Thank you, Aaron Meurer. Sympy solve took so long that I lost my patient and killed it.
Sympy nsolve does give me one solution, i.e., the solution close to the initial guess, when the guess is good. Although Mathematica gave all 6 solutions, Sympy might work for me at this moment. Thanks very much. On Mon, Nov 24, 2014 at 7:01 PM, Aaron Meurer <[email protected]> wrote: > Mathematica's NSolve likely uses numerical algorithms. SymPy also has > nsolve(), which uses numerical algorithms (I couldn't get it to work > with your system but you may have better luck if you have a better > guess at the root than I do). solve() works symbolically, which has > advantages and disadvantages. A disadvantage is that it can be slow, > and basically overkill if you only care about a numerical solution. It > also may not find a solution if it isn't available in "closed form". > An advantage is that it might find more solutions than the numeric > algorithm because you don't have to guess at a root and then hope to > converge to it. > > In short, however, SymPy's symbolic routines do not perform so well > with floating point numbers. > > Aaron Meurer > > On Mon, Nov 24, 2014 at 11:45 AM, Junwei Huang <[email protected]> > wrote: > > Thanks Mateusz for your help. Since I have copied the three polynomial > > equations in the original post, could you or any developer use them to > track > > down the bug? > > > > btw, Mathematica(TM) NSolve can handle it and gave 6 solutions. But I > would > > really like to see sympy can do the same work, as I really like python > > coding environment. > > > > Thanks, > > Junwei > > > > > > On Monday, November 24, 2014 3:12:48 AM UTC-5, Mateusz Paprocki wrote: > >> > >> Hi, > >> > >> On 23 November 2014 at 22:13, Junwei Huang <[email protected]> wrote: > >> > Hi > >> > I am quite new to sympy. I found sympy as I was searching a way to > solve > >> > a > >> > system of 3 6-order polynomials for 3 unknowns. I tried to solve this > >> > system > >> > using either solve_poly_system or solve_triangulated but got the same > >> > error. > >> > Here is the part of code: > >> > " > >> > eq1 = 0. > >> > eq2 = 0. > >> > eq3 = 0. > >> > m=0 > >> > for k in range(0,7): > >> > for j in range(0,7-k): > >> > for i in range(0,7-k-j): > >> > if mod(i+j+k,2)==0: > >> > eq1 = eq1 + e1C[m]*p**i*q**j*r**k > >> > eq2 = eq2 + e2C[m]*p**i*q**j*r**k > >> > eq3 = eq3 + e3C[m]*p**i*q**j*r**k > >> > m=m+1 > >> > > >> > #rr = solve_poly_system([eq1, eq2, eq3], p, q, r) > >> > rr= solve_triangulated([eq1, eq2, eq3], p, q, r) > >> > " > >> > e1C, e2C, and e3C are constant coefficients and eq1, eq2, and eq3 are > >> > the > >> > three polynomial equations. I got the following error: > >> > > >> > > >> > > -------------------------------------------------------------------------- > >> > KeyError Traceback (most recent call > >> > last > >> > <ipython-input-12-9cbae56e6534> in <module>() > >> > ----> 1 rr = sympy.solve_triangulated([eq1, eq2, eq3], p, q, r) > >> > > >> > /usr/local/lib/python2.7/dist-packages/sympy/solvers/polysys.pyc in > >> > solve_trngulated(polys, *gens, **args) > >> > 263 > >> > 264 """ > >> > --> 265 G = groebner(polys, gens, polys=True) > >> > 266 G = list(reversed(G)) > >> > 267 > >> > > >> > /usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.pyc in > >> > groebner, *gens, **args) > >> > 6380 > >> > 6381 """ > >> > -> 6382 return GroebnerBasis(F, *gens, **args) > >> > 6383 > >> > 6384 > >> > > >> > /usr/local/lib/python2.7/dist-packages/sympy/polys/polytools.pyc in > >> > __new__(s, F, *gens, **args) > >> > 6420 polys[i] = ring.from_dict(poly.rep.to_dict()) > >> > 6421 > >> > -> 6422 G = _groebner(polys, ring, method=opt.method) > >> > 6423 G = [Poly._from_dict(g, opt) for g in G] > >> > 6424 > >> > > >> > /usr/local/lib/python2.7/dist-packages/sympy/polys/groebnertools.pyc > in > >> > groeer(seq, ring, method) > >> > 43 seq = [ s.set_ring(ring) for s in seq ] > >> > 