CODEWITHSUNDEEP
pythonsage
CameronJWhitehead
CameronJWhitehead

Reputation: 133

Permutation vectors with unknowns in Sage

I'm trying to do some work with Sage, and I can't understand how to do the following.

I've written some little code:

def ElementDr1(r):
    G = SymmetricGroup(r)
    E = G.list()
    O = G.order()
    coeff = ZeroCoeff(O)

    for i in range(0,O):
        if E[i] == G("(1,r)"): 
            coeff [i]=1
        if E[i] == G("(2,3)*(1,r)"):
            coeff [i]=1
        if E[i] == G("(1,3)*(1,r)"):
            coeff [i]=-1
    return coeff

and Sage says that the permutation vector (1,r) is invalid. I'm sure there must be a way to write permutation vectors with unknowns, but I can't find what this method is by looking at the Sage help.

Upvotes: 1

Views: 98

Answers (2)

user3717023
user3717023

Reputation:

Several issues here:

  1. The syntax for creating an element from cycle decomposition is G("(1,2)(3,4)") with no * in between.
  2. The cycles must be disjoint, i.e., no element can appear twice. You have 1 appearing twice.
  3. Using r inside a string instead of substituting: Samuel Lelièvre commented on that already.

Since (1,3)(1,r) is not a valid cycle decomposition, what you want to do is to multiply (1,3) by (1,r). To this end, create these elements first and then multiply them (using * operator). Since the elements are cycles, you don't even need a string: an element can be created from a tuple. 

def ElementDr1(r):
    G = SymmetricGroup(r)
    E = G.list()
    O = G.order()
    coeff = [0 for i in range(0,O)]  # self-contained examples are good

    for i in range(0,O):
        if E[i] == G((1,r)):
            coeff[i] = 1
        if E[i] == G((2,3))*G((1,r)):
            coeff[i] = 1
        if E[i] == G((1,3))*G((1,r)):
            coeff[i] = -1
    return coeff

Now it runs, outputting, for example, [-1, 0, 0, 1, 0, 1] with r=3.

Upvotes: 2

Samuel Lelièvre
Samuel Lelièvre

Reputation: 3453

The error is likely due to calling G("...") with strings containing r. Replace r by its value in these strings, for example as follows:

def ElementDr1(r):
    G = SymmetricGroup(r)
    E = G.list()
    O = G.order()
    coeff = ZeroCoeff(O)

    for i in range(0,O):
        if E[i] == G("(1,%s)"%r): 
            coeff[i] = 1
        if E[i] == G("(2,3)*(1,%s)"%r):
            coeff[i] = 1
        if E[i] == G("(1,3)*(1,%s)"%r):
            coeff[i] = -1
    return coeff

Upvotes: 1

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