|\^/| Maple 18 (X86 64 LINUX) ._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014 \ MAPLE / All rights reserved. Maple is a trademark of <____ ____> Waterloo Maple Inc. | Type ? for help. > interface(quiet=true): ############################################################################ # Computing for the Grassmannian G(2,4) All cases okay! Number of problems= 1 Number with [zero, one, at least 2] solutions = [0, 0, 1]. This took 0.01 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(2,5) All cases okay! Number of problems= 4 Number with [zero, one, at least 2] solutions = [0, 1, 3]. This took 0.03 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(2,6) All cases okay! Number of problems= 10 Number with [zero, one, at least 2] solutions = [0, 1, 9]. This took 0.12 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(2,7) All cases okay! Number of problems= 23 Number with [zero, one, at least 2] solutions = [0, 2, 21]. This took 0.36 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(2,8) All cases okay! Number of problems= 47 Number with [zero, one, at least 2] solutions = [0, 3, 44]. This took 1.28 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(2,9) All cases okay! Number of problems= 90 Number with [zero, one, at least 2] solutions = [0, 4, 86]. This took 3.63 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(2,10) All cases okay! Number of problems= 164 Number with [zero, one, at least 2] solutions = [0, 5, 159]. This took 11.43 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(2,11) All cases okay! Number of problems= 288 Number with [zero, one, at least 2] solutions = [0, 7, 281]. This took 40.04 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(3,5) All cases okay! Number of problems= 4 Number with [zero, one, at least 2] solutions = [0, 1, 3]. This took 0.29 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(3,6) There were 2 Schubert problems that I could not tell were at least alternating: 6 = [3, 5, 6]^5 [2, 3, 6]^1 42 = [3, 5, 6]^9 Number of problems= 39 Number with [zero, one, at least 2] solutions = [1, 4, 34]. This took 5.81 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(3,7) There were 3 Schubert problems that I could not tell were at least alternating: 6 = [4, 6, 7]^4 [3, 6, 7]^1 [2, 3, 7]^1 10 = [4, 6, 7]^6 [2, 3, 7]^1 6 = [4, 5, 7]^5 [3, 6, 7]^1 Number of problems= 270 Number with [zero, one, at least 2] solutions = [9, 25, 236]. This took 30.16 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(3,8) There were 7 Schubert problems that I could not tell were at least alternating: 6 = [5, 7, 8]^4 [3, 7, 8]^1 [2, 3, 8]^1 6 = [5, 7, 8]^3 [4, 7, 8]^2 [2, 3, 8]^1 10 = [5, 7, 8]^5 [4, 7, 8]^1 [2, 3, 8]^1 15 = [5, 7, 8]^7 [2, 3, 8]^1 10 = [4, 6, 8]^1 [3, 6, 8]^3 6 = [5, 6, 8]^4 [4, 5, 8]^1 [3, 7, 8]^1 10 = [5, 6, 8]^6 [3, 7, 8]^1 Number of problems= 1337 Number with [zero, one, at least 2] solutions = [40, 67, 1230]. This took 227.53 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(3,9) There were 14 Schubert problems that I could not tell were at least alternating: 6 = [6, 8, 9]^4 [3, 8, 9]^1 [2, 3, 9]^1 6 = [6, 8, 9]^3 [5, 8, 9]^1 [4, 8, 9]^1 [2, 3, 