Unimodular transformation of a linear ordinary differential equation
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ode::unimodular(Ly, y(x)) tests if the linear
homogeneous differential equation
Ly has a unimodular
Galois group (i.e. the wronskian lies in the base field ℚ(x)),
if not transforms
Ly into a unimodular one (by
changing the second highest coefficient to zero) and returns a
table with index
respectively the transformed differential equation and the factor
Wn such that a solution of the
transformed equation multiplied by
Wn is a solution
If the option
Transform is given then
transformed unconditionally even if
Ly has yet
a unimodular Galois group.
We test if the following differential equation has a unimodular Galois group:
Ly := y(x)*6+x*diff(y(x),x)*(-2)+diff(y(x),x$2)*(-x^2+1)
It is unimodular since the factor of transformation is
We can also check this by computing the wronskian of
is a rational function:
Now we transform
Ly into a differential equation
whose wronskian is
ode::unimodular(Ly, y(x), Transform)
A homogeneous linear differential equation over ℚ(x).
The dependent function of