomials with non-negative integer coefficients ?

You can not (yet?) define polynomials over NN in Sage, because it is not a ring. What you can do is to define your polynomial over ZZ, find its factors (as elements of ZZ[x]), and then recombine them to find polynomials with non-negative entries.

2013-11-03 06:06:34 +0100 asked a question How to factor polynomials in var('x') over the semi-ring of polynomials with non-negative integer coefficients ?

Is there an easy way in sage to determine the factorization of a polynomial in the variable x ( having non-negative integer coefficients), over the semi-ring of polynomials in the variable x with non-negative integer coefficients.

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2013-02-05 12:20:48 +0100 commented answer How to get the list of user defined variables

Thank you very much!

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2013-02-05 12:17:03 +0100 marked best answer How to get the list of user defined variables

That's a good question. You can inspect the global variables that have been defined at any given point in a session, but most of those will be defined when various modules load on Sage startup. You can look just at those globals whose type is sage.symbolic.expression.Expression, there aren't too many at startup:

sage: G = globals()
sage: for k in G:
....:     if type(G[k]) == sage.symbolic.expression.Expression:
....:         print k
golden_ratio
log2
NaN
merten
I
twinprime
pi
catalan
brun
euler_gamma
x
khinchin
i
glaisher
mertens

Anything not on that list is a global symbolic expression that is defined in your loaded session. Variables will be among these.

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2013-02-01 18:32:41 +0100 asked a question How to get the list of user defined variables

How do I get the list of user defined variables in a sage session I just loaded using the load_session command ?