Permutation vectors with unknowns in Sage -

i'm trying work sage, , can't understand how following.

i've written little code:

def elementdr1(r):     g = symmetricgroup(r)     e = g.list()     o = g.order()     coeff = zerocoeff(o)      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 permutation vector (1,r) invalid. i'm sure there must way write permutation vectors unknowns, can't find method looking @ sage help.

several issues here:

1. the syntax creating element cycle decomposition g("(1,2)(3,4)") no * in between.
2. the cycles must disjoint, i.e., no element can appear twice. have 1 appearing twice.
3. using r inside string instead of substituting: samuel lelièvre commented on already.

since (1,3)(1,r) not valid cycle decomposition, want multiply (1,3) (1,r). end, create these elements first , then multiply them (using * operator). since elements cycles, don't need string: element can created tuple.

def elementdr1(r):     g = symmetricgroup(r)     e = g.list()     o = g.order()     coeff = [0 in range(0,o)]  # self-contained examples      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 runs, outputting, example, [-1, 0, 0, 1, 0, 1] r=3.