ClemFanJC07's profile - activity

Specifically, I am trying to sum up al multinomial coefficients that have two equal parts. I am using the code: for n in range(21): t=0; for i in range(n+1): t = t + Combinations(n,i).cardinality()*Combinations(n-i,i).cardinality(); t=3*t; if gcd(n,3)==3: t = t-2*Combinations(n, n/3).cardinality()*Combinations(2*n/3, n/3).cardinality(); print t However, for n=3 the answer should be 18 not 15. Ideas?

I am trying to do an if block in sage. For example, I have code:

for n in range(7):
    if gcd(n,3)==3:
        n=n/3;
        n=n+1;
    print(n)

This "should" only add one when n is divisible by 3, but seems to do this all the time. Any ideas?

The pair group normally comes up in Polya enumeration of non-isomorphic graphs. So if we are looking at graphs with p vertices, then the group acting on the vertices is S_p. This induces a group on the edges of G, namely the pair group, S_p^{(2)}. I believe that Harary defined the pair group in "Graph Theory" and "Graphical Enumeration." I'm just curious if it is implemented in Sage the way it is in Mathematica.

In this case, G=S_p. In any case, if G is finite, then it is (isomorphic to) a subgroup of S_p for some suitably chosen p (Cayley's Theorem). The pair group only depends on G. However, the interesting and important case is when we use the full symmetric group for G.

In this case, p is the number of letters in the symmetric group. So, S_p is the pth symmetric group.

Is there a way to implement the "pair group" in sage like there is in mathematica?

sf. http://mathworld.wolfram.com/PairGrou...

I am trying to get Sage to give me the group acting on the potential edges of graph with n vertices for the purposes of Polya enumeration.

I know sage will give me the nth sysmmetric group, S_n. What I want is the group acting on the pairs, usually referred to as S_n^{(2)} in the literature. Any ideas?

I know how to generate a multivairiable Taylor series and extract its coefficients. What I want to do is to extract all the terms where the exponents of the individual variables satisfy certain requirements.

So for instance, my function is f(x,y)=(1/(1-xy))(1/(1-xy^2))(1/(1-xy^3))(1-x*y^4))

What I want is all terms in the Taylor series such that the exponent on x is at most 10 and the exponent on y is at most 20. Ideas?

I know that S4 = SymmetricGroup(4) P = S4.cycle_index()

will return the cycle index polynomial for S_4. What I want to do is substitute variables into this polynomial for Polya Enumeration problems. So for instance, how do I substitute x+y into the cycles of length 1, x^2+y^2 into the cycles of length 2, etc.

How do you get sage to factor into exact values. For instance, I want it to factor x^2-2 and return (x-sqrt(2))*(x+sqrt(2))

However, when I input

realpoly.<x> = PolynomialRing(CC) factor(x^2-2,x)

Sage returns

(x - 1.41421356237310) * (x + 1.41421356237310)

Any ideas?