Difference between using "vpasolve" in these 2 codes?

In the following code, I had defined f(x) using syms and to solve this equation, I used vpasolve(f).

syms  f(x)
alpha=5;
mio=0.6;
B=2;
if alpha==5
      if mio==0.6
            if B==2 
                bast=(x/0.5).^(alpha*(mio-1));
                mqam_part1=3*B*((sqrt(3)/2).^(alpha*mio));
                mqam_part2=((0.5*sqrt(3)).^(-alpha))+((1.5*sqrt(3)).^(-alpha));
                mqam_part3=3*(((x/0.5)).^(alpha*mio));
                mqam_part4=((sqrt(3)-(x/0.5)).^-alpha);
                mqam_part5=((2*sqrt(3))-(x/0.5)).^-alpha;
                mqam_part6=mqam_part4+mqam_part5;
                mqam_part7=2*((3-(x/0.5)).^-alpha);
                mqam_part8=6*(((x/0.5)).^(alpha*mio));
                mqam_part9=6*B*(2.^-alpha);
                eqn_LHS=bast/(mqam_part1+mqam_part2)+(mqam_part3*(mqam_part6+mqam_part7));
                eqn_RHS=B/((mqam_part8*mqam_part6)+mqam_part9);
                f(x)=eqn_LHS-eqn_RHS;
                sol_positive = vpasolve(f);
            end
     end
end

After running this code, it has the following output:

sol_positive =

                                       -0.088528537330827491688440727135052
                                        0.089168332029743739883884412606126
                                         0.33826394036632543530763273039833
                                          1.1599250419465014133554207319948
                                          1.2989629568831597716493684806851
                                          1.6240554937821142318780347702386
                                          4.1380104774956983606108108853334
   0.36340277619978535323175586579368 - 0.17885283113851906156582968732142i
    1.2992644818621369190151455557302 - 0.31440379416295109163597261773161i
     1.4897230890912773483095146949368 - 1.3150774672581101958523122516833i
   1.6282605813254473735848321984622 - 0.083684308295293467728903801421506i
    1.6955614120462881985070978123707 - 0.34019756525211237400051800951627i
     2.8366220103150973884193959600945 - 2.0075730328576518221908039773448i
    0.96894287293815413579933338616546 - 1.0029719645739903595813767103315i
     2.8366220103150973884193959600945 + 2.0075730328576518221908039773448i
    1.2992644818621369190151455557302 + 0.31440379416295109163597261773161i
     1.4897230890912773483095146949368 + 1.3150774672581101958523122516833i
   0.36340277619978535323175586579368 + 0.17885283113851906156582968732142i
    0.96894287293815413579933338616546 + 1.0029719645739903595813767103315i
   1.6282605813254473735848321984622 + 0.083684308295293467728903801421506i
    1.1475584718883716605696238712257 + 0.23111120566119037717218445710823i
    1.6955614120462881985070978123707 + 0.34019756525211237400051800951627i
   0.67755561933436425842885030639685 + 0.89740492763981823171766701235696i
   0.35356088917929933509194226805741 + 0.46392937489127504001635787211895i
    1.1475584718883716605696238712257 - 0.23111120566119037717218445710823i
   0.35356088917929933509194226805741 - 0.46392937489127504001635787211895i
   0.67755561933436425842885030639685 - 0.89740492763981823171766701235696i

But, in the following code,I had defined the parameters of the equation *B,x,mio using syms and to solve this equation, I used vpasolve(eqn1,x,[0 Inf]).

syms alpha mio B x
alpha=5;
mio=0.6;
B=2;
if alpha==5
      if mio==0.6
            if B==2 
                bast=(x/0.5).^(alpha*(mio-1));
                mqam_part1=3*B*((sqrt(3)/2).^(alpha*mio));
                mqam_part2=((0.5*sqrt(3)).^(-alpha))+((1.5*sqrt(3)).^(-alpha));
                mqam_part3=3*(((x/0.5)).^(alpha*mio));
                mqam_part4=((sqrt(3)-(x/0.5)).^-alpha);
                mqam_part5=((2*sqrt(3))-(x/0.5)).^-alpha;
                mqam_part6=mqam_part4+mqam_part5;
                mqam_part7=2*((3-(x/0.5)).^-alpha);
                mqam_part8=6*(((x/0.5)).^(alpha*mio));
                mqam_part9=6*B*(2.^-alpha);
                eqn_LHS=bast/(mqam_part1+mqam_part2)+(mqam_part3*(mqam_part6+mqam_part7));
                eqn_RHS=B/((mqam_part8*mqam_part6)+mqam_part9);
                eqn1=eqn_LHS==eqn_RHS;
                sol_positive = vpasolve(eqn1,x,[0 Inf]);
            end
     end
end

After running this code, it has the following output:

sol_positive =

   0.089168332029743739883884412606126
    0.33826394036632543530763273039833
     1.1599250419465014133554207319948
     1.2989629568831597716493684806851
     1.6240554937821142318780347702386
     4.1380104774956983606108108853334

So, my question is: what is the difference between using vpasolve in the 2 codes and how does it work to give these outputs??

[Image Analyst]

Original question

What is the difference between using "vpasolve" in the following 2 codes?