44 > >> > ---> 45 G = _groebner(seq, ring) > >> > 46 > >> > 47 if orig is not None: > >> > > >> > /usr/local/lib/python2.7/dist-packages/sympy/polys/groebnertools.pyc > in > >> > _buchberger(f, ring) > >> > 236 # ordering divisors is on average more efficient [Cox] > >> > page > >> > 111 > >> > 237 G1 = sorted(G, key=lambda g: order(f[g].LM)) > >> > --> 238 ht = normal(h, G1) > >> > 239 > >> > 240 if ht: > >> > > >> > /usr/local/lib/python2.7/dist-packages/sympy/polys/groebnertools.pyc > in > >> > normal(g, J) > >> > 102 > >> > 103 def normal(g, J): > >> > --> 104 h = g.rem([ f[j] for j in J ]) > >> > 105 > >> > 106 if not h: > >> > > >> > /usr/local/lib/python2.7/dist-packages/sympy/polys/rings.pyc in rem(f, > >> > G) > >> > 1419 c1 = get(m1, zero) - c*cg > >> > 1420 if not c1: > >> > -> 1421 del f[m1] > >> > 1422 else: > >> > 1423 f[m1] = c1 > >> > > >> > KeyError: (0, 0, 7) > >> > ------------------------------------------------------- > >> > eq1, eq2, and eq3 are like this: > >> > In[13]: eq1.simplify() > >> > Out[13]: 5105.00458755661*p**6 - 108.473959633689*p**5*q + > >> > 2402.41285238498*p**5*r + 9008.47267975219*p**4*q**2 - > >> > 1255.39607773283*p**4*q*r + 11277.0701891541*p**4*r**2 - > >> > 1307.26969182159*p**4 + 2011.04932840783*p**3*q**3 + > >> > 4868.72300813206*p**3*q**2*r + 2350.26623001839*p**3*q*r**2 + > >> > 83.2810004274752*p**3*q + 5306.9841358631*p**3*r**3 - > >> > 410.133684217865*p**3*r + 3581.05378966718*p**2*q**4 - > >> > 1494.32987338524*p**2*q**3*r + 9663.32292693404*p**2*q**2*r**2 - > >> > 1603.980521043*p**2*q**2 - 1554.39827080096*p**2*q*r**3 + > >> > 146.877127581136*p**2*q*r + 6189.03791479042*p**2*r**4 - > >> > 1951.0971844993*p**2*r**2 + 104.459609097912*p**2 + > >> > 2059.68147982275*p*q**5 > >> > + 2434.36150406603*p*q**4*r + 4573.37297182227*p*q**3*r**2 - > >> > 129.155224299263*p*q**3 + 5326.78736764999*p*q**2*r**3 - > >> > 414.231578475927*p*q**2*r + 2541.58989447865*p*q*r**4 - > >> > 163.881993246563*p*q*r**2 - 7.32935355549153*p*q + > >> > 2912.55844639838*p*r**5 - > >> > 459.09272674491*p*r**3 + 16.3862149483427*p*r - 267.46300018096*q**6 - > >> > 251.079215546565*q**5*r - 551.942706049301*q**4*r**2 - > >> > 383.602775058541*q**4 > >> > - 518.132756933654*q**3*r**3 + 48.9590425270454*q**3*r - > >> > 281.245218262232*q**2*r**4 - 921.212155372886*q**2*r**2 + > >> > 67.1547741681612*q**2 - 264.01718641355*q*r**5 + > 51.0079896560767*q*r**3 > >> > - > >> > 2.33274553975296*q*r - 541.968982299977*r**4 + 79.5536696127415*r**2 - > >> > 2.47202741879275 > >> > > >> > In [14]: eq2.simplify() > >> > Out[14]: -533.530507020419*p**6 + 4905.43084014754*p**5*q - > >> > 251.079215546566*p**5*r - 582.162658435345*p**4*q**2 + > >> > 2434.36150406603*p**4*q*r - 1101.00564042678*p**4*r**2 - > >> > 114.412696339151*p**4 + 8753.94762999568*p**3*q**3 - > >> > 1494.32987338524*p**3*q**2*r + 10767.2083390326*p**3*q*r**2 - > >> > 723.759577198517*p**3*q - 518.132756933655*p**3*r**3 + > >> > 48.9590425270454*p**3*r + 2518.77143858425*p**2*q**4 + > >> > 4868.72300813206*p**2*q**3*r + 2371.36169096872*p**2*q**2*r**2 - > >> > 570.416841704303*p**2*q**2 + 5326.78736764999*p**2*q*r**3 - > >> > 414.231578475927*p**2*q*r - 561.023034195364*p**2*r**4 - > >> > 380.66073794717*p**2*r**2 + 29.9539788526177*p**2 + > >> > 3767.68958665181*p*q**5 > >> > - 1255.39607773283*p*q**4*r + 9621.24207100615*p*q**3*r**2 - > >> > 610.744183471118*p*q**3 - 1554.39827080096*p*q**2*r**3 + > >> > 146.877127581136*p*q**2*r + 5907.79269652819*p*q*r**4 - > >> > 812.539281619356*p*q*r**2 + 22.3950435470699*p*q - > >> > 264.01718641355*p*r**5 + > >> > 51.0079896560767*p*r**3 - 2.33274553975296*p*r + > 2559.17857546841*q**6 + > >> > 2402.41285238498*q**5*r + 5653.28315129873*q**4*r**2 - > >> > 655.344482123229*q**4 > >> > + 5306.9841358631*q**3*r**3 - 410.133684217865*q**3*r + > >> > 3102.61292867402*q**2*r**4 - 978.100220594949*q**2*r**2 + > >> > 52.3664159395267*q**2 + 2912.55844639838*q*r**5 - > 459.09272674491*q*r**3 > >> > + > >> > 16.3862149483428*q*r - 271.69327358712*r**4 + 39.8808744205781*r**2 - > >> > 1.23924660588265 > >> > > >> > In [15]: eq3.simplify() > >> > Out[15]: 5638.53509457703*p**5*r + 624.630294795803*p**4*q*r + > >> > 2653.49206793155*p**4*r**2 - 205.066842108932*p**4 + > >> > 10215.2656329833*p**3*q**2*r - 1036.26551386731*p**3*q*r**2 + > >> > 97.9180850540909*p**3*q + 12378.0758295808*p**3*r**3 - > >> > 975.548592249651*p**3*r + 3472.3673313955*p**2*q**3*r + > >> > 5326.78736764999*p**2*q**2*r**2 - 414.231578475927*p**2*q**2 + > >> > 3961.13372056658*p**2*q*r**3 - 272.271365596867*p**2*q*r + > >> > 5825.11689279675*p**2*r**4 - 918.18545348982*p**2*r**2 + > >> > 32.7724298966855*p**2 + 4534.64968247843*p*q**4*r - > >> > 1036.26551386731*p*q**3*r**2 + 97.9180850540908*p*q**3 + > >> > 11253.0949565319*p*q**2*r**3 - 866.875718496121*p*q**2*r - > >> > 1056.0687456542*p*q*r**4 + 204.031958624307*p*q*r**2 - > >> > 9.33098215901183*p*q > >> > + 6750.06094898578*p*r**5 - 1083.93796459995*p*r**3 + > >> > 39.7768348063708*p*r + > >> > 2826.64157564937*q**5*r + 2653.49206793155*q**4*r**2 - > >> > 205.066842108932*q**4 > >> > + 6205.22585734804*q**3*r**3 - 489.050110297474*q**3*r + > >> > 5825.11689279675*q**2*r**4 - 918.18545348982*q**2*r**2 + > >> > 32.7724298966855*q**2 + 3383.85814693625*q*r**5 - > >> > 543.386547174239*q*r**3 + > >> > 19.9404372102891*q*r + 3176.57563281193*r**6 - 765.15107460148*r**4 + > >> > 56.1568814642871*r**2 - 1.16333498638407 > >> > > >> > Could anyone please suggest what is causing this error? Is there any > >> > other > >> > way of solving this system of polynomial equations in Python? Thanks > >> > very > >> > much. > >> > >> SymPy is unable to detect (floating point) zero, so intermediate > >> polynomials have erroneous terms, causing this error. This is a bug > >> and has to be fixed, thought at this point I'm not sure where exactly > >> the issue occurs. > >> > >> Mateusz > >> > >> > -- > >> > You received this message because you are subscribed to the Google > >> > Groups > >> > "sympy" group. > >> > To unsubscribe from this group and stop receiving emails from it, send > >> > an > >> > email to [email protected]. > >> > To post to this group, send email to [email protected]. > >> > Visit this group at http://groups.google.com/group/sympy. > >> > To view this discussion on the web visit > >> > > >> > > https://groups.google.com/d/msgid/sympy/f2516e57-6bf9-4d41-b82a-8b788c6024a5%40googlegroups.com > . > >> > For more options, visit https://groups.google.com/d/optout. > > > > -- > > You received this message because you are subscribed to the Google Groups > > "sympy" group. > > To unsubscribe from this group and stop receiving emails from it, send an > > email to [email protected]. > > To post to this group, send email to [email protected]. > > Visit this group at http://groups.google.com/group/sympy. > > To view this discussion on the web visit > > > https://groups.google.com/d/msgid/sympy/d78920db-6490-40f4-a436-95971df98b73%40googlegroups.com > . > > > > For more options, visit https://groups.google.com/d/optout. > > -- > You received this message because you are subscribed to a topic in the > Google Groups "sympy" group. > To unsubscribe from this topic, visit > https://groups.google.com/d/topic/sympy/_nONKfongyk/unsubscribe. > To unsubscribe from this group and all its topics, send an email to > [email protected]. > To post to this group, send email to [email protected]. > Visit this group at http://groups.google.com/group/sympy. > To view this discussion on the web visit > https://groups.google.com/d/msgid/sympy/CAKgW%3D6K%2Bb0o%3Do0jmsa60hDstt_LrUHqaNRkr%2Bbd2dtk-ygwhsQ%40mail.gmail.com > . > For more options, visit https://groups.google.com/d/optout. > -- You received this message because you are subscribed to the Google Groups "sympy" group. 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