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algebraic substitution

How can I imitate the algsubs function of Maple? A little example:

p = x^18

algsubs(x^2=x+1,p)

The reult in Maple is:

x^9+9x^8+36x^7+84x^6+126x^5+126x^4+84x^3+36x^2+9x+1.