1 | initial version |

You can probably proceed like the code below, or some version of it. I am not very familiar with symmetric polynomials in Sage, so this is something I could figure out in the 5min I looked at the docs.

```
sage: s = SymmetricFunctionAlgebra(QQ)
sage: f = s([2,1])
sage: p = f.expand(2); p
x0^2*x1 + x0*x1^2
sage: (x0, x1) = p.variables() # p.inject_variables() seems to be missing?
sage: p.subs(x0=x0^2, x1=x1^2)
x0^4*x1^2 + x0^2*x1^4
```

I must say the docs need a fair amount of work. I get zero idea from the documentation what `s([2,1])`

does. And there could be an elementary introduction in the `SymmetricFunctionAlgebra`

function about the effect of the different basis, or at least some examples which show the differences.

2 | No.2 Revision |

You can probably proceed like the code below, or some version of it. I am not very familiar with symmetric polynomials in Sage, so this is something I could figure out in the 5min I looked at the ~~docs.~~docs. The main thing used is to determine the variables and use the `.subs()`

method to substitute the squares of the variables. This can be extended so that it is all handled programmatically, instead of manually as I have done below.

```
sage: s = SymmetricFunctionAlgebra(QQ)
sage: f = s([2,1])
sage: p = f.expand(2); p
x0^2*x1 + x0*x1^2
sage: (x0, x1) = p.variables() # p.inject_variables() seems to be missing?
sage: p.subs(x0=x0^2, x1=x1^2)
x0^4*x1^2 + x0^2*x1^4
```

I must say the docs need a fair amount of work. I get zero idea from the documentation what `s([2,1])`

does. And there could be an elementary introduction in the `SymmetricFunctionAlgebra`

function about the effect of the different basis, or at least some examples which show the differences.

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