Annotation of OpenXM_contrib2/asir2018/lib/cyclic, Revision 1.1
1.1 ! noro 1: /*
! 2: * Copyright (c) 1994-2000 FUJITSU LABORATORIES LIMITED
! 3: * All rights reserved.
! 4: *
! 5: * FUJITSU LABORATORIES LIMITED ("FLL") hereby grants you a limited,
! 6: * non-exclusive and royalty-free license to use, copy, modify and
! 7: * redistribute, solely for non-commercial and non-profit purposes, the
! 8: * computer program, "Risa/Asir" ("SOFTWARE"), subject to the terms and
! 9: * conditions of this Agreement. For the avoidance of doubt, you acquire
! 10: * only a limited right to use the SOFTWARE hereunder, and FLL or any
! 11: * third party developer retains all rights, including but not limited to
! 12: * copyrights, in and to the SOFTWARE.
! 13: *
! 14: * (1) FLL does not grant you a license in any way for commercial
! 15: * purposes. You may use the SOFTWARE only for non-commercial and
! 16: * non-profit purposes only, such as academic, research and internal
! 17: * business use.
! 18: * (2) The SOFTWARE is protected by the Copyright Law of Japan and
! 19: * international copyright treaties. If you make copies of the SOFTWARE,
! 20: * with or without modification, as permitted hereunder, you shall affix
! 21: * to all such copies of the SOFTWARE the above copyright notice.
! 22: * (3) An explicit reference to this SOFTWARE and its copyright owner
! 23: * shall be made on your publication or presentation in any form of the
! 24: * results obtained by use of the SOFTWARE.
! 25: * (4) In the event that you modify the SOFTWARE, you shall notify FLL by
! 26: * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
! 27: * for such modification or the source code of the modified part of the
! 28: * SOFTWARE.
! 29: *
! 30: * THE SOFTWARE IS PROVIDED AS IS WITHOUT ANY WARRANTY OF ANY KIND. FLL
! 31: * MAKES ABSOLUTELY NO WARRANTIES, EXPRESSED, IMPLIED OR STATUTORY, AND
! 32: * EXPRESSLY DISCLAIMS ANY IMPLIED WARRANTY OF MERCHANTABILITY, FITNESS
! 33: * FOR A PARTICULAR PURPOSE OR NONINFRINGEMENT OF THIRD PARTIES'
! 34: * RIGHTS. NO FLL DEALER, AGENT, EMPLOYEES IS AUTHORIZED TO MAKE ANY
! 35: * MODIFICATIONS, EXTENSIONS, OR ADDITIONS TO THIS WARRANTY.
! 36: * UNDER NO CIRCUMSTANCES AND UNDER NO LEGAL THEORY, TORT, CONTRACT,
! 37: * OR OTHERWISE, SHALL FLL BE LIABLE TO YOU OR ANY OTHER PERSON FOR ANY
! 38: * DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNITIVE OR CONSEQUENTIAL
! 39: * DAMAGES OF ANY CHARACTER, INCLUDING, WITHOUT LIMITATION, DAMAGES
! 40: * ARISING OUT OF OR RELATING TO THE SOFTWARE OR THIS AGREEMENT, DAMAGES
! 41: * FOR LOSS OF GOODWILL, WORK STOPPAGE, OR LOSS OF DATA, OR FOR ANY
! 42: * DAMAGES, EVEN IF FLL SHALL HAVE BEEN INFORMED OF THE POSSIBILITY OF
! 43: * SUCH DAMAGES, OR FOR ANY CLAIM BY ANY OTHER PARTY. EVEN IF A PART
! 44: * OF THE SOFTWARE HAS BEEN DEVELOPED BY A THIRD PARTY, THE THIRD PARTY
! 45: * DEVELOPER SHALL HAVE NO LIABILITY IN CONNECTION WITH THE USE,
! 46: * PERFORMANCE OR NON-PERFORMANCE OF THE SOFTWARE.
! 47: *
! 48: * $OpenXM$
! 49: */
! 50: def mkc(L,N)
! 51: {
! 52: if (L >= N) L -= N;
! 53: if (L >= 0)
! 54: return strtov("c"+rtostr(L));
! 55: return 0;
! 56: }
! 57:
! 58: /* generate cyclic N-th roots systems */
! 59:
! 60: def cyclic(N)
! 61: {
! 62: R = [];
! 63: for (L = 1; L <= N; L++) {
! 64: for (A = 0, I = 0; I <= N-1; I++) {
! 65: for (B = 1,J = I; J < L+I; J++) {
! 66: B *= mkc(J,N);
! 67: }
! 68: A += B;
! 69: }
! 70: A = ptozp(A);
! 71: if (L == N)
! 72: A += -1;
! 73: R = cons(A,R);
! 74: }
! 75: return R;
! 76: }
! 77:
! 78: def rcyclic(N)
! 79: {
! 80: R = [];
! 81: for (L = 1; L <= N; L++) {
! 82: for (A = 0, I = 0; I < 3; I++) {
! 83: for (B = 1,J = I; J < L+I; J++) {
! 84: B *= mkc(J,N);
! 85: }
! 86: A += B;
! 87: }
! 88: A = ptozp(A);
! 89: if (L == N)
! 90: A += -1;
! 91: R = cons(A,R);
! 92: }
! 93: return R;
! 94: }
! 95:
! 96: /* generate homogenized cyclic N-th roots systems */
! 97:
! 98: def hcyclic(N)
! 99: {
! 100: R = [];
! 101: for (L = 1; L <= N; L++) {
! 102: for (A = 0, I = 0; I <= N-1; I++) {
! 103: for (B = 1,J = I; J < L+I; J++) {
! 104: B *= mkc(J,N);
! 105: }
! 106: A += B;
! 107: }
! 108: A = ptozp(A);
! 109: if (L == N)
! 110: A += -c^N;
! 111: R = cons(A,R);
! 112: }
! 113: return R;
! 114: }
! 115:
! 116: def homo(X)
! 117: {
! 118: X=nm(red(subst(X,a,a/t,b,b/t,c,c/t)));
! 119: }
! 120:
! 121: BJ6 = [a^2*b*c+a*b^2*c+a*b*c^2+a*b+b*c+c*a,a^2*b^2*c+a*b^2*c^2+b*c^2+c+a+a^2*b,
! 122: a^2*b^2*c^2+b^2*c^2+c^2+1+a^2+a^2*b^2]$
! 123: HBJ6 = [homo(BJ6[0]),homo(BJ6[1]),homo(BJ6[2])]$
! 124: BJ7 = [nm(red(a+b+c+1+1/c+1/b+1/a)),nm(red(a*b+b*c+c+1/c+1/(b*c)+1/(a*b)+1)),
! 125: nm(red(a*b*c+b*c+1+1/(b*c)+1/(a*b*c)+1/b+b))]$
! 126: HBJ7 = [homo(BJ7[0]),homo(BJ7[1]),homo(BJ7[2])]$
! 127: end$
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