-
Casus irreducibilis (from Latin 'the
irreducible case') is the name
given by
mathematicians of the 16th
century to
cubic equations that
cannot be solved...
-
solutions in
radicals involve roots of
complex numbers. This is
casus irreducibilis for the quintic,
which is
discussed in Dummit.: p.17 Indeed, if an...
- root test, if the
cubic is irreducible; this is the so-called
casus irreducibilis ("irreducible case"). This
conundrum led
Italian mathematician Gerolamo...
- for the
solutions of this equation,
because it is an
example of
casus irreducibilis. The
approximate lengths of the
diagonals in
terms of the side of the...
- This case has thus been
called casus irreducibilis,
meaning irreducible case in Latin. In
casus irreducibilis, Cardano's
formula can
still be used, but...
- straightedge. Otherwise, it is
solvable in radicals, but one are in the
casus irreducibilis, that is,
every expression of the
roots in
terms of
radicals involves...
- and
taking nth
roots without resorting to
complex numbers (see
casus irreducibilis). For example,
consider the
algebraic function determined by the equation...
- has
three real
roots but is
irreducible in Q[x] (the so-called
casus irreducibilis), then the
roots cannot be
expressed from the
coefficients using real...
-
function § Reducible
quartics Cubic function § Factorization
Casus irreducibilis, the
irreducible cubic with
three real
roots Quadratic equation § Quadratic...
- all
three roots of the
cubic are real, this is an
instance of
casus irreducibilis, and the
expression would require taking the cube root of a complex...
