Back to Forum | View unanswered posts | View active topics
 
|
Page 1 of 1
|
[ 3 posts ] |
|
| Author |
Message |
|
songuke
|
Post subject: Singular and Maxima gives different solutions  Posted: Thu Jun 30, 2011 5:38 am |
|
|
|
Hi, I've a system of linear-quadratic equations to solve. I tried Maxima and it gives me the correct solution. Singular gives me a complex solution, which is not accurate. Below is my code and outputs in Maxima and Singular. Singular: Code: number rax, ray, raz = 8.076651, -5.766802, 3.363392;
number rbx, rby, rbz = 6.532685, -6.184719, 4.475940;
number rcx, rcy, rcz = 7.850585, -4.163334, 4.243473;
number dax, day, daz = 10.079651, -2.603802, 0.338392;
number dbx, dby, dbz = 8.535685, -3.021719, 1.450940;
number dcx, dcy, dcz = 9.853585, -1.000334, 1.218473;
number la = 5.189281;
number lb = 2.145810;
number lc = 2.236297;
number ta = 4.788316;
number tb = 0.935814;
number tc = 4.252196;
number fab = 0.093240;
number fac = 0.512108;
number fbc = 1.061882;
poly f1 = raz*maz+ray*may+rax*max - la;
poly f2 = daz*maz+day*may+dax*max - ta;
poly f3 = rbz*mbz+rby*mby+rbx*mbx - lb;
poly f4 = dbz*mbz+dby*mby+dbx*mbx - tb;
poly f5 = rcz*mcz+rcy*mcy+rcx*mcx - lc;
poly f6 = dcz*mcz+dcy*mcy+dcx*mcx - tc;
poly f7 = -raz*rbz*maz*mbz-raz*rby*may*mbz-raz*rbx*max*mbz+la*raz*mbz
-ray*rbz*maz*mby-ray*rby*may*mby-ray*rbx*max*mby
+la*ray*mby-rax*rbz*maz*mbx-rax*rby*may*mbx
-rax*rbx*max*mbx+la*rax*mbx+lb*rbz*maz+lb*rby*may
+lb*rbx*max-la*lb+fab
;
poly f8 = -raz*rcz*maz*mcz-raz*rcy*may*mcz-raz*rcx*max*mcz+la*raz*mcz
-ray*rcz*maz*mcy-ray*rcy*may*mcy-ray*rcx*max*mcy
+la*ray*mcy-rax*rcz*maz*mcx-rax*rcy*may*mcx
-rax*rcx*max*mcx+la*rax*mcx+lc*rcz*maz+lc*rcy*may
+lc*rcx*max-la*lc+fac
;
poly f9 = -rbz*rcz*mbz*mcz-rbz*rcy*mby*mcz-rbz*rcx*mbx*mcz+lb*rbz*mcz
-rby*rcz*mbz*mcy-rby*rcy*mby*mcy-rby*rcx*mbx*mcy
+lb*rby*mcy-rbx*rcz*mbz*mcx-rbx*rcy*mby*mcx
-rbx*rcx*mbx*mcx+lb*rbx*mcx+lc*rcz*mbz+lc*rcy*mby
+lc*rcx*mbx-lb*lc+fbc
;
ideal I = f1, f2, f3, f4, f5, f6, f7, f8, f9;
ideal G = groebner(I);
dim(G);
vdim(G);
G;
def s = solve(I, 12);
Maxima: Code: ra : [8.076651, -5.766802, 3.363392];
rb : [6.532685, -6.184719, 4.475940];
rc : [7.850585, -4.163334, 4.243473];
da : [10.079651, -2.603802, 0.338392];
db : [8.535685, -3.021719, 1.450940];
dc : [9.853585, -1.000334, 1.218473];
la : 5.189281;
lb : 2.145810;
lc : 2.236297;
ta : 4.788316;
tb : 0.935814;
tc : 4.252196;
fab : 0.093240;
fac : 0.512108;
fbc : 1.061882;
ma : [max, may, maz];
mb : [mbx, mby, mbz];
mc : [mcx, mcy, mcz];
Hab : expand((ma . rb - la) * (lb - mb . ra));
Hac : expand((ma . rc - la) * (lc - mc . ra));
Hbc : expand((mb . rc - lb) * (lc - mc . rb));
eqns : [ma . ra = la, ma . da = ta, mb . rb = lb, mb . db = tb, mc . rc = lc, mc . dc = tc, Hab + fab = 0, Hac + fac = 0, Hbc + fbc = 0];
eqns;
sols : solve(eqns, [max, may, maz, mbx, mby, mbz, mcx, mcy, mcz]);
solsf : bfloat(sols);
The ground truth solution is Code: ma: 0.397328 -0.288674, 0.093798
mb: -0.007418 -0.283056, 0.099119
mc: 0.459667 0.599035, 0.264318
Output of Singular: Code: [1]:
[1]:
(0.396501063225-i*0.0585142482085)
[2]:
(-0.292459889853-i*0.267965150227)
[3]:
(0.0892914674573-i*0.318934797814)
[4]:
(-0.0228603746306-i*0.0180139060626)
[5]:
(-0.380524257884-i*0.113697415565)
[6]:
(-0.0130221380534-i*0.130812174086)
[7]:
(0.467285747848+i*0.00508868957766)
[8]:
(0.302313482452-i*0.198182075022)
[9]:
(-0.0408951640129-i*0.20385360867)
[2]:
[1]:
(0.396501063225+i*0.0585142482085)
[2]:
(-0.292459889853+i*0.267965150227)
[3]:
(0.0892914674573+i*0.318934797814)
[4]:
(-0.0228603746306+i*0.0180139060626)
[5]:
(-0.380524257884+i*0.113697415565)
[6]:
(-0.0130221380534+i*0.130812174086)
[7]:
(0.467285747848-i*0.00508868957766)
[8]:
(0.302313482452+i*0.198182075022)
[9]:
(-0.0408951640129+i*0.20385360867)
Output of Maxima: Code: [[max = 3.463461b-1,may = -5.2214398b-1,maz = -1.8408099b-1,
mbx = -2.3113602b-2,mby = -3.8212235b-1,mbz = -1.4860691b-2,
mcx = 4.6593653b-1,mcy = 3.5486107b-1,mcz = 1.3156148b-2],
[max = 3.973295b-1,may = -2.8866626b-1,maz = 9.3806532b-2,
mbx = -7.4168349b-3,mby = -2.8304991b-1,mbz = 9.9125014b-2,
mcx = 4.5966645b-1,mcy = 5.9905295b-1,mcz = 2.6433629b-1]]
Did I do something wrong in Singular? Thanks for your help.