9]^1 10 = [6, 8, 9]^5 [4, 8, 9]^1 [2, 3, 9]^1 6 = [6, 8, 9]^2 [5, 8, 9]^3 [2, 3, 9]^1 10 = [6, 8, 9]^4 [5, 8, 9]^2 [2, 3, 9]^1 15 = [6, 8, 9]^6 [5, 8, 9]^1 [2, 3, 9]^1 21 = [6, 8, 9]^8 [2, 3, 9]^1 6 = [6, 7, 9]^4 [4, 5, 9]^1 [3, 8, 9]^1 10 = [5, 7, 9]^1 [3, 7, 9]^3 8 = [4, 8, 9]^1 [3, 7, 9]^3 6 = [6, 7, 9]^3 [5, 6, 9]^2 [3, 8, 9]^1 10 = [6, 7, 9]^5 [5, 6, 9]^1 [3, 8, 9]^1 15 = [6, 7, 9]^7 [3, 8, 9]^1 42 = [6, 7, 9]^9 Number of problems= 5786 Number with [zero, one, at least 2] solutions = [150, 184, 5452]. This took 2825.56 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(4,6) All cases okay! Number of problems= 10 Number with [zero, one, at least 2] solutions = [0, 1, 9]. This took 9.10 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(4,7) There were 3 Schubert problems that I could not tell were at least alternating: 6 = [3, 5, 6, 7]^4 [3, 4, 6, 7]^1 [2, 3, 4, 7]^1 10 = [3, 5, 6, 7]^6 [2, 3, 4, 7]^1 6 = [3, 4, 6, 7]^1 [2, 5, 6, 7]^5 Number of problems= 270 Number with [zero, one, at least 2] solutions = [9, 25, 236]. This took 215.50 seconds ############################################################################ ############################################################################ # Computing for the Grassmannian G(4,8) There were 33 Schubert problems that I could not tell were at least alternating: 6 = [4, 6, 7, 8]^4 [3, 5, 7, 8]^1 [2, 3, 4, 8]^1 6 = [4, 6, 7, 8]^3 [4, 5, 7, 8]^1 [3, 6, 7, 8]^1 [2, 3, 4, 8]^1 10 = [4, 6, 7, 8]^5 [4, 5, 7, 8]^1 [2, 3, 4, 8]^1 10 = [4, 6, 7, 8]^5 [3, 6, 7, 8]^1 [2, 3, 4, 8]^1 20 = [4, 6, 7, 8]^7 [2, 3, 4, 8]^1 6 = [4, 6, 7, 8]^4 [3, 4, 7, 8]^1 [2, 3, 5, 8]^1 36 = [4, 6, 7, 8]^6 [4, 5, 6, 8]^1 [2, 4, 5, 8]^1 6 = [4, 5, 7, 8]^1 [3, 6, 7, 8]^1 [2, 4, 6, 8]^2 6 = [4, 5, 7, 8]^4 [3, 6, 7, 8]^1 [2, 3, 7, 8]^1 6 = [4, 5, 7, 8]^1 [3, 6, 7, 8]^4 [3, 4, 5, 8]^1 6 = [3, 4, 7, 8]^4 4 = [3, 5, 6, 8]^1 [3, 4, 7, 8]^2 [2, 5, 7, 8]^1 4 = [3, 5, 6, 8]^2 [2, 5, 7, 8]^2 4 = [4, 6, 7, 8]^1 [4, 5, 6, 8]^1 [3, 4, 7, 8]^2 [2, 5, 7, 8]^1 4 = [4, 6, 7, 8]^1 [4, 5, 6, 8]^1 [3, 5, 6, 8]^1 [2, 5, 7, 8]^2 4 = [4, 6, 7, 8]^1 [3, 5, 6, 8]^1 [3, 4, 7, 8]^2 [2, 6, 7, 8]^1 4 = [4, 6, 7, 8]^1 [3, 5, 6, 8]^2 [2, 6, 7, 8]^1 [2, 5, 7, 8]^1 32 = [4, 6, 7, 8]^4 [3, 4, 7, 8]^3 4 = [4, 6, 7, 8]^2 [4, 5, 6, 8]^2 [2, 5, 7, 8]^2 4 = [4, 6, 7, 8]^2 [3, 4, 7, 8]^2 [2, 6, 7, 8]^1 [4, 5, 6, 8]^1 4 = [4, 6, 7, 8]^2 [3, 5, 6, 8]^1 [2, 6, 7, 8]^1 [4, 5, 6, 8]^1 [2, 5, 7, 8]^1 4 = [4, 6, 7, 8]^2 [3, 5, 6, 8]^2 [2, 6, 7, 8]^2 280 = [4, 6, 7, 8]^8 [3, 4, 7, 8]^2 6 = [3, 5, 7, 8]^1 [2, 6, 7, 8]^3 [2, 5, 7, 8]^1 42 = [3, 5, 7, 8]^4 [3, 4, 7, 8]^1 4 = [4, 6, 7, 8]^3 [4, 5, 6, 8]^2 [2, 6, 7, 8]^1 [2, 5, 7, 8]^1 4 = [4, 6, 7, 8]^3 [3, 5, 6, 8]^1 [2, 6, 7, 8]^2 [4, 5, 6, 8]^1 2640 = [4, 6, 7, 8]^12 [3, 4, 7, 8]^1 6 = [4, 5, 6, 8]^4 [3, 6, 7, 8]^1 [4, 5, 7, 8]^1 6 = [4, 5, 7, 8]^1 [3, 6, 7, 8]^1 [2, 6, 7, 8]^4 4 = [4, 6, 7, 8]^4 [4, 5, 6, 8]^2 [2, 6, 7, 8]^2 420 = [4, 6, 7, 8]^10 [4, 5, 6, 8]^1 [2, 6, 7, 8]^1 24024 = [4, 6, 7, 8]^16 Number of problems= 3802 Number with [zero, one, at least 2] solutions = [121, 180, 3501]. This took 15807.38 seconds ############################################################################