Changeset 837fed in git


Ignore:
Timestamp:
May 3, 2005, 3:02:59 PM (19 years ago)
Author:
Hans Schönemann <hannes@…>
Branches:
(u'spielwiese', '17f1d200f27c5bd38f5dfc6e8a0879242279d1d8')
Children:
cfbe751106c543ddd2e453c6273a3b0dd2a216fa
Parents:
15ce8e2f21f7e6cb9798d2a41cb4caacce86296e
Message:
*hannes?lossen: new sole.lib::ures


git-svn-id: file:///usr/local/Singular/svn/trunk@8017 2c84dea3-7e68-4137-9b89-c4e89433aadc
Files:
7 edited

Legend:

Unmodified
Added
Removed

  • Singular/LIB/solve.lib

    r15ce8e r837fed  
    11///////////////////////////////////////////////////////////////////////////////
    2 version="$Id: solve.lib,v 1.30 2005-05-03 07:28:29 Singular Exp $";
     2version="$Id: solve.lib,v 1.31 2005-05-03 13:02:54 Singular Exp $";
    33category="Symbolic-numerical solving";
    44info="
    … …  
    4646         parameters.
    4747RETURN:  list of (complex) roots of the polynomial f, depending on n. The
    48          result is of type@*
     48         entries of the result are of type@*
    4949          string: if the basering is not complex,@*
    5050          number: otherwise.
    … …  
    13521352proc ures_solve( ideal gls, list # )
    13531353"USAGE:   ures_solve(i [, k, p] ); i = ideal, k, p = integers
    1354    k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky,
    1355    k=1: use resultant matrix of Macaulay which works only for
    1356           homogeneous ideals,
     1354   k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky, @*
     1355   k=1: use resultant matrix of Macaulay which works only for 
     1356          homogeneous ideals,@*
    13571357   p>0: defines precision of the long floats for internal computation
    13581358          if the basering is not complex (in decimal digits),
    13591359   (default: k=0, p=30)
    1360 ASSUME:  i is a zerodimensional ideal with
    1361          nvars(basering) = ncols(i) = number of vars
    1362          actually occurring in i,
    1363 RETURN:  list of all (complex) roots of the polynomial system i = 0; the
    1364          result is of type
    1365    string: if the basering is not complex,
    1366    number: otherwise.
     1360ASSUME:  i is a zerodimensional ideal given by a quadratic system, that is,@*
     1361         nvars(basering) = ncols(i) = number of vars actually occurring in i,
     1362RETURN:  If the ground field is the field of complex numbers: list of numbers
     1363         (the complex roots of the polynomial system i=0). @*
     1364         Otherwise: ring @code{R} with the same number of variables but with
     1365         complex coefficients (and precision p). @code{R} comes with a list
     1366         @code{SOL} of numbers, in which complex roots of the polynomial
     1367         system i are stored: @*
    13671368EXAMPLE: example ures_solve; shows an example
    13681369"
    … …  
    13901391    }
    13911392
    1392     return(uressolve(gls,typ,prec,1));
    1393     // the last nonzero parameter gives an extra run of
    1394     // Laguerre's algorithm leading to better results
     1393    list LL=uressolve(gls,typ,prec,1);
     1394    int sizeLL=size(LL);
     1395    if (sizeLL==0) {
     1396      dbprint(printlevel-voice+3,"No solution found!");
     1397      return(list());
     1398    }   
     1399    if (typeof(LL[1][1])=="string") {
     1400      int ii,jj;
     1401      int nv=size(LL[1]);
     1402      execute("ring rinC =(complex,"+string(prec)+",I),("
     1403                           +varstr(basering)+"),lp;");
     1404      list SOL,SOLnew;
     1405      for (ii=1; ii<=sizeLL; ii++) {
     1406        SOLnew=list();
     1407        for (jj=1; jj<=nv; jj++) {
     1408          execute("SOLnew["+string(jj)+"]="+LL[ii][jj]+";");
     1409        }
     1410        SOL[ii]=SOLnew;
     1411      }
     1412      kill SOLnew;
     1413      export SOL;
     1414      dbprint( printlevel-voice+3,"
     1415// 'ures_solve' created a ring, in which a list SOL of numbers (the complex
     1416// solutions) is stored.
     1417// To access the list of complex solutions, type (if the name R was assigned
     1418// to the return value):
     1419        setring R; SOL; ");
     1420      return(rinC);
     1421    }
     1422    else {
     1423      return(LL);
     1424    }
    13951425}
    13961426example
    … …  
    14001430    ring rsq = 0,(x,y),lp;
    14011431    ideal gls=  x2 + y2 - 10, x2 + xy + 2y2 - 16;
    1402     ures_solve(gls,0,16);
     1432    def R=ures_solve(gls,0,16);
     1433    setring R; SOL;
    14031434    // result is a list (x,y)-coordinates as strings
    14041435

  • Tst/Long/solve_l.res.gz.uu

    r15ce8e r837fed  
    11begin 640 solve_l.res.gz
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    123125`
    124126end

