CODEWITHSUNDEEP
matrixsympy
mrrclb48z
mrrclb48z

Reputation: 207

how to sympy determinant list

Thank you in advance and sorry for the bad English! sympy determinant 3x3 a11 ---> a[1,1]

from sympy import *
var('a11 a12 a13')
var('a21 a22 a23')
var('a31 a32 a33')
print("#",det(Matrix([[a11, a12, a13], [a21, a22, a23], [a31, a32, a33]])))
# a11*a22*a33 - a11*a23*a32 - a12*a21*a33 + a12*a23*a31 + a13*a21*a32 - a13*a22*a31

how convert?

from sympy import *
var('a')
# ?????
# ?????
print("#",det(Matrix([[a[1,1], a[1,2], a[1,3]], [a[2,1], a[2,2], a[2,3]], [a[3,1], a[3,2], a[3,3]]])))
# I want
# a[1,1]*a[2,2]*a[3,3] - a[1,1]*a[2,3]*a[3,2] - a[1,2]*a[2,1]*a[3,3] + a[1,2]*a[2,3]*a[3,1] + a[1,3]*a[2,1]*a[3,2] - a[1,3]*a[2,2]*a[3,1]
# TypeError: 'Symbol' object is not subscriptable

Upvotes: 0

Views: 78

Answers (2)

mrrclb48z
mrrclb48z

Reputation: 207

from sympy import *
a = MatrixSymbol('a', 3, 3)
print("#",type(a))
print("#",a)
b=a.as_explicit()
print("#",type(b))
print("#",b)
c=det(a.as_explicit())
print("#",type(c))
print("#",c)
# <class 'sympy.matrices.expressions.matexpr.MatrixSymbol'>
# a
# <class 'sympy.matrices.immutable.ImmutableDenseMatrix'>
# Matrix([[a[0, 0], a[0, 1], a[0, 2]], [a[1, 0], a[1, 1], a[1, 2]], [a[2, 0], a[2, 1], a[2, 2]]])
# <class 'sympy.core.add.Add'>
# a[0, 0]*a[1, 1]*a[2, 2] - a[0, 0]*a[1, 2]*a[2, 1] - a[0, 1]*a[1, 0]*a[2, 2] + a[0, 1]*a[1, 2]*a[2, 0] + a[0, 2]*a[1, 0]*a[2, 1] - a[0, 2]*a[1, 1]*a[2, 0]

https://docs.sympy.org/latest/modules/matrices/expressions.html#sympy.matrices.expressions.MatrixExpr.as_explicit

Upvotes: 0

Oscar Benjamin
Oscar Benjamin

Reputation: 14500

You should use MatrixSymbol if you want a symbol representing a matrix:

In [40]: a = MatrixSymbol('a', 3, 3)                                                                 

In [41]: a                                                                                           
Out[41]: a

In [42]: a[0, 0]                                                                                     
Out[42]: a₀₀

In [43]: a.as_explicit()                                                                             
Out[43]: 
⎡a₀₀  a₀₁  a₀₂⎤
⎢             ⎥
⎢a₁₀  a₁₁  a₁₂⎥
⎢             ⎥
⎣a₂₀  a₂₁  a₂₂⎦

In [44]: det(a.as_explicit())                                                                        
Out[44]: a₀₀⋅a₁₁⋅a₂₂ - a₀₀⋅a₁₂⋅a₂₁ - a₀₁⋅a₁₀⋅a₂₂ + a₀₁⋅a₁₂⋅a₂₀ + a₀₂⋅a₁₀⋅a₂₁ - a₀₂⋅a₁₁⋅a₂₀

https://docs.sympy.org/latest/modules/matrices/expressions.html

Upvotes: 2

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