Le mardi 30 novembre 2021 à 18:18:35 UTC+1, cyrille piatecki a écrit :
> Thanks Emmanuel for your so precious answer. But obviously the doc must be > upgraded. From > > "maxima", "fricas", "sympy", "giac" > > only "sympy" has a reference. > (Almost) right : the documentation I pointed to doesn’t list anything but maxima. The up to date documentation <https://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/relation.html> is similar, but gives example of algorithm="sympy" uses… Would you care to file a ticket against that ? A further problem being that the documentatin mentions the use of algorithm for single-equation solving, whereas your current example shows success for (an) equation *system*. This should be clarified… > I wonder If one could add a parameter asking, in all cases, only for Real > solutions. > Beware : There Might Be Tygers ! (Hint : I left you an exercise... ;-) > > ----- Mail d’origine ----- > De: Emmanuel Charpentier <emanuel.c...@gmail.com> > À: sage-support <sage-s...@googlegroups.com> > Envoyé: Tue, 30 Nov 2021 14:54:31 +0100 (CET) > Objet: Re: [sage-support] Re: Constrained optimization with strange result. > > Le lundi 29 novembre 2021 à 16:33:41 UTC+1, cyrille piatecki a écrit : > > > > Thanks Emmanuel for your precious answer. But It generates some few new >> questions : >> - is there a place in the documentation where I can find the information >> on `solve()` and mainly its options ? >> > > > The documentation > <https://doc.sagemath.org/html/en/reference/calculus/sage/symbolic/relation.html>, > > of course… > > > > >> - if I understand clearly z_{6497} is an integer but how to fix it to >> zero --- when the number change at each iteration >> > > > That’s why I used a methods sequence to designate it, rather than using > its name… > > > > >> - sympy seems to be the good approach >> > > > Beware : see below… > > > > but it is not self evident that to call y one must typpeset sol2[0][x] >> > > > It is, because algorithm="sympy" will cause the results to be expressed > as dictionaries and D[x] is the canonical way to get the value of the > entry of dictionary D indexed by x. Basic Python… > > > > >> - the giac way is certainly the better but it keeps no track of the >> variable's order. >> > > > Again, ask for a solution dictionary. As for algorithm="giac", I have > seen it go pear-shaped a couple times… > > Now for the various expression of solutions : consider : > > print(table([[u,solve(FOC,[x,y,l], solution_dict=True, algorithm=u)] for u in > ["maxima", "fricas", "sympy", "giac"]])) > maxima [{l: 1/p_y, x: (p_x/p_y)^(1/a)*e^(2*I*pi*z3541/a), y: > -(p_x*(p_x/p_y)^(1/a)*e^(2*I*pi*z3541/a) - R)/p_y}] > fricas [{l: 1/p_y, x: (p_x/p_y)^(1/a)*e^(2*I*pi*z3892/a), y: > -(p_x*(p_x/p_y)^(1/a)*e^(2*I*pi*z3892/a) - R)/p_y}] > sympy [{x: (p_x/p_y)^(1/a), l: 1/p_y, y: -(p_x*(p_x/p_y)^(1/a) - R)/p_y}] > giac [{x: (p_x/p_y)^(1/a), y: -(p_x*(p_x/p_y)^(1/a) - R)/p_y, l: 1/p_y}] > > Both maxima and fricas try to explicitly express the set of solutions of > the equation z^a==p_x/p_y, which is a set of a complexes if a is a > positive integer. (I leave to you (as en exercise ;-) to determine what it > means (if any…) if a is rational, algebraic or transcendental, real or > complex…). > > OTOH, both sympy and giac use the notation (p_x/p_y)^(1/a) to *implicitly* > denote *the very same set of solutions to the very same equation. One could > say that tey are glossing over whatever maxima and fricas insist on. > Choose your poison… > > HTH, > > > > >> >> I have tried my solution assuming l>0 on the 3 conditions but it changes >> nothing. >> >> >> >> ----- Mail d’origine ----- >> De: Emmanuel Charpentier <emanuel.c...@gmail.com> >> À: sage-support <sage-s...