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Annotation of OpenXM_contrib2/asir2000/lib/sturm, Revision 1.2

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
        !            26:  * e-mail at risa-admin@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: OpenXM_contrib2/asir2000/lib/sturm,v 1.1.1.1 1999/12/03 07:39:11 noro Exp $
        !            49: */
1.1       noro       50: /* find intervals which include roots of a polynomial */
                     51:
                     52: #include "defs.h"
                     53:
                     54: def slice(P,XR,YR,WH) {
                     55:        X = FIRST(XR); XMIN = SECOND(XR); XMAX = THIRD(XR);
                     56:        Y = FIRST(YR); YMIN = SECOND(YR); YMAX = THIRD(YR);
                     57:        W = FIRST(WH); H = SECOND(WH);
                     58:        XS = (XMAX-XMIN)/W; YS = (YMAX-YMIN)/H;
                     59:        T = ptozp(subst(P,X,X*XS+XMIN,Y,Y*YS+YMIN));
                     60:        R = newvect(W+1);
                     61:        for ( I = 0; I <= W; I++ ) {
                     62:                S = sturm(subst(T,X,I));
                     63:                R[I] = numch(S,Y,0)-numch(S,Y,H);
                     64:        }
                     65:        return R;
                     66: }
                     67:
                     68: def slice1(P,XR,YR,WH) {
                     69:        X = FIRST(XR); XMIN = SECOND(XR); XMAX = THIRD(XR);
                     70:        Y = FIRST(YR); YMIN = SECOND(YR); YMAX = THIRD(YR);
                     71:        W = FIRST(WH); H = SECOND(WH);
                     72:        XS = (XMAX-XMIN)/W; YS = (YMAX-YMIN)/H;
                     73:        T = ptozp(subst(P,X,X*XS+XMIN,Y,Y*YS+YMIN));
                     74:        R = newvect(W+1);
                     75:        for ( I = 0; I <= W; I++ ) {
                     76:                S = sturm(subst(T,X,I));
                     77:                R[I] = newvect(H+1);
                     78:                seproot(S,Y,0,H,R[I]);
                     79:        }
                     80:        return R;
                     81: }
                     82:
                     83: def seproot(S,X,MI,MA,R) {
                     84:        N = car(size(S));
                     85:        for ( I = MI; I <= MA; I++ )
                     86:                if ( !(T = subst(S[0],X,I)) )
                     87:                        R[I] = -1;
                     88:                else
                     89:                        break;
                     90:        if ( I > MA )
                     91:                return;
                     92:        for ( J = MA; J >= MI; J-- )
                     93:                if ( !(T = subst(S[0],X,J)) )
                     94:                        R[J] = -1;
                     95:                else
                     96:                        break;
                     97:        R[I] = numch(S,X,I); R[J] = numch(S,X,J);
                     98:        if ( J <= I+1  )
                     99:                return;
                    100:        if ( R[I] == R[J] ) {
                    101:                for ( K = I + 1; K < J; K++ )
                    102:                        R[K] = R[I];
                    103:                return;
                    104:        }
                    105:        T = idiv(I+J,2);
                    106:        seproot(S,X,I,T,R);
                    107:        seproot(S,X,T,J,R);
                    108: }
                    109:
                    110: /* compute the sturm sequence of P */
                    111:
                    112: def sturm(P) {
                    113:        V = var(P); N = deg(P,V); T = newvect(N+1);
                    114:        G1 = T[0] = P; G2 = T[1] = ptozp(diff(P,var(P)));
                    115:        for ( I = 1, H = 1, X = 1; ; ) {
                    116:                if ( !deg(G2,V) )
                    117:                        break;
                    118:                D = deg(G1,V)-deg(G2,V);
                    119:                if ( (L = LCOEF(G2)) < 0 )
                    120:                        L = -L;
                    121:                if ( !(R = -srem(L^(D+1)*G1,G2)) )
                    122:                        break;
                    123:                if ( type(R) == 1 ) {
                    124:                        T[++I] = (R>0?1:-1); break;
                    125:                }
                    126:                M = H^D; G1 = G2;
                    127:                G2 = T[++I] = sdiv(R,M*X);
                    128:                if ( (X = LCOEF(G1)) < 0 )
                    129:                        X = -X;
                    130:                H = X^D*H/M;
                    131:        }
                    132:        S = newvect(I+1);
                    133:        for ( J = 0; J <= I; J++ )
                    134:                S[J] = T[J];
                    135:        return S;
                    136: }
                    137:
                    138: def numch(S,V,A) {
                    139:        N = car(size(S));
                    140:        for ( T = subst(S[0],V,A), I = 1, C = 0; I < N; I++ ) {
                    141:                T1 = subst(S[I],V,A);
                    142:                if ( !T1 )
                    143:                        continue;
                    144:                if ( (T1 > 0 && T < 0) || (T1 < 0 && T > 0) )
                    145:                        C++;
                    146:                T = T1;
                    147:        }
                    148:        return C;
                    149: }
                    150:
                    151: def numch0(S,V,A,T) {
                    152:        N = car(size(S));
                    153:        for ( I = 1, C = 0; I < N; I++ ) {
                    154:                T1 = subst(S[I],V,A);
                    155:                if ( !T1 )
                    156:                        continue;
                    157:                if ( (T1 > 0 && T < 0) || (T1 < 0 && T > 0) )
                    158:                        C++;
                    159:                T = T1;
                    160:        }
                    161:        return C;
                    162: }
                    163: end;

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