OpenWrite::noopen: Cannot open /stmp/mathematica/tmp_342748.txt. Content-type: text/html MGROUPS
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The magnetic space groups derived from the Fedorov space group: 029 > 029 (id = 27928)HHHHRead tr. matrix for the supergroup from /tmp/wp-supertrm27928.trnHHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHinverted:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHRead tr. matrix for the subgroup from /tmp/wp-subtrm27928.trnHHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHinverted:HHHH1.000000 0.000000 0.000000 0.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHRead tr. matrix from /tmp/wp-trm27928.trnHHHH7.000000 0.000000 0.000000 1.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHTransformation matrix:HHHH7.000000 0.000000 0.000000 1.000000 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHdeterminant: 7.000000(det-ONE=6.000000)HHHHInverted of the transformation matrix:HHHH0.142857 0.000000 0.000000 -0.142857 HHHH0.000000 1.000000 0.000000 0.000000 HHHH0.000000 0.000000 1.000000 0.000000 HHHHSubgroup generators: 2, general positions: 4HHHH(x,y,z)HHHH(-x, -y, 0.500000 +z)HHHH(0.500000 - x,y, 0.500000 +z)HHHH(0.500000 +x, -y,z)HHHHSubgroup Wyckoff positions:HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:4HHHHLetter:aHHHH(x,y,z)HHHH(-x, -y, 0.500000 +z)HHHH(0.500000 - x,y, 0.500000 +z)HHHH(0.500000 +x, -y,z)HHHHtr. matrix:(1.000000 + 7.000000x,y,z)HHHHdet = 7.000000HHHHSupergroup is transformed to unconventional setting.HHHHtake memory for 9 cells.HHHHtr. matrix:(1.000000 + 7.000000x,y,z)HHHHNumber of gen. pos. = 4, det = 7.000000. New number of general positions: 28HHHHchange the basis with the matrix (1.000000 + 7.000000x,y,z)HHHHAfter checking group we obtain 28 elementsHHHH000HHHHBefore expanding:HHHH(x,y,z)HHHH(0.714286 - x, -y, 0.500000 +z)HHHH(0.071429 +x, -y,z)HHHH(0.785714 - x,y, 0.500000 +z)HHHHAfter expanding general positions: number of cells: 1HHHHNumber of gen. pos. = 0, det = 7.000000. New number of general positions: 0HHHH(x,y,z)HHHH(0.142857 +x,y,z)HHHH(0.285714 +x,y,z)HHHH(0.428571 +x,y,z)HHHH(0.571429 +x,y,z)HHHH(0.714286 +x,y,z)HHHH(0.857143 +x,y,z)HHHH(0.714286 - x, -y, 0.500000 +z)HHHH(0.857143 - x, -y, 0.500000 +z)HHHH(-x, -y, 0.500000 +z)HHHH(0.142857 - x, -y, 0.500000 +z)HHHH(0.285714 - x, -y, 0.500000 +z)HHHH(0.428571 - x, -y, 0.500000 +z)HHHH(0.571429 - x, -y, 0.500000 +z)HHHH(0.071429 +x, -y,z)HHHH(0.214286 +x, -y,z)HHHH(0.357143 +x, -y,z)HHHH(0.500000 +x, -y,z)HHHH(0.642857 +x, -y,z)HHHH(0.785714 +x, -y,z)HHHH(0.928571 +x, -y,z)HHHH(0.785714 - x,y, 0.500000 +z)HHHH(0.928571 - x,y, 0.500000 +z)HHHH(0.071429 - x,y, 0.500000 +z)HHHH(0.214286 - x,y, 0.500000 +z)HHHH(0.357143 - x,y, 0.500000 +z)HHHH(0.500000 - x,y, 0.500000 +z)HHHH(0.642857 - x,y, 0.500000 +z)HHHH000HHHHSupergroup is transformed (28 gen.pos.)