In [1]:

    

from __future__ import division
from sympy import *
from IPython.display import display, Math, Latex
from IPython.core.display import display_html
init_session(quiet=True, use_latex='mathjax')
init_printing()


    

    




IPython console for SymPy 0.7.6 (Python 2.7.6-32-bit) (ground types: python)

In [2]:

    

x1,x2,tau,delta = symbols('x1,x2,tau,delta')
L11 = symbols('L11', cls=Function)(x1,x2,tau,delta)
L12 = symbols('L12', cls=Function)(x1,x2,tau,delta)
L21 = symbols('L21', cls=Function)(x1,x2,tau,delta)
L22 = symbols('L22', cls=Function)(x1,x2,tau,delta)


    

In [3]:

    

Lstar = Matrix([[L11,L12],[L21,L22]])
L1star = Lstar.det()
deriv1 = L1star.diff(t)
deriv2 = (Lstar.adjugate()*Lstar.diff(t)).trace()

Mstar = Matrix([[L11,L12],[Lstar.det().diff(x1),Lstar.det().diff(x2)]])

deriv1 = Mstar.det().diff(tau)
deriv2 = (Mstar.adjugate()*Mstar.diff(tau)).trace()
simplify(deriv1-deriv2)


    

    
Out[3]:





$$0$$

In [7]:

    

Mstar = Matrix([[0.00112865, 8.76232e-006],[9.57021e-007, 7.42578e-009]])
dMstar_dTau = Matrix([[-0.000245724,-0.00118232],[3.20921e-006, -7.171e-008]])
adjM = Matrix([[7.42578e-009,-9.57021e-007],[-8.76232e-006, 0.00112865]])
(adjM*dMstar_dTau).trace()
print Mstar.adjugate()
print adjM


    

    




Matrix([[7.42578000000000e-9, -8.76232000000000e-6], [-9.57021000000000e-7, 0.00112865000000000]])
Matrix([[7.42578000000000e-9, -9.57021000000000e-7], [-8.76232000000000e-6, 0.00112865000000000]])

In [11]:

    

a,b,c,d = symbols('a,b,c,d')
M = Matrix([[a,b],[c,d]])
display(M)
M.adjugate()


    

    






$$\left[\begin{matrix}a & b\\c & d\end{matrix}\right]$$






    
Out[11]:





$$\left[\begin{matrix}d & - b\\- c & a\end{matrix}\right]$$

In [ ]: