Supposet that I have a matrix $m=(a_{i,j})$, where $a_{i,j}$ is some Schur function. By default, m.det() will give the determinant using the original multiplication. But I want to use kronecker product for Schur functions. I did not find any options to set kronecker product as default in the ring of Schur functions or matrix class.
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Multiplying two Schur Functions use kronecker product as default to obtian the determinant of a matrix.
Multiplying two Schur Functions use kronecker product as default to obtian the determinant of a matrix.
Supposet that I have a matrix $m=(a_{i,j})$, where $a_{i,j}$ is some Schur function. By default, m.det() will give the determinant using the original multiplication. But I want to use kronecker product for Schur functions. I did not find any options to set kronecker product as default in the ring of Schur functions or matrix class.
Multiplying two Schur Functions use kronecker product as default to obtian the Compute determinant of a matrix.matrix of Schur functions using Kronecker product
Supposet that I have Given a matrix $m=(a_{i,j})$, where each $a_{i,j}$ is some a Schur function. By function,
by default, m.det() m.det() will give the determinant using the original multiplication. multiplication.
But I want it to use kronecker the Kronecker product for Schur functions. functions.
I did not find any options to set kronecker the Kronecker product as default default
multiplication operator in the ring of Schur functions or in the matrix class.
To give an example, let us define such a matrix:
sage: Sym = SymmetricFunctions(QQ)
sage: s = Sym.schur()
sage: f = s[2]
sage: m = matrix([[f, 0], [0, f]])
sage: m
[s[2] 0]
[ 0 s[2]]
Then compare:
sage: m.det()
s[2, 2] + s[3, 1] + s[4]
sage: f * f
s[2, 2] + s[3, 1] + s[4]
sage: f.kronecker_product(f)
s[2]
