ruidongshuai@gmail.com's profile - activity

I want to input an element of Sn with SymmetricGroup(),for example, I know SymmetricGroup(5)((1,2,3))is the element (1,2,3)in S5,however, I do not know how to input something like (1,2)(3,4) using SymmetricGroup()

I want to define a polynomial ring R with 5 variables, and a function f belonging to R with 2 variables, for example, f=x1+x2,however, the arguments of f are just x1 and x2, how can I let the arguments of f be x0,x1,x2,x3,x4?

R=PolynomialRing(QQ,5,"x",order='lex')
vx=[var("x"+str(i))for i in range(5)]
vx=R.gens()
f=x1+x2;f
f.args()
g=R.random_element();g
g.args()

Thanks for your answer very much! However, there is still a small problem, when I type in a polynomial f=x1+x2, and n=5, sigma=(1,2,3),it shows an error says that the number of arguments must be less than or equal to 2. How can I make the arguments of f be x1,x2,x3 instead of just x1 and x2?

I want to define a function, the input are a permutation sigma belonging to Sn, and a multivariate polynomial f=f(x1,x2,...,xn) over Q, and the output is a multivariate polynomial f=f(x(sigma(1)),x(sigma(2)),...,x(sigma(n))), for example, if sigma=(3,1,2),f=x1+x2x3, then the output should be f=x3+x1x2. It is worth mentioning that this should work for any n not just when n=3. How should I do that?