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**Problem 2:**

Write a function that takes as input a positive integer $n$ and outputs the first $n$ levels of the
cyclotomic $\ZZ_3$-extension of $\QQ$ as a tower of relative extensions (so each field has
degree 3 over the one below it).   The code should 'work' in general, though
of course it will likely be very, very slow as $n$ gets bigger.    How big of $n$ can you
give as input before this starts taking a long time or getting slow?

Figuring out what I mean by "the cyclotomic $\ZZ_3$ extension of $\QQ$" is part of this problem.
If you don't know, start by asking any student of Ralph Greenberg.
︡733f67ec-5e54-45ac-9c22-56d23c821173︡︡{"done":true,"md":"\n**Problem 2:**\n\nWrite a function that takes as input a positive integer $n$ and outputs the first $n$ levels of the\ncyclotomic $\\ZZ_3$-extension of $\\QQ$ as a tower of relative extensions (so each field has\ndegree 3 over the one below it).   The code should 'work' in general, though\nof course it will likely be very, very slow as $n$ gets bigger.    How big of $n$ can you\ngive as input before this starts taking a long time or getting slow?\n\nFiguring out what I mean by \"the cyclotomic $\\ZZ_3$ extension of $\\QQ$\" is part of this problem.\nIf you don't know, start by asking any student of Ralph Greenberg."}
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