Changeset 2109:98a87cfac4d7 for sage/combinat/combinat.py
- Timestamp:
- 12/10/06 22:02:24 (6 years ago)
- Branch:
- default
- Children:
- 2110:3058a1513352, 2111:015c2a6ce65f
- File:
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- 1 edited
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sage/combinat/combinat.py (modified) (2 diffs)
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sage/combinat/combinat.py
r1855 r2109 707 707 ['n', 'e'], ['s', 'i'], ['t', 'i'], ['e', 'i'], ['i', 'i'], ['n', 'i'], ['s', 'n'], 708 708 ['t', 'n'], ['e', 'n'], ['i', 'n'], ['n', 'n']] 709 sage: mset = [x for x in GF(4,'a') if x!=0] 710 sage: tuples(mset,2) 711 [[1, 1], 712 [a, 1], 713 [a + 1, 1], 714 [1, a], 715 [a, a], 716 [a + 1, a], 717 [1, a + 1], 718 [a, a + 1], 719 [a + 1, a + 1]] 709 710 The Set(...) comparisons are necessary because finite fields are not 711 enumerated in a standard order. 712 sage: K.<a> = GF(4, 'a') 713 sage: mset = [x for x in K if x!=0] 714 sage: ts = tuples(mset,2) 715 sage: T = Set([tuple(t) for t in ts]) 716 sage: S = Set([(K(1), K(1)), (a, K(1)), (a + K(1), K(1)), (K(1), a), (a, a), (a + K(1), a), (K(1), a + K(1)), (a, a + K(1)), (a + K(1), a + K(1))]) 717 sage: S == T 718 True 720 719 721 720 AUTHOR: Jon Hanke (2006-08?) … … 997 996 SAGE verifies that the first several coefficients do instead agree: 998 997 999 sage: q = PowerSeriesRing(QQ,'q').gen() 1000 sage: prod((1-q^k)^(-1) for k in range(1,20)) ## partial product of 1001 1 + q + 2*q^2 + 3*q^3 + 5*q^4 + 7*q^5 + 11*q^6 + 15*q^7 + 22*q^8 + 30*q^9 + 42*q^10 1002 + 56*q^11 + 77*q^12 + 101*q^13 + 135*q^14 + 176*q^15 + 231*q^16 + 297*q^17 + 385*q^18 1003 + 490*q^19 + O(q^20) 998 sage: q = PowerSeriesRing(QQ, 'q', default_prec=9).gen() 999 sage: prod([(1-q^k)^(-1) for k in range(1,9)]) ## partial product of 1000 1 + q + 2*q^2 + 3*q^3 + 5*q^4 + 7*q^5 + 11*q^6 + 15*q^7 + 22*q^8 + O(q^9) 1004 1001 sage: [number_of_partitions_list(k) for k in range(2,10)] 1005 1002 [2, 3, 5, 7, 11, 15, 22, 30]
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