# Revision history [back]

The problem is that Sage is unable to convert 1/t^2, seen as an element in the fraction field of the univariate polynomial ring in t, to the ring of Laurent polynomials.

You could define an inverse function as follows for your needs.

def inv(m):
r"""
Return the inverse of this matrix over a ring of Laurent polynomials

Raises ZeroDivisionError if matrix has zero determinant,
and ArithmeticError if matrix is nonsquare.

Uses the meth:__invert__ method in src/sage/matrix/matrix0.pyx,
which returns a matrix over the fraction field. This is then
converted back to the ring of Laurent polynomials, with the trick
that the fraction field of a ring of Laurent polynomials is really
the fraction field of the corresponding ring of polynomials.

EXAMPLE::

sage: R.<t> = LaurentPolynomialRing(ZZ)
sage: f = t^2
sage: m = matrix([[f]])
sage: m.parent()
Full MatrixSpace of 1 by 1 dense matrices over
Univariate Laurent Polynomial Ring in t over Integer Ring
sage: mi = inv(m)
sage: mi
[1/t^2]
sage: mi.parent()
Full MatrixSpace of 1 by 1 dense matrices over
Univariate Laurent Polynomial Ring in t over Integer Ring
"""
M = m.parent()
R = m.base_ring()
l = m.inverse().list()
return M([R(x.numerator()) * R(x.denominator()).inverse_of_unit() for x in l])


The problem is that Sage is unable to convert 1/t^2, seen as an element in the fraction field of the univariate polynomial ring in t, to the ring of Laurent polynomials.polynomials in t.

You could define an inverse The following function as follows for should fit your needs.

def inv(m):
r"""
Return the inverse of this matrix over a ring of Laurent polynomials

Raises ZeroDivisionError if matrix has zero determinant,
and ArithmeticError if matrix is nonsquare.

Uses the meth:__invert__ method in src/sage/matrix/matrix0.pyx,
which returns a matrix over the fraction field. This is then
converted back to the ring of Laurent polynomials, with the trick
that the fraction field of a ring of Laurent polynomials is really
the fraction field of the corresponding ring of polynomials.

EXAMPLE::

sage: R.<t> = LaurentPolynomialRing(ZZ)
sage: f = t^2
sage: m = matrix([[f]])
matrix([[t^2]])
sage: m.parent()
Full MatrixSpace of 1 by 1 dense matrices over
Univariate Laurent Polynomial Ring in t over Integer Ring
sage: mi = inv(m)
sage: mi
[1/t^2]
sage: mi.parent()
Full MatrixSpace of 1 by 1 dense matrices over
Univariate Laurent Polynomial Ring in t over Integer Ring
"""
M = m.parent()
R = m.base_ring()
l = m.inverse().list()
return M([R(x.numerator()) * R(x.denominator()).inverse_of_unit() for x in l])


Then, as in the example,

sage: R.<t> = LaurentPolynomialRing(ZZ)
sage: m = matrix([[t^2]])
sage: inv(m)
[1/t^2]