|
|
|
| Top |
|
 |
|
songuke
|
Post subject: Re: Singular and Maxima gives different solutions Posted: Fri Jul 01, 2011 9:23 am |
|
Joined: Thu Jun 30, 2011 6:23 am
Posts: 1
|
Previously, the declared ring is Code: ring r1 = real, (max, may, maz, mbx, mby, mbz, mcx, mcy, mcz), lp;
It seems like there are something wrong when the ring is declared with real type. I switch to the following ring Code: ring r1 = 0, (max, may, maz, mbx, mby, mbz, mcx, mcy, mcz), lp;
and convert all floating point numbers to rational form. The solver gives solution similar to Maxima now. The full working code is as follows: Code: ring r1 = 0, (max, may, maz, mbx, mby, mbz, mcx, mcy, mcz), lp;
number rax, ray, raz = 2318/287, -1459/253, 2499/743;
number rbx, rby, rbz = 2698/413, -971/157, 837/187;
number rcx, rcy, rcz = 8722/1111, -1249/300, 6501/1532;
number dax, day, daz = 1139/113, -1781/684, 223/659;
number dbx, dby, dbz = 10166/1191, -3200/1059, 695/479;
number dcx, dcy, dcz = 3163/321, -2994/2993, 686/563;
number la = 1453/280;
number lb = 1972/919;
number lc = 1836/821;
number ta = 6311/1318;
number tb = 1283/1371;
number tc = 1450/341;
number fab = 491/5266;
number fac = 571/1115;
number fbc = 2042/1923;
poly f1 = raz*maz+ray*may+rax*max - la;
poly f2 = daz*maz+day*may+dax*max - ta;
poly f3 = rbz*mbz+rby*mby+rbx*mbx - lb;
poly f4 = dbz*mbz+dby*mby+dbx*mbx - tb;
poly f5 = rcz*mcz+rcy*mcy+rcx*mcx - lc;
poly f6 = dcz*mcz+dcy*mcy+dcx*mcx - tc;
poly f7 = -raz*rbz*maz*mbz-raz*rby*may*mbz-raz*rbx*max*mbz+la*raz*mbz
-ray*rbz*maz*mby-ray*rby*may*mby-ray*rbx*max*mby
+la*ray*mby-rax*rbz*maz*mbx-rax*rby*may*mbx
-rax*rbx*max*mbx+la*rax*mbx+lb*rbz*maz+lb*rby*may
+lb*rbx*max-la*lb+fab
;
poly f8 = -raz*rcz*maz*mcz-raz*rcy*may*mcz-raz*rcx*max*mcz+la*raz*mcz
-ray*rcz*maz*mcy-ray*rcy*may*mcy-ray*rcx*max*mcy
+la*ray*mcy-rax*rcz*maz*mcx-rax*rcy*may*mcx
-rax*rcx*max*mcx+la*rax*mcx+lc*rcz*maz+lc*rcy*may
+lc*rcx*max-la*lc+fac
;
poly f9 = -rbz*rcz*mbz*mcz-rbz*rcy*mby*mcz-rbz*rcx*mbx*mcz+lb*rbz*mcz
-rby*rcz*mbz*mcy-rby*rcy*mby*mcy-rby*rcx*mbx*mcy
+lb*rby*mcy-rbx*rcz*mbz*mcx-rbx*rcy*mby*mcx
-rbx*rcx*mbx*mcx+lb*rbx*mcx+lc*rcz*mbz+lc*rcy*mby
+lc*rcx*mbx-lb*lc+fbc
;
ideal I = f1, f2, f3, f4, f5, f6, f7, f8, f9;
def s = solve(I, 12);
Could anybody help explain why I cannot define a ring with real data type to use with the solve function? Thanks.
|
|
|
|
| Top |
|
|
|
hannes
|
Post subject: Re: Singular and Maxima gives different solutions Posted: Mon Jul 04, 2011 11:14 am |
|
Joined: Wed May 25, 2005 4:16 pm
Posts: 275
|
|
As soon as one calls groebner or std in a ring with inexact coefficients
(like real or complex),
most probably the result will be unusable.
|
|
| Top |
|
|
|
|
Page 1 of 1
|
[ 3 posts ] |
|
|
You can post new topics in this forum
You can reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum
|
|
It is currently Fri May 13, 2022 11:02 am
|
|
Login
Register
Forum FAQ
Forum Search