->return the new group.HHHH(x,y,z)HHHH(0.142857 +x,y,z)HHHH(0.285714 +x,y,z)HHHH(0.428571 +x,y,z)HHHH(0.571429 +x,y,z)HHHH(0.714286 +x,y,z)HHHH(0.857143 +x,y,z)HHHH(0.714286 - x, -y, 0.500000 +z)HHHH(0.857143 - x, -y, 0.500000 +z)HHHH(-x, -y, 0.500000 +z)HHHH(0.142857 - x, -y, 0.500000 +z)HHHH(0.285714 - x, -y, 0.500000 +z)HHHH(0.428571 - x, -y, 0.500000 +z)HHHH(0.571429 - x, -y, 0.500000 +z)HHHH(0.071429 +x, -y,z)HHHH(0.214286 +x, -y,z)HHHH(0.357143 +x, -y,z)HHHH(0.500000 +x, -y,z)HHHH(0.642857 +x, -y,z)HHHH(0.785714 +x, -y,z)HHHH(0.928571 +x, -y,z)HHHH(0.785714 - x,y, 0.500000 +z)HHHH(0.928571 - x,y, 0.500000 +z)HHHH(0.071429 - x,y, 0.500000 +z)HHHH(0.214286 - x,y, 0.500000 +z)HHHH(0.357143 - x,y, 0.500000 +z)HHHH(0.500000 - x,y, 0.500000 +z)HHHH(0.642857 - x,y, 0.500000 +z)HHHHSupergroup is transformed to the subgroup basis. there are 28 general positionsHHHHSupergroup generators: xxx, general positions:28HHHHSubgroup basis:HHHH(x,y,z)HHHH(0.142857 +x,y,z)HHHH(0.285714 +x,y,z)HHHH(0.428571 +x,y,z)HHHH(0.571429 +x,y,z)HHHH(0.714286 +x,y,z)HHHH(0.857143 +x,y,z)HHHH(0.714286 - x, -y, 0.500000 +z)HHHH(0.857143 - x, -y, 0.500000 +z)HHHH(-x, -y, 0.500000 +z)HHHH(0.142857 - x, -y, 0.500000 +z)HHHH(0.285714 - x, -y, 0.500000 +z)HHHH(0.428571 - x, -y, 0.500000 +z)HHHH(0.571429 - x, -y, 0.500000 +z)HHHH(0.071429 +x, -y,z)HHHH(0.214286 +x, -y,z)HHHH(0.357143 +x, -y,z)HHHH(0.500000 +x, -y,z)HHHH(0.642857 +x, -y,z)HHHH(0.785714 +x, -y,z)HHHH(0.928571 +x, -y,z)HHHH(0.785714 - x,y, 0.500000 +z)HHHH(0.928571 - x,y, 0.500000 +z)HHHH(0.071429 - x,y, 0.500000 +z)HHHH(0.214286 - x,y, 0.500000 +z)HHHH(0.357143 - x,y, 0.500000 +z)HHHH(0.500000 - x,y, 0.500000 +z)HHHH(0.642857 - x,y, 0.500000 +z)HHHHnumber of cells: 1HHHH000HHHHSupergroup Wyckoff positions:HHHHOwn basis.HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:4HHHHLetter:aHHHH(x,y,z)HHHHSubgroup basis.HHHHList of Wyckoff positions:HHHHOrbit No:0HHHHMultiplicity:4HHHHLetter:aHHHH(1.000000 + 0.142857 (-1.000000 +x),y,z)HHHHindex : 7HHHHSplitting of the general position of the supergroup...HHHHThe general position splits into 7 suborbits.HHHH&Splitting of all