# Extracting coefficients from symbolic expressions

Assume a list of symbolic expressions (x0, x1,... are symbolic variables) like

[0, -15*x1^3/x0^7 + 10*x1*x2/x0^6 - x3/x0^5, 15*x1^2/x0^6 - 4*x2/x0^5, -6*x1/x0^5, x0^(-4)]


I want to extract the integer coefficients and get as result

[, [-15, 10, -1], [15, -4], [-6], ]


What is the most efficient/elegant method to accomplish this?

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A possibility is to transform each element as a fraction and look at the coefficients of the numerator. The main issue is about the leading 0 which is not an element of the symbolic ring, and whose list of coefficients is empty. So here is a way (the fill function transforms [] into ):

sage: L  = [0, -15*x1^3/x0^7 + 10*x1*x2/x0^6 - x3/x0^5, 15*x1^2/x0^6 - 4*x2/x0^5, -6*x1/x0^5, x0^(-4)]

sage: fill = lambda x :  if not x else x
sage: [fill(SR(p).fraction(ZZ).numerator().coefficients()) for p in L]
[, [-15, 10, -1], [15, -4], [-6], ]

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