Thank you,Peter.
I have another stupid question that does not related to this topic, I think it 
difficult to write a matrix as a list of list in Sage.And it is confused that 
matrix is immutable that I cannot modify the element of a matrix.
Is there some smart way to define and use a matrix in Sage?
Thanks again.

Peter Bruin <p.br...@warwick.ac.uk>提到:

>Hello,
>
>> I want to use FiniteDimensionalAlgebra to check if a given table of
>> multiplicayion can form a associative algebra. But the function
>> FiniteDimensionalAlgebra do not check for association.
>
>A FiniteDimensionalAlgebra can be very general: any finite-dimensional
>vector space A equipped with a bilinear map A x A -> A is regarded as a
>finite-dimensional algebra.  You can use methods like is_associative()
>to check if your algebra has certain properties:
>
>sage: A = 
>FiniteDimensionalAlgebra(CC,[Matrix([[1,1],[1,0]]),Matrix([[0,1],[1,1]])])
>sage: A.is_associative()
>False
>sage: A.is_commutative()
>False
>sage: A.is_unitary()
>False
>
>Peter
>
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