In the following code, I had defined f(x) using syms and to solve this equation, I used vpasolve(f).

syms  f(x)
alpha=5;
mio=0.6;
B=2;
if alpha==5
      if mio==0.6
            if B==2 
                bast=(x/0.5).^(alpha*(mio-1));
                mqam_part1=3*B*((sqrt(3)/2).^(alpha*mio));
                mqam_part2=((0.5*sqrt(3)).^(-alpha))+((1.5*sqrt(3)).^(-alpha));
                mqam_part3=3*(((x/0.5)).^(alpha*mio));
                mqam_part4=((sqrt(3)-(x/0.5)).^-alpha);
                mqam_part5=((2*sqrt(3))-(x/0.5)).^-alpha;
                mqam_part6=mqam_part4+mqam_part5;
                mqam_part7=2*((3-(x/0.5)).^-alpha);
                mqam_part8=6*(((x/0.5)).^(alpha*mio));
                mqam_part9=6*B*(2.^-alpha);
                eqn_LHS=bast/(mqam_part1+mqam_part2)+(mqam_part3*(mqam_part6+mqam_part7));
                eqn_RHS=B/((mqam_part8*mqam_part6)+mqam_part9);
                f(x)=eqn_LHS-eqn_RHS;
                sol_positive = vpasolve(f);
            end
     end
end

After running this code, it has the following output:

sol_positive =

                                       -0.088528537330827491688440727135052
                                        0.089168332029743739883884412606126
                                         0.33826394036632543530763273039833
                                          1.1599250419465014133554207319948
                                          1.2989629568831597716493684806851
                                          1.6240554937821142318780347702386
                                          4.1380104774956983606108108853334
   0.36340277619978535323175586579368 - 0.17885283113851906156582968732142i
    1.2992644818621369190151455557302 - 0.31440379416295109163597261773161i
     1.4897230890912773483095146949368 - 1.3150774672581101958523122516833i
   1.6282605813254473735848321984622 - 0.083684308295293467728903801421506i
    1.6955614120462881985070978123707 - 0.34019756525211237400051800951627i
     2.8366220103150973884193959600945 - 2.0075730328576518221908039773448i
    0.96894287293815413579933338616546 - 1.0029719645739903595813767103315i
     2.8366220103150973884193959600945 + 2.0075730328576518221908039773448i
    1.2992644818621369190151455557302 + 0.31440379416295109163597261773161i
     1.4897230890912773483095146949368 + 1.3150774672581101958523122516833i
   0.36340277619978535323175586579368 + 0.17885283113851906156582968732142i
    0.96894287293815413579933338616546 + 1.0029719645739903595813767103315i
   1.6282605813254473735848321984622 + 0.083684308295293467728903801421506i
    1.1475584718883716605696238712257 + 0.23111120566119037717218445710823i
    1.6955614120462881985070978123707 + 0.34019756525211237400051800951627i
   0.67755561933436425842885030639685 + 0.89740492763981823171766701235696i
   0.35356088917929933509194226805741 + 0.46392937489127504001635787211895i
    1.1475584718883716605696238712257 - 0.23111120566119037717218445710823i
   0.35356088917929933509194226805741 - 0.46392937489127504001635787211895i
   0.67755561933436425842885030639685 - 0.89740492763981823171766701235696i

But, in the following code,I had defined the parameters of the equation *B,x,mio using syms and to solve this equation, I used vpasolve(eqn1,x,[0 Inf]).

syms alpha mio B x
alpha=5;
mio=0.6;
B=2;
if alpha==5
      if mio==0.6
            if B==2 
                bast=(x/0.5).^(alpha*(mio-1));
                mqam_part1=3*B*((sqrt(3)/2).^(alpha*mio));
                mqam_part2=((0.5*sqrt(3)).^(-alpha))+((1.5*sqrt(3)).^(-alpha));
                mqam_part3=3*(((x/0.5)).^(alpha*mio));
                mqam_part4=((sqrt(3)-(x/0.5)).^-alpha);
                mqam_part5=((2*sqrt(3))-(x/0.5)).^-alpha;
                mqam_part6=mqam_part4+mqam_part5;
                mqam_part7=2*((3-(x/0.5)).^-alpha);
                mqam_part8=6*(((x/0.5)).^(alpha*mio));
                mqam_part9=6*B*(2.^-alpha);
                eqn_LHS=bast/(mqam_part1+mqam_part2)+(mqam_part3*(mqam_part6+mqam_part7));
                eqn_RHS=B/((mqam_part8*mqam_part6)+mqam_part9);
                eqn1=eqn_LHS==eqn_RHS;
                sol_positive = vpasolve(eqn1,x,[0 Inf]);
            end
     end
end

After running this code, it has the following output:

sol_positive =

   0.089168332029743739883884412606126
    0.33826394036632543530763273039833
     1.1599250419465014133554207319948
     1.2989629568831597716493684806851
     1.6240554937821142318780347702386
     4.1380104774956983606108108853334

So, my question is: what is the difference between using vpasolve in the 2 codes and how does it work to give these outputs??

[Eman S]

@Image Analyst

It will cause confusion to the reader to have comment has the same content of the question. So, please delete this comment. For the original question, It would be the same as it. I only shorten the title of the question.Don't worry, it wouldn't be edited or deleted.

Answer 1

[Walter Roberson]

The fact that you got multiple outputs tells us that the equations define a polynomial. In the case of a polynomial, vpasolve returns all of solutions that meet the defined constraints. In the first case there are no constraints so it returns all of solutions whether real or complex valued. In the second case you included a range, which is equivalent to having added in(x, 0, inf), or (x >= 0 & x <= inf), which acts to eliminate the negative and complex valued solutions.