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Annotation of OpenXM_contrib2/asir2000/lib/cyclic, Revision 1.3

1.2       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
1.3     ! noro       26:  * e-mail at risa-admin@sec.flab.fujitsu.co.jp of the detailed specification
1.2       noro       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.
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                     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:  *
1.3     ! noro       48:  * $OpenXM: OpenXM_contrib2/asir2000/lib/cyclic,v 1.2 2000/08/21 08:31:41 noro Exp $
1.2       noro       49: */
1.1       noro       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: /* generate homogenized cyclic N-th roots systems */
                     79:
                     80: def hcyclic(N)
                     81: {
                     82:        R = [];
                     83:        for (L = 1; L <= N; L++) {
                     84:                for (A = 0, I = 0; I <= N-1; I++) {
                     85:                        for (B = 1,J = I; J < L+I; J++) {
                     86:                                B *= mkc(J,N);
                     87:                        }
                     88:                        A += B;
                     89:                }
                     90:                A = ptozp(A);
                     91:                if (L == N)
                     92:                        A += -c^N;
                     93:                R = cons(A,R);
                     94:        }
                     95:        return R;
                     96: }
                     97:
                     98: def homo(X)
                     99: {
                    100:        X=nm(red(subst(X,a,a/t,b,b/t,c,c/t)));
                    101: }
                    102:
                    103: 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,
                    104: a^2*b^2*c^2+b^2*c^2+c^2+1+a^2+a^2*b^2]$
                    105: HBJ6 = [homo(BJ6[0]),homo(BJ6[1]),homo(BJ6[2])]$
                    106: 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)),
                    107: nm(red(a*b*c+b*c+1+1/(b*c)+1/(a*b*c)+1/b+b))]$
                    108: HBJ7 = [homo(BJ7[0]),homo(BJ7[1]),homo(BJ7[2])]$
                    109: end$