Warning: Equation solved, but no element can be extracted from the solution set.

Hi all:

I am new to symbolab and have encountered an error with the solve function:

Warning: Equation solved, but no element can be extracted from the solution set.

There is indeed a solution that I have found via optimization. But for future work I'd rather use symbolab.

Below is the code. Not many lines at all! Thanks in advance.

N = 2000000/2.5;
W = 70000;
t = 600;
ra = 45000;
pK = 1;
 
alp = 0.14;
gam = 0.6;
  g = 0.0005;
tht = 3;
 gg = alp*(1-gam);
 
syms x d real

nfun(x,d) = x*(tht*ra/gg) / (W-t*d)^(1/gg) * (W-t*x).^((1-gg)/gg);
    n2fun = int(nfun,x,0,d);
d0 = solve(n2fun == N,d,'PrincipalValue',true);

Answer 1

[Walter Roberson]

tic

Q = @(v) sym(v);

N = Q(2000000)/Q(2.5)

N = 

800000

W = Q(70000)

W = 

70000

t = Q(600)

t = 

600

ra = Q(45000)

ra = 

45000

pK = Q(1)

pK = 

1

 
alp = Q(0.14)

alp = 

gam = Q(0.6)

gam = 

  g = Q(0.0005)

g = 

tht = Q(3)

tht = 

3

 gg = alp*(1-gam);
 
syms x d real

nfun(x,d) = x*(tht*ra/gg) / (W-t*d)^(1/gg) * (W-t*x).^((1-gg)/gg);
n2fun = int(nfun,x,0,d);
sold = solve(n2fun == N, d, 'returnconditions', true)

sold = struct with fields:
             d: [1×1 sym]
    parameters: [1×1 sym]
    conditions: [1×1 sym]

cparts = children(sold.conditions)

cparts = 1×3 cell array
    {1×1 sym}    {1×1 sym}    {1×1 sym}

digits(50)
%cparts{1} is in(x, 'real')
%cparts{2} is roots of a degree 132 polynomial
%cparts{3} is conditions that simplify to -18806/5 <= x
csol = vpasolve(cparts{2})

csol = 

lb = lhs(simplify(cparts{3}))

lb = 

mask = simplify(imag(csol) == 0 & lb - 1e-50 <= real(csol));

d_solutions = csol(mask)

d_solutions = 

toc

Elapsed time is 17.998978 seconds.

The conditions found for the original solve() include a lower-bound -18806/5 <= x and that is exactly the value for the first 7 values. However due to round-off, the numeric values csol(1:7) - lb differ by up to +/- 1e-54 (assuming digits 50), so I introduce a tolerance of 1e-50 into the comparison.

[Ryan Greenaway-McGrevy]

Thank you so much! Very clear explanation.