# OK to post homework
# Vikrant, Apr 03 2022, Assignment 19

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# 0. Code that has been given.
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read("C19.txt"):

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# 1. Umbras; apply x1^a1*...*xk^ak -> P^na1*...*P^nak, then multinomial.
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UmbT:=
    proc(P,var,N)
        local n,i:
        [seq(Umb(subs({seq(var[i]=P^n,i=1..nops(var))},P),var),n=1..N)]:
    end:

# UmbT(x+y,[x,y],20);
# UmbT(x+y+z,[x,y,z],20);
# UmbT(x1+x2+x3+x4,[x1,x2,x3,x4],20);
# UmbT(1+2*x+3*y,[x,y],20);
# UmbT((1+x)*(1+y)*(1+z),[x,y,z],20);

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# 2. Discrepancy between outputs of Zs(..)/2[v] and NuC(v,[[0,1,1],[0,0,1]]).
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# IsCond3G(v,[[0,1,1],[0,0,1]]) does not do what you think it does when v is even.
# It biases comparisons between 1 and 3 towards 3 winning.
# More specifically, ties between 1 and 3 are counted as 3 winning 1.
# Fixing the conditionals in IsCond3G(..) to remove this bias results in the outputs 
# of NuC(..), which calls IsCond3G(..), matching that of Zs(..)/2.

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# 3. <Admin>
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