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Let's say I have the following expression (from a wide range of possibilities) :

pol =  3*a*x^(-b)*log(x)*b^2 - 6*a*b*c*sinx(x*b) + 3*a*c^2 + 5

And I want to extract the coefficients of the polynomial over the polynomial ring over a & c, so that these result in:

a^0*c^0  :  5
a^1*c^0  :  3*x^(-b)*log(x)*b^2
a^0*c^1  :  0
a^1*c^1  :  -6*b*sinx(x*b)
etc.

How can I define the polynomial ring?

How can I map an existing expression that defines "pol" (which is the result of other manipulations) into such ring?

Let's say I have the following expression (from a wide range of possibilities) :

pol =  3*a*x^(-b)*log(x)*b^2 - 6*a*b*c*sinx(x*b) 6*a*b*c*sin(x*b) + 3*a*c^2 + 5

And I want to extract the coefficients of the polynomial over the polynomial ring over a & c, so that these result in:

a^0*c^0  :  5
a^1*c^0  :  3*x^(-b)*log(x)*b^2
a^0*c^1  :  0
a^1*c^1  :  -6*b*sinx(x*b)
-6*b*sin(x*b)
etc.

How can I define the polynomial ring?

How can I map an existing expression that defines "pol" (which is the result of other manipulations) into such ring?