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abs(x)+abs(y)=1 la ecuación

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Solución numérica:

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Solución

Ha introducido [src] 
|x| + |y| = 1
$$\left|{x}\right| + \left|{y}\right| = 1$$
Simplificar
Gráfica
Suma y producto de raíces [src] 
suma
    //1 - |y|  for -1 + |y| <= 0\     //1 - |y|  for -1 + |y| <= 0\       //-1 + |y|  for -1 + |y| < 0\     //-1 + |y|  for -1 + |y| < 0\
I*im|<                          | + re|<                          | + I*im|<                          | + re|<                          |
    \\  nan        otherwise    /     \\  nan        otherwise    /       \\  nan        otherwise    /     \\  nan        otherwise    /
$$\left(\operatorname{re}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) + \left(\operatorname{re}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$ 
=
    //1 - |y|  for -1 + |y| <= 0\       //-1 + |y|  for -1 + |y| < 0\     //1 - |y|  for -1 + |y| <= 0\     //-1 + |y|  for -1 + |y| < 0\
I*im|<                          | + I*im|<                          | + re|<                          | + re|<                          |
    \\  nan        otherwise    /       \\  nan        otherwise    /     \\  nan        otherwise    /     \\  nan        otherwise    /
$$\operatorname{re}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + \operatorname{re}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$ 
producto
/    //1 - |y|  for -1 + |y| <= 0\     //1 - |y|  for -1 + |y| <= 0\\ /    //-1 + |y|  for -1 + |y| < 0\     //-1 + |y|  for -1 + |y| < 0\\
|I*im|<                          | + re|<                          ||*|I*im|<                          | + re|<                          ||
\    \\  nan        otherwise    /     \\  nan        otherwise    // \    \\  nan        otherwise    /     \\  nan        otherwise    //
$$\left(\operatorname{re}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right) \left(\operatorname{re}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}\right)$$ 
=
/           2             
|-(-1 + |y|)   for |y| < 1
<                         
|    nan        otherwise 
\
$$\begin{cases} - \left(\left|{y}\right| - 1\right)^{2} & \text{for}\: \left|{y}\right| < 1 \\\text{NaN} & \text{otherwise} \end{cases}$$ 
Piecewise((-(-1 + |y|)^2, |y| < 1), (nan, True))
Respuesta rápida [src] 
         //1 - |y|  for -1 + |y| <= 0\     //1 - |y|  for -1 + |y| <= 0\
x1 = I*im|<                          | + re|<                          |
         \\  nan        otherwise    /     \\  nan        otherwise    /
$$x_{1} = \operatorname{re}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} 1 - \left|{y}\right| & \text{for}\: \left|{y}\right| - 1 \leq 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$ 
         //-1 + |y|  for -1 + |y| < 0\     //-1 + |y|  for -1 + |y| < 0\
x2 = I*im|<                          | + re|<                          |
         \\  nan        otherwise    /     \\  nan        otherwise    /
$$x_{2} = \operatorname{re}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)} + i \operatorname{im}{\left(\begin{cases} \left|{y}\right| - 1 & \text{for}\: \left|{y}\right| - 1 < 0 \\\text{NaN} & \text{otherwise} \end{cases}\right)}$$ 
x2 = re(Piecewise((Abs(y - 1, |y| - 1 < 0), (nan, True))) + i*im(Piecewise((|y| - 1, |y| - 1 < 0), (nan, True))))
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