positions:HHHHGGGG4a: 4a 4a 4a 4a 4a 4a 4aHHHH&Splitting of Wyckoff position 4a: 4a 4a 4a 4a 4a 4a 4aHHHHOrbit 0:HHHH[0]TTTT(x,y,z)TTTT(0.142857 (-1.000000 +x),y,z)TTTT4aTTTT(x,y,z)HHHH[1]TTTT(-5.000000 - x, -y, 0.500000 +z)TTTT(0.142857 (-6.000000 - x), -y, 0.500000 +z)TTTT4aTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-3.500000 +x, -y,z)TTTT(0.071429 (-9.000000 + 2.000000x), -y,z)TTTT4aTTTT(0.500000 +x, -y,z)HHHH[3]TTTT(-1.500000 - x,y, 0.500000 +z)TTTT(0.071429 (-5.000000 - 2.000000x),y, 0.500000 +z)TTTT4aTTTT(0.500000 - x,y, 0.500000 +z)HHHHOrbit 1:HHHH[0]TTTT(-6.000000 +x,y,z)TTTT(0.142857 (-7.000000 +x),y,z)TTTT4aTTTT(x,y,z)HHHH[1]TTTT(-6.000000 - x, -y, 0.500000 +z)TTTT(-1.000000 - 0.142857x, -y, 0.500000 +z)TTTT4aTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-2.500000 +x, -y,z)TTTT(-0.500000 + 0.142857x, -y,z)TTTT4aTTTT(0.500000 +x, -y,z)HHHH[3]TTTT(-2.500000 - x,y, 0.500000 +z)TTTT(-0.500000 - 0.142857x,y, 0.500000 +z)TTTT4aTTTT(0.500000 - x,y, 0.500000 +z)HHHHOrbit 2:HHHH[0]TTTT(-5.000000 +x,y,z)TTTT(0.142857 (-6.000000 +x),y,z)TTTT4aTTTT(x,y,z)HHHH[1]TTTT(-x, -y, 0.500000 +z)TTTT(0.142857 (-1.000000 - x), -y, 0.500000 +z)TTTT4aTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-1.500000 +x, -y,z)TTTT(0.071429 (-5.000000 + 2.000000x), -y,z)TTTT4aTTTT(0.500000 +x, -y,z)HHHH[3]TTTT(-3.500000 - x,y, 0.500000 +z)TTTT(0.071429 (-9.000000 - 2.000000x),y, 0.500000 +z)TTTT4aTTTT(0.500000 - x,y, 0.500000 +z)HHHHOrbit 3:HHHH[0]TTTT(-4.000000 +x,y,z)TTTT(0.142857 (-5.000000 +x),y,z)TTTT4aTTTT(x,y,z)HHHH[1]TTTT(-1.000000 - x, -y, 0.500000 +z)TTTT(0.142857 (-2.000000 - x), -y, 0.500000 +z)TTTT4aTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-0.500000 +x, -y,z)TTTT(0.071429 (-3.000000 + 2.000000x), -y,z)TTTT4aTTTT(0.500000 +x, -y,z)HHHH[3]TTTT(-4.500000 - x,y, 0.500000 +z)TTTT(0.071429 (-11.000000 - 2.000000x),y, 0.500000 +z)TTTT4aTTTT(0.500000 - x,y, 0.500000 +z)HHHHOrbit 4:HHHH[0]TTTT(-3.000000 +x,y,z)TTTT(0.142857 (-4.000000 +x),y,z)TTTT4aTTTT(x,y,z)HHHH[1]TTTT(-2.000000 - x, -y, 0.500000 +z)TTTT(0.142857 (-3.000000 - x), -y, 0.500000 +z)TTTT4aTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(0.500000 +x, -y,z)TTTT(0.071429 (-1.000000 + 2.000000x), -y,z)TTTT4aTTTT(0.500000 +x, -y,z)HHHH[3]TTTT(-5.500000 - x,y, 0.500000 +z)TTTT(0.071429 (-13.000000 - 2.000000x),y, 0.500000 +z)TTTT4aTTTT(0.500000 - x,y, 0.500000 +z)HHHHOrbit 5:HHHH[0]TTTT(-2.000000 +x,y,z)TTTT(0.142857 (-3.000000 +x),y,z)TTTT4aTTTT(x,y,z)HHHH[1]TTTT(-3.000000 - x, -y, 0.500000 +z)TTTT(0.142857 (-4.000000 - x), -y, 0.500000 +z)TTTT4aTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-5.500000 +x, -y,z)TTTT(0.071429 (-13.000000 + 2.000000x), -y,z)TTTT4aTTTT(0.500000 +x, -y,z)HHHH[3]TTTT(0.500000 - x,y, 0.500000 +z)TTTT(0.071429 (-1.000000 - 2.000000x),y, 0.500000 +z)TTTT4aTTTT(0.500000 - x,y, 0.500000 +z)HHHHOrbit 6:HHHH[0]TTTT(-1.000000 +x,y,z)TTTT(0.142857 (-2.000000 +x),y,z)TTTT4aTTTT(x,y,z)HHHH[1]TTTT(-4.000000 - x, -y, 0.500000 +z)TTTT(0.142857 (-5.000000 - x), -y, 0.500000 +z)TTTT4aTTTT(-x, -y, 0.500000 +z)HHHH[2]TTTT(-4.500000 +x, -y,z)TTTT(0.071429 (-11.000000 + 2.000000x), -y,z)TTTT4aTTTT(0.500000 +x, -y,z)HHHH[3]TTTT(-0.500000 - x,y, 0.500000 +z)TTTT(0.071429 (-3.000000 - 2.000000x),y, 0.500000 +z)TTTT4aTTTT(0.500000 - x,y, 0.500000 +z)HHHHGGGG&{{4, a}}${{{4, a}, {4, a}, {4, a}, {4, a}, {4, a}, {4, a}, {4, a}}}${{{{x, y, z}, {-5 - x, -y, 1/2 + z}, {-7/2 + x, -y, z}, {-3/2 - x, y, 1/2 + z}}, {{-6 + x, y, z}, {-6 - x, -y, 1/2 + z}, {-5/2 + x, -y, z}, {-5/2 - x, y, 1/2 + z}}, {{-5 + x, y, z}, {-x, -y, 1/2 + z}, {-3/2 + x, -y, z}, {-7/2 - x, y, 1/2 + z}}, {{-4 + x, y, z}, {-1 - x, -y, 1/2 + z}, {-1/2 + x, -y, z}, {-9/2 - x, y, 1/2 + z}}, {{-3 + x, y, z}, {-2 - x, -y, 1/2 + z}, {1/2 + x, -y, z}, {-11/2 - x, y, 1/2 + z}}, {{-2 + x, y, z}, {-3 - x, -y, 1/2 + z}, {-11/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}, {{-1 + x, y, z}, {-4 - x, -y, 1/2 + z}, {-9/2 + x, -y, z}, {-1/2 - x, y, 1/2 + z}}}}${{{{(-1 + x)/7, y, z}, {(-6 - x)/7, -y, 1/2 + z}, {(-9 + 2*x)/14, -y, z}, {(-5 - 2*x)/14, y, 1/2 + z}}, {{(-7 + x)/7, y, z}, {-1 - x/7, -y, 1/2 + z}, {-1/2 + x/7, -y, z}, {-1/2 - x/7, y, 1/2 + z}}, {{(-6 + x)/7, y, z}, {(-1 - x)/7, -y, 1/2 + z}, {(-5 + 2*x)/14, -y, z}, {(-9 - 2*x)/14, y, 1/2 + z}}, {{(-5 + x)/7, y, z}, {(-2 - x)/7, -y, 1/2 + z}, {(-3 + 2*x)/14, -y, z}, {(-11 - 2*x)/14, y, 1/2 + z}}, {{(-4 + x)/7, y, z}, {(-3 - x)/7, -y, 1/2 + z}, {(-1 + 2*x)/14, -y, z}, {(-13 - 2*x)/14, y, 1/2 + z}}, {{(-3 + x)/7, y, z}, {(-4 - x)/7, -y, 1/2 + z}, {(-13 + 2*x)/14, -y, z}, {(-1 - 2*x)/14, y, 1/2 + z}}, {{(-2 + x)/7, y, z}, {(-5 - x)/7, -y, 1/2 + z}, {(-11 + 2*x)/14, -y, z}, {(-3 - 2*x)/14, y, 1/2 + z}}}}${{{{x, y, z}, {-x, -y, 1/2 + z}, {1/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}, {{x, y, z}, {-x, -y, 1/2 + z}, {1/2 + x, -y, z}, {1/2 - x, y, 1/2 + z}}}}&OK! (#)

Listed with respect to the BNS setting:


Listed with respect to the OG setting:



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