  • Tst/Long/solve_l.stat

    r15ce8e r837fed  
    1 1 >> tst_memory_0 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:668828
    2 1 >> tst_memory_1 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:1355220
    3 1 >> tst_memory_2 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:1355220
    4 1 >> tst_timer_1 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:338
     11 >> tst_memory_0 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:669932
     21 >> tst_memory_1 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:1354644
     31 >> tst_memory_2 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:1354644
     41 >> tst_timer_1 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:326

  • Tst/Long/solve_l.tst

    r15ce8e r837fed  
    44LIB "tst.lib";
    55tst_init();
    6 tst_ignore("CVS ID $Id: solve_l.tst,v 1.3 2005-05-02 07:42:46 Singular Exp $");
     6tst_ignore("CVS ID $Id: solve_l.tst,v 1.4 2005-05-03 13:02:59 Singular Exp $");
    77
    88LIB "solve.lib";
    … …  
    2020ideal im=f0,f1,f2,f3;
    2121
    22 ures_solve(homog(i,h),1);
     22def A=ures_solve(homog(i,h),1);
     23setring A; SOL;
     24kill A;
     25setring rs1;
    2326mp_res_mat(homog(im,h),1);
    2427
    … …  
    3336ideal im=f0,f1,f2,f3;
    3437
    35 ures_solve(i);
     38def A=ures_solve(i);
     39setring A; SOL;
     40kill A;
     41setring rs2;
    3642mp_res_mat(im);
    3743
    … …  
    6874ideal im=f0,f1,f2,f3;
    6975
    70 ures_solve(homog(i,x0),1);
     76def A=ures_solve(homog(i,x0),1);
     77setring A; SOL;
     78kill A;
     79setring rs3;
    7180mp_res_mat(homog(im,x0),1);
    7281
    … …  
    8190ideal im=f0,f1,f2,f3;
    8291
    83 ures_solve(i);
     92def A=ures_solve(i);
     93setring A; SOL;
     94kill A;
     95setring rs4;
    8496mp_res_mat(im);
    8597

  • Tst/Short/solve_s.res.gz.uu

    r15ce8e r837fed  
    11begin 640 solve_s.res.gz
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     73M!QOQRAY"(Q8#Q@)3$,"T6+(-+4]WVQE>M3O#ZXJ-5Z-0T+/%I*[K?[U<UAGU
     74M8G[^/KO&3N;G,S:=O&/IKSH=_/SO'W[YYZN?P^9>QS2+N10G4=IDN%MW&\X6
     75M"-YYW0.8C595F.#==#P[JN^OA?#"K<EL<CUF;-43_9!1>[)?/ZVXZE$?R17I
     76M!Q]5/Q_V>;(\K6=8SD<([L412\/32ZX5I-??ACA$>9KWQE<8)[-Q);/U_$$!
     77M3MG;%;"U"V7]@?KK!RJ#@N-:0:6_H"(YT:"05(0/4,&""A^AF(V6\\F*+6;(
     78MN.%__0?U!3)%^*$BG!;%0<<D@*$H(8+?,OSNDJDU10%F.V6"?K96)8)DMQX?
     79M!.)/'1U8,78&3]2+&HAUGVK=:4HKVHC-NL0^C>:3$4(I"0GDS6TAK%:'.HE$
     80MNBUYW"E)'9+#34F(UCTR;)!ALW%ZBUG!S@J&WS/`,@-\,T*N9=G.ZD$>EZX#
     81M<;45>/_!*CSS2Q6%CRJ<$I7')PJ^5Q87T^[-#A9OUZ0I_/VXRP7"YL5W!_\%
     82(TE.;7]A.````
    8183`
    8284end

  • Tst/Short/solve_s.stat

    r15ce8e r837fed  
    1 1 >> tst_memory_0 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:450864
    2 1 >> tst_memory_1 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:830932
    3 1 >> tst_memory_2 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:830932
    4 1 >> tst_timer_1 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:157
     11 >> tst_memory_0 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:451808
     21 >> tst_memory_1 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:830356
     31 >> tst_memory_2 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:830356
     41 >> tst_timer_1 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:160

  • Tst/Short/solve_s.tst

    r15ce8e r837fed  
    44LIB "tst.lib";
    55tst_init();
    6 tst_ignore("CVS ID $Id: solve_s.tst,v 1.5 2005-05-02 07:42:56 Singular Exp $");
     6tst_ignore("CVS ID $Id: solve_s.tst,v 1.6 2005-05-03 13:02:58 Singular Exp $");
    77
    88LIB "solve.lib";
    … …  
    2020ideal im=f0,f1,f2,f3;
    2121
    22 ures_solve(homog(i,h),1);
     22def A=ures_solve(homog(i,h),1);
     23setring A; SOL;
     24kill A;
     25setring rs1;
    2326mp_res_mat(homog(im,h),1);
    2427
    … …  
    3336ideal im=f0,f1,f2,f3;
    3437
    35 ures_solve(i);
     38def A=ures_solve(i);
     39setring A; SOL;
     40kill A;
     41setring rs2;
    3642mp_res_mat(im);
    3743
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