MuPAD Pexpect Interface
sage: mupad.package('"MuPAD-Combinat"')
sage: combinat = mupad.combinat
sage: examples = mupad.examples
sage: S = examples.SymmetricFunctions()
sage: S.s[2,1]^2
s[3, 3] + s[4, 2] + s[2, 2, 1, 1] + s[2, 2, 2] + 2 s[3, 2, 1] + s[4, 1, 1] +
s[3, 1, 1, 1]
sage: S.omega( S.s[3] )
s[1, 1, 1]
sage: s = S.s
sage: p = S.p
sage: s[2,1] + p[2,1]
- e[2, 1] - e[3] + e[1, 1, 1]
sage: s(_)
s[2, 1] + s[3] - s[1, 1, 1]
sage: combinat.tableaux.list(3)
-- +---+ --
| | 3 | |
| +---+ +---+ +---+ |
| | 3 | | 2 | | 2 | |
| +---+---+---+ +---+---+ +---+---+ +---+ |
| | 1 | 2 | 3 |, | 1 | 2 |, | 1 | 3 |, | 1 | |
-- +---+---+---+ +---+---+ +---+---+ +---+ --
sage: t = _[1]
sage: t
+---+---+---+
| 1 | 2 | 3 |
+---+---+---+
sage: combinat.tableaux.conjugate(t)
+---+
| 3 |
+---+
| 2 |
+---+
| 1 |
+---+
sage: combinat.ribbonsTableaux.list([2,2],[1,1],2)
-- +---+---+ +---+---+ --
| | | 2 | | 2 | |
| + + +, +---+---+ |
| | 1 | | | 1 | |
-- +---+---+ +---+---+ --
sage: combinat.tableaux.kAtom([3,2,1],3)
-- +---+ +---+ --
| | 3 | | 3 | |
| +---+---+ +---+ +---+---+ +---+ |
| | 2 | 2 | | 2 | | 2 | 2 | | 2 | |
| +---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+---+ |
| | 1 | 1 | 1 |, | 1 | 1 | 1 | 2 |, | 1 | 1 | 1 | 3 |, | 1 | 1 | 1 | 2 | 3 | |
-- +---+---+---+ +---+---+---+---+ +---+---+---+---+ +---+---+---+---+---+ --
sage: M = S.Macdonald()
sage: M.P[1]^2
(q t - 1) (t - 1) / 1
- ------------------ P[2] - (t - 1) | ----------------- +
2 | 3 2
t - q t + q t - 1 \ - t + t + t - 1
q - t \ 2
----------------------------- | (t - 1) P[1, 1]
3 2 |
(q t - 1) (- t + t + t - 1) /
sage: mupad.mapcoeffs(_, 'normal')
q - t + q t - 1
P[2] + --------------- P[1, 1]
q t - 1 
