```
from funciones_forma_lagrange import lagrangiana_1D, lagrangiana_2D, lagrangiana_3D
from funciones_forma_lagrange import recorrer_matriz_espiral, guardar_matriz_espiral
from funciones_forma_lagrange import recorrer_matriz_3d_espiral, guardar_matriz_3d_espiral
from funciones_forma_lagrange import hermitiana_1D
from sympy import Symbol, lambdify, latex
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import axes3d
from mayavi import mlab

x = Symbol('x')
y = Symbol('y')
z = Symbol('z')
```


```
A1 = hermitiana_1D(x, 2)

for i in range(len(A1)):
    print A1[i]

X1 = np.arange(-1, 1, 0.01)

for i in range(len(A1)):
    Y1 = lambdify(x, A1[i])
    plt.plot(X1, Y1(X1))
    plt.title('Funcion de forma de ' + str(len(A1) / 2) + ' nodos')
plt.show()
```

Las ecuaciones obtenidas son:

\begin{eqnarray}
0.125 x^{3} + 0.125 x^{2} - 0.625 x + 0.375 \\\
0.25 x^{3} - 0.25 x^{2} - 0.25 x + 0.25 \\\
- 0.125 x^{3} + 0.125 x^{2} + 0.625 x + 0.375 \\\
0.25 x^{3} + 0.25 x^{2} - 0.25 
\end{eqnarray}


```
A2 = hermitiana_1D(x, 3)

for i in range(len(A2)):
    print latex(A2[i])

X2 = np.arange(-1, 1, 0.01)

for i in range(len(A2)):
    Y2 = lambdify(x, A2[i])
    plt.plot(X2, Y2(X2))
    plt.title('Funcion de forma de ' + str(len(A2) / 2) + ' nodos')
plt.show()
```

Las ecuaciones obtenidas son:

\begin{eqnarray}
0.375 x^{5} - 0.125 x^{4} - 0.875 x^{3} + 0.625 x^{2} \\\
0.25 x^{5} - 0.25 x^{4} - 0.25 x^{3} + 0.25 x^{2} \\\
1.0 x^{4} - 2.0 x^{2} + 1.0 \\\
1.0 x^{5} - 2.0 x^{3} + 1.0 x \\\
- 0.375 x^{5} - 0.125 x^{4} + 0.875 x^{3} + 0.625 x^{2} \\\
0.25 x^{5} + 0.25 x^{4} - 0.25 x^{3} - 0.25 x^{2}
\end{eqnarray}

f89eb9c6d034eafec75be911aebebd24d089846d
ipynb
Jupyter Notebook
Funciones de forma/hermitiana.ipynb
ClaudioVZ/Teoria-FEM-Python
8a4532f282c38737fb08d1216aa859ecb1e5b209
Artistic-2.0
2021-09-28T00:23:45.000Z
2021-09-28T00:23:45.000Z
Funciones de forma/hermitiana.ipynb
ClaudioVZ/Teoria-FEM-Python
8a4532f282c38737fb08d1216aa859ecb1e5b209
Artistic-2.0
Funciones de forma/hermitiana.ipynb
ClaudioVZ/Teoria-FEM-Python
8a4532f282c38737fb08d1216aa859ecb1e5b209
Artistic-2.0
2015-12-04T12:42:00.000Z
2019-10-31T21:50:32.000Z
Qwen/Qwen-72B
1. YES
2. YES