leading coefficient polynomial

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Sage trac ticket 21608 provides methods for "leading term", "leading coefficient", "leading monomial", and is available in Sage 7.5.beta6.

If you have

P=7*x^3+2*x^4+2

then type P.[TAB] to see a list of possible "attributes" or "methods" attached to P. Other people have mentioned P.coefficients(). You might also hope that there is something like a leading_coefficient method, so try P.l[TAB] to find everything starting with the letter l. Then you should see P.leading_coefficient, so type

P.leading_coefficient?

to find out how to use it.

For example,

P=7*x^3+2*x^4+2

you can extract its coefficients as follows:

P.coefficients()

to get

[[2, 0], [7, 3], [2, 4]]

So the last sublist contains the answer, in this case 2 is the coefficient of x^4.

To extract this automatically you can define a function that takes a polynomial as argument:

def get_highest_coeff(P):
    m = P.coefficients()
    ncoeffs = len(m)
    return m[ncoeffs - 1][0]

And use it like this:

get_highest_coeff(P)

to get 2 as the answer. Hope this helps you get going!

Hint: if P is your polynomial, you should ask for its coefficients, you will get a list, the last element of that list is the leading coefficient.