@googlegroups.com> >> Envoyé: Mon, 29 Nov 2021 11:03:37 +0100 (CET) >> Objet: [sage-support] Re: Constrained optimization with strange result. >> >> Variables of the form z_xxxx are *integer* variables created by Maxima, >> which attempts to give you *also* the complex roots, if any, thus >> ignoring the assumptions on x, y and l. Note that : >> >> sage: solve(FOC[0], x) >> --------------------------------------------------------------------------- >> >> [ Snip… ] >> >> TypeError: Computation failed since Maxima requested additional constraints; >> using the 'assume' command before evaluation *may* help (example of legal >> syntax is 'assume(l>0)', see `assume?` for more details) >> Is l positive, negative or zero? >> sage: with assuming(l>0): print(solve(FOC[0], x)) >> [ >> x == (l*p_x)^(1/a) >> ] >> sage: with assuming(l<0): print(solve(FOC[0], x)) >> [ >> x^a == l*p_x >> ] >> sage: with assuming(l<0): print(solve(FOC[0], x, to_poly_solve=True)) >> [x == (l*p_x)^(1/a)*e^(2*I*pi*z4353/a)] >> >> Interestingly: >> >> sage: solve([FOC[0]==0,FOC[1]==0,FOC[2]==0],x,y,l) >> [[l == (1/p_y), x == (p_x/p_y)^(1/a)*e^(2*I*pi*z3540/a), y == >> -(p_x*(p_x/p_y)^(1/a)*e^(2*I*pi*z3540/a) - R)/p_y]] >> sage: solve([FOC[0]==0,FOC[1]==0,FOC[2]==0],x,y,l, algorithm="sympy") >> [{x: (p_x/p_y)^(1/a), l: 1/p_y, y: -(p_x*(p_x/p_y)^(1/a) - R)/p_y}] >> sage: solve([FOC[0]==0,FOC[1]==0,FOC[2]==0],x,y,l, algorithm="fricas") >> [[l == (1/p_y), x == (p_x/p_y)^(1/a)*e^(2*I*pi*z3891/a), y == >> -(p_x*(p_x/p_y)^(1/a)*e^(2*I*pi*z3891/a) - R)/p_y]] >> sage: giac.solve(giac(FOC),giac([x,y,l])).sage() >> [[(p_x/p_y)^(1/a), -(p_x*(p_x/p_y)^(1/a) - R)/p_y, 1/p_y]] >> >> HTH, >> >> Le dimanche 28 novembre 2021 à 22:13:12 UTC+1, cyrille piatecki a écrit : >> >>> On my computer the solution of >>> >>> var('a x y p_x p_y D Rev R l') >>> assume(a,'real') >>> assume(x,'real') >>> assume(y,'real') >>> assume(p_x,'real') >>> assume(p_y,'real') >>> assume(D,'real') >>> assume(Rev,'real') >>> assume(R,'real') >>> assume(l,'real') >>> assume(a<1) >>> assume(a>0) >>> assume(p_x>0) >>> assume(p_y>0) >>> assume(R>0) >>> U =(1/(a+1))*x^(a+1)+y >>> show(LatexExpr(r'\text{La fonction d}^\prime\text{utilité est }U(x,y) = >>> '),U) >>> D= x*p_x + y*p_y >>> show(LatexExpr(r'\text{La Dépense } D = '),D) >>> Rev= R >>> show(LatexExpr(r'\text{Le Revenu } Rev = '),R) >>> L=U+l*(Rev-D) >>> show(LatexExpr(r'\text{Le lagrangien est } \mathcal{L}(x, y, λ) = '),L) >>> FOC = [diff(L,x),diff(L,y),diff(L,l)] >>> show(LatexExpr(r'\text{Les condition du premier ordre sont } >>> \left\{\begin{array}{c}\mathcal{L}_x= 0\\\mathcal{L}_y= 0\\\mathcal{L}_λ= >>> 0\end{array}\right. ')) >>> show(LatexExpr(r'\text{soit }')) >>> show(LatexExpr(r'\mathcal{L}_x= 0 \Longleftrightarrow '),FOC[0]==0) >>> show(LatexExpr(r'\mathcal{L}_y= 0 \Longleftrightarrow '),FOC[1]==0) >>> show(LatexExpr(r'\mathcal{L}_λ= 0 \Longleftrightarrow '),FOC[2]==0) >>> sol=solve([FOC[0]==0,FOC[1]==0,FOC[2]==0],x,y,l) >>> show(sol) >>> >>> Is nearly correct, but an extra complex exponential term multiplies $x$ >>> and then modifies $y$. Even as an element I do not understand its form : >>> >>> $e^{(2iπz_{5797}a)}$ >>> >>> Could some one explain why ? >>> >>> >> >> >> -- >> >> 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...@googlegroups.com. >> >> To view this discussion on the web visit >> https://groups.google.com/d/msgid/sage-support/e745f8a7-df76-4def-b3b9-09ac7684e9a3n%40googlegroups.com >> >> <https://groups.google.com/d/msgid/sage-support/e745f8a7-df76-4def-b3b9-09ac7684e9a3n%40googlegroups.com?utm_medium=email&utm_source=footer> >> . >> >> >> > > > -- > > 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...@googlegroups.com. > > To view this discussion on the web visit > https://groups.google.com/d/msgid/sage-support/04561da4-79da-43de-b55c-7b1f65a48984n%40googlegroups.com > > <https://groups.google.com/d/msgid/sage-support/04561da4-79da-43de-b55c-7b1f65a48984n%40googlegroups.com?utm_medium=email&utm_source=footer> > . > > > -- You received this message because you are subscribed to the Google Groups "sage-support" group. 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