# Changeset 837fed in git

Ignore:
Timestamp:
May 3, 2005, 3:02:59 PM (19 years ago)
Branches:
(u'spielwiese', '82fc009ea2b0098c1a4896c841bb70860976bdfc')
Children:
cfbe751106c543ddd2e453c6273a3b0dd2a216fa
Parents:
15ce8e2f21f7e6cb9798d2a41cb4caacce86296e
Message:
```*hannes?lossen: new sole.lib::ures

Files:
7 edited

Unmodified
Removed
• ## Singular/LIB/solve.lib

 r15ce8e /////////////////////////////////////////////////////////////////////////////// version="\$Id: solve.lib,v 1.30 2005-05-03 07:28:29 Singular Exp \$"; version="\$Id: solve.lib,v 1.31 2005-05-03 13:02:54 Singular Exp \$"; category="Symbolic-numerical solving"; info=" parameters. RETURN:  list of (complex) roots of the polynomial f, depending on n. The result is of type@* entries of the result are of type@* string: if the basering is not complex,@* number: otherwise. proc ures_solve( ideal gls, list # ) "USAGE:   ures_solve(i [, k, p] ); i = ideal, k, p = integers k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky, k=1: use resultant matrix of Macaulay which works only for homogeneous ideals, k=0: use sparse resultant matrix of Gelfand, Kapranov and Zelevinsky, @* k=1: use resultant matrix of Macaulay which works only for homogeneous ideals,@* p>0: defines precision of the long floats for internal computation if the basering is not complex (in decimal digits), (default: k=0, p=30) ASSUME:  i is a zerodimensional ideal with nvars(basering) = ncols(i) = number of vars actually occurring in i, RETURN:  list of all (complex) roots of the polynomial system i = 0; the result is of type string: if the basering is not complex, number: otherwise. ASSUME:  i is a zerodimensional ideal given by a quadratic system, that is,@* nvars(basering) = ncols(i) = number of vars actually occurring in i, RETURN:  If the ground field is the field of complex numbers: list of numbers (the complex roots of the polynomial system i=0). @* Otherwise: ring @code{R} with the same number of variables but with complex coefficients (and precision p). @code{R} comes with a list @code{SOL} of numbers, in which complex roots of the polynomial system i are stored: @* EXAMPLE: example ures_solve; shows an example " } return(uressolve(gls,typ,prec,1)); // the last nonzero parameter gives an extra run of // Laguerre's algorithm leading to better results list LL=uressolve(gls,typ,prec,1); int sizeLL=size(LL); if (sizeLL==0) { dbprint(printlevel-voice+3,"No solution found!"); return(list()); } if (typeof(LL[1][1])=="string") { int ii,jj; int nv=size(LL[1]); execute("ring rinC =(complex,"+string(prec)+",I),(" +varstr(basering)+"),lp;"); list SOL,SOLnew; for (ii=1; ii<=sizeLL; ii++) { SOLnew=list(); for (jj=1; jj<=nv; jj++) { execute("SOLnew["+string(jj)+"]="+LL[ii][jj]+";"); } SOL[ii]=SOLnew; } kill SOLnew; export SOL; dbprint( printlevel-voice+3," // 'ures_solve' created a ring, in which a list SOL of numbers (the complex // solutions) is stored. // To access the list of complex solutions, type (if the name R was assigned // to the return value): setring R; SOL; "); return(rinC); } else { return(LL); } } example ring rsq = 0,(x,y),lp; ideal gls=  x2 + y2 - 10, x2 + xy + 2y2 - 16; ures_solve(gls,0,16); def R=ures_solve(gls,0,16); setring R; SOL; // result is a list (x,y)-coordinates as strings
• ## Tst/Long/solve_l.res.gz.uu

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• ## Tst/Long/solve_l.stat

 r15ce8e 1 >> tst_memory_0 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:668828 1 >> tst_memory_1 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:1355220 1 >> tst_memory_2 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:1355220 1 >> tst_timer_1 :: 1115019332:2005043019:3-0-0:ix86-Linux:nepomuck:338 1 >> tst_memory_0 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:669932 1 >> tst_memory_1 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:1354644 1 >> tst_memory_2 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:1354644 1 >> tst_timer_1 :: 1115125327:2005050311:3-0-0:ix86-Linux:nepomuck:326
• ## Tst/Long/solve_l.tst

 r15ce8e LIB "tst.lib"; tst_init(); tst_ignore("CVS ID \$Id: solve_l.tst,v 1.3 2005-05-02 07:42:46 Singular Exp \$"); tst_ignore("CVS ID \$Id: solve_l.tst,v 1.4 2005-05-03 13:02:59 Singular Exp \$"); LIB "solve.lib"; ideal im=f0,f1,f2,f3; ures_solve(homog(i,h),1); def A=ures_solve(homog(i,h),1); setring A; SOL; kill A; setring rs1; mp_res_mat(homog(im,h),1); ideal im=f0,f1,f2,f3; ures_solve(i); def A=ures_solve(i); setring A; SOL; kill A; setring rs2; mp_res_mat(im); ideal im=f0,f1,f2,f3; ures_solve(homog(i,x0),1); def A=ures_solve(homog(i,x0),1); setring A; SOL; kill A; setring rs3; mp_res_mat(homog(im,x0),1); ideal im=f0,f1,f2,f3; ures_solve(i); def A=ures_solve(i); setring A; SOL; kill A; setring rs4; mp_res_mat(im);
• ## Tst/Short/solve_s.res.gz.uu

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• ## Tst/Short/solve_s.stat

 r15ce8e 1 >> tst_memory_0 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:450864 1 >> tst_memory_1 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:830932 1 >> tst_memory_2 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:830932 1 >> tst_timer_1 :: 1115019239:2005043019:3-0-0:ix86-Linux:nepomuck:157 1 >> tst_memory_0 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:451808 1 >> tst_memory_1 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:830356 1 >> tst_memory_2 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:830356 1 >> tst_timer_1 :: 1115125145:2005050311:3-0-0:ix86-Linux:nepomuck:160
• ## Tst/Short/solve_s.tst

 r15ce8e LIB "tst.lib"; tst_init(); tst_ignore("CVS ID \$Id: solve_s.tst,v 1.5 2005-05-02 07:42:56 Singular Exp \$"); tst_ignore("CVS ID \$Id: solve_s.tst,v 1.6 2005-05-03 13:02:58 Singular Exp \$"); LIB "solve.lib"; ideal im=f0,f1,f2,f3; ures_solve(homog(i,h),1); def A=ures_solve(homog(i,h),1); setring A; SOL; kill A; setring rs1; mp_res_mat(homog(im,h),1); ideal im=f0,f1,f2,f3; ures_solve(i); def A=ures_solve(i); setring A; SOL; kill A; setring rs2; mp_res_mat(im);
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