Changeset b9d0f4e in git
 Timestamp:
 Feb 26, 2018, 3:17:40 PM (5 years ago)
 Branches:
 (u'spielwiese', '0d6b7fcd9813a1ca1ed4220cfa2b104b97a0a003')
 Children:
 dc9b97b94d6347995be139057074bed6e378f7d4
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 a2cd284766c6d39d5f8d6fb5b7f7f9ebf9d9cb02
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 1 edited
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Singular/LIB/fpalgebras.lib
ra2cd284 rb9d0f4e 642 642 643 643 proc dyckGrp1(int n, int d, intvec P) 644 " 645 The Dyck group with the following presentation 646 < x_1, x_2, ... , x_n  (x_1)^p1 = (x_2)^p2 = ... = (x_n)^pn = x_1 * x_2 * ... * x_n = 1 > 647 negative exponents are allowed 648 representation in the form x_i^p_i  x_(i+1)^p_(i+1) 644 "USAGE: dyckGrp1(n,d,P); n an integer, d an integer, P an intvec 645 RETURN: ring 646 NOTE:  the ring contains the ideal I, which contains the required relations 647 @*  The Dyck group with the following presentation 648 @* < x_1, x_2, ... , x_n  (x_1)^p1 = (x_2)^p2 = ... = (x_n)^pn = x_1 * x_2 * ... * x_n = 1 > 649 @*  negative exponents are allowed 650 @*  representation in the form x_i^p_i  x_(i+1)^p_(i+1) 651 @*  d gives the degreebound for the Letterplace ring 649 652 " 650 653 { … … 682 685 683 686 proc dyckGrp2(int n, int d, intvec P) 684 " 685 The Dyck group with the following presentation 686 < x_1, x_2, ... , x_n  (x_1)^p1 = (x_2)^p2 = ... = (x_n)^pn = x_1 * x_2 * ... * x_n = 1 > 687 negative exponents are allowed 688 representation in the form x_i^p_i  1 687 "USAGE: dyckGrp2(n,d,P); n an integer, d an integer, P an intvec 688 RETURN: ring 689 NOTE:  the ring contains the ideal I, which contains the required relations 690 @*  The Dyck group with the following presentation 691 @* < x_1, x_2, ... , x_n  (x_1)^p1 = (x_2)^p2 = ... = (x_n)^pn = x_1 * x_2 * ... * x_n = 1 > 692 @*  negative exponents are allowed 693 @*  representation in the form x_i^p_i  1 694 @*  d gives the degreebound for the Letterplace ring 689 695 " 690 696 { … … 723 729 724 730 proc dyckGrp3(int n, int d, intvec P) 725 " 726 The Dyck group with the following presentation 727 < x_1, x_2, ... , x_n  (x_1)^p1 = (x_2)^p2 = ... = (x_n)^pn = x_1 * x_2 * ... * x_n = 1 > 728 only positive exponents are allowed 729 no inverse generators needed 731 "USAGE: dyckGrp2(n,d,P); n an integer, d an integer, P an intvec 732 RETURN: ring 733 NOTE:  the ring contains the ideal I, which contains the required relations 734 @*  The Dyck group with the following presentation 735 @* < x_1, x_2, ... , x_n  (x_1)^p1 = (x_2)^p2 = ... = (x_n)^pn = x_1 * x_2 * ... * x_n = 1 > 736 @*  only positive exponents are allowed 737 @*  no inverse generators needed 738 @*  d gives the degreebound for the Letterplace ring 730 739 " 731 740 { … … 767 776 //////////////////////////////////////////////////////////////////// 768 777 769 proc fibGroup(int m, int d) 770 "The Fibonacci group F(2, m) with the following presentation 771 < x_1, x_2, ... , x_m  x_i * x_(i + 1) = x_(i + 2) > 772 TODO: basefield Q oder F2? 773 inverse Elemente! 774 " 778 proc fibonacciGroup(int m, int d) 779 "USAGE: fibonacciGroup(m,d); m an integer, d an integer 780 RETURN: ring 781 NOTE:  the ring contains the ideal I, which contains the required relations 782 @*  The Fibonacci group F(2, m) with the following presentation 783 @* < x_1, x_2, ... , x_m  x_i * x_(i + 1) = x_(i + 2) > 784 @*  d gives the degreebound for the Letterplace ring 785 " 786 // TODO: basefield Q oder F2? 787 // TODO: inverse Elemente! 775 788 { 776 789 if (m < 3) {ERROR("At least three generators are required!");} … … 810 823 //////////////////////////////////////////////////////////////////// 811 824 812 proc tetrahedron (int g, int d) 813 "The following examples are found in 825 proc tetrahedronGroup(int g, int d) 826 "USAGE: tetrahedronGroup(g,d); g an integer, d an integer 827 RETURN: ring 828 NOTE:  the ring contains the ideal I, which contains the required relations 829 @*  g gives the number of the example 830 @*  d gives the degreebound for the Letterplace ring 831 @* 832 The examples are found in 814 833 Classification of the finite generalized tetrahedron groups 815 834 by Gerhard Rosenberger and Martin Scheer. 816 The following5 examples are denoted in Proposition 1.9 and concern835 The 5 examples are denoted in Proposition 1.9 and concern 817 836 finite generalized tetrahedron group in the Tsarnarovcase, which are 818 837 not equivalent to a presentation for an ordinary tetrahedron group. 819 g gives the number of the example 838 @* 820 839 " 821 840 { … … 864 883 //////////////////////////////////////////////////////////////////// 865 884 866 proc trianGrp(int g, int d) 867 "The following examples are found in 885 proc triangularGroup(int g, int d) 886 "USAGE: triangularGroup(g,d); g an integer, d an integer 887 RETURN: ring 888 NOTE:  the ring contains the ideal I, which contains the required relations 889 @*  g gives the number of the example 890 @*  d gives the degreebound for the Letterplace ring 891 @* 892 The examples are found in 868 893 Classification of the finite generalized tetrahedron groups 869 894 by Gerhard Rosenberger and Martin Scheer. 870 T riangle groups, asin theorem 2.12871 g is the number of the example 895 The 14 examples are denoted in theorem 2.12 896 @* 872 897 " 873 898 {
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