Another datapoint : Sympy seems to be able to (slowly) solve this system, via :
from sympy.solvers import solve as ssolve ssol=ssolve([e.rhs()-e.lhs() for e in [eq1,eq2,eq3]],[x,y,z]) The output can be converted to Sage via: Ssol=map(lambda S:map(lambda v,s:v==SR(repr(s)).simplify_full(), [x,y,z], S), ssol) HTH, -- Emmanuel Charpentier Le samedi 7 octobre 2017 20:19:55 UTC+2, Emmanuel Charpentier a écrit : > > Inspired by an as.sagemath question > <https://ask.sagemath.org/question/39040/solving-a-system-of-equations-small-known-number-hinders-the-solution/>, > > I tried to solve a not-so-simple system, and found that Sagemath (8.1beta7) > is currently unable to solve it : > > sage: var("x,y,z,K") > (x, y, z, K) > sage: xi=3/4 > sage: yi=0 > sage: zi=0 > sage: eq1=K==y^2*z/x^2 > sage: eq2=xi+yi==x+y > sage: eq3=2*xi+yi+2*zi==2*x+y+2*z > sage: solve([eq1,eq2,eq3],[x,y,z]) > [] > > However, this system *is* solvable : one ca solve [eq2,eq3] for y and z, > substitute the (only) solution in eq1 and solve it for x, which turns out > to give three solutions (looking suspiciously close to the solution of a > cubic) ; substituting each of these solutions in the solutions for y and z > gives three (not-so-light) solutions for the system. > > Trying to solve it with maxima invoked from sage also fails : > > sage: %%maxima > ....: display2d:false; > ....: xi:3/4$ > ....: yi:0$ > ....: zi:0$ > ....: eq1:K=y^2*z/x^2$ > ....: eq2:xi+yi=x+y$ > ....: eq3:2*xi+y+2*zi=2*x+y+2*z$ > ....: sys:[eq1,eq2,eq3]; > ....: sol:solve(sys,[x,y,z])$ > ....: l:length(sol)$ > ....: l; > ....: > false > > > > > > > [K=(y^2*z)/x^2,3/4=y+x,y+3/2=2*z+y+2*x] > > > 0 > > Printing the value of sys shows that it is defined. Printing the length of > the solution that this solution is indeed has length 0 (no solution) and > that failing to print it is *not* an interprocess communication problem > caused by a "too long" result. > > However, when running the same Maxima program in the interpreter from the > command line does give a solution (much more massive, by the way, that the > one obtained manually). See enclosed source and output, obtained by : > > cat ttstSolve.mac | sage --maxima > ttstSolve.out > > Therefore, the problem seems to exist in Sage's interface to maxima, not > in Maxima itself. > > Perusing the list <https://trac.sagemath.org/wiki/symbolics> of symbolics > tickets didn't allow me to recognize this bug. A cursory inspection of > Maxima-related tickets gave no more results. > > Questions : > 1) Is this a new bug ? > 2) Does it deserve a ticket ? > > For what it's worth, Mathematica has no problem solving the system (in its > native interface) and gives relatively lightweight solutions ; I failed to > obtain solutions from fricas, giac and maple, as well as to get > Mathematica's answer through its Sage interface. > > HTH, > > -- > Emmanuel Charpentier > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. To unsubscribe from this group and stop receiving emails from it, send an email to sage-support+unsubscr...@googlegroups.com. To post to this group, send email to sage-support@googlegroups.com. Visit this group at https://groups.google.com/group/sage-support. For more options, visit https://groups.google.com/d/optout.
