Return degree of polynomial in InfinitePolynomialRing

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I find it cumbersome, also because in my case, I generate polynomials in arbitrarily many variables that I pass to other (self-defined) functions where I have to extract the degree relative to a specific variable a[d], where d is automatically calculated and can be arbitrarily large, so in general I don't know until where I would have to add zeros. I wonder if there is an elegant solution.

Unfortunately, implementation of InfinitePolynomialRingappears to be very shallow. You are welcome to submit a bugreport requesting it to be fixed/enhanced in a particular way - e.g. see mine at https://trac.sagemath.org/ticket/34758

Meanwhile, as a workaround you can use a custom degree function like:

def mydegree(p,v):
    return p.degree(v.variable()) if v in p.variables() else 0

It still doesn't work when you start with a[3] (in this example). Try the following

def mydegree(p,v):
    return p.degree(v.variable()) if v in p.variables() else 0
R.<a> = InfinitePolynomialRing(QQ)
p = a[1]*a[2]^2
mydegree(p,a[3])   # yields an error and changes the internal configuration
mydegree(p,a[2])   # now yields an error too

Whenever I type a[3], it messes up the originally good behaviour and I have to create p again in order to make it work.

However, p.degrees()[-d-1] does the job and at least doesn't mess up anything. Try the following:

R.<a> = InfinitePolynomialRing(QQ)
p = a[1]*a[2]^2
p.degrees()[-3-1]   # yields an error, but doesn't change the internal configuration
p.degrees()[-2-1]   # still works (because we didn't introduce a[3])

Feel free to add an answer to your own question for benefits of other users.