Papers by Raja Appapurapu
We study the problem of bounding a polynomial away from polynomials,
which are absolutely irreduc... more We study the problem of bounding a polynomial away from polynomials,
which are absolutely irreducible. Such separation bounds are useful for testing
whether a numerical polynomial is absolutely irreducible, given a certain
tolarence on its coecients. Using the absolutely irreducible criterion due
to Rupport, we are able to nd useful separation bounds, in several norms,
for bivariate polynomials. We consider the problem of factoring a bivariate
polynomial
f(x; y) =
Xm; n
i=0; j=0
ci;jxiyj 2 C[x; y]
where the actual coecients of f are rational or complex numbers and the
C is a eld of complex numbers. The idea is more precisely that we compute
a B(f) 2 R > 0 such that all ~ f 2 C[x; y] with jjf ~ fjj < B(f); and
deg( ~ f) deg(f) must remain absolutely irreducible. If B(f) is not too small,
one can then declare f as a numerically irreducible. The largest possible
B(f) constitutes the distance to the nearest factorizable polynomial and can
be called the radius of irreducibility.
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Papers by Raja Appapurapu
which are absolutely irreducible. Such separation bounds are useful for testing
whether a numerical polynomial is absolutely irreducible, given a certain
tolarence on its coecients. Using the absolutely irreducible criterion due
to Rupport, we are able to nd useful separation bounds, in several norms,
for bivariate polynomials. We consider the problem of factoring a bivariate
polynomial
f(x; y) =
Xm; n
i=0; j=0
ci;jxiyj 2 C[x; y]
where the actual coecients of f are rational or complex numbers and the
C is a eld of complex numbers. The idea is more precisely that we compute
a B(f) 2 R > 0 such that all ~ f 2 C[x; y] with jjf ~ fjj < B(f); and
deg( ~ f) deg(f) must remain absolutely irreducible. If B(f) is not too small,
one can then declare f as a numerically irreducible. The largest possible
B(f) constitutes the distance to the nearest factorizable polynomial and can
be called the radius of irreducibility.
which are absolutely irreducible. Such separation bounds are useful for testing
whether a numerical polynomial is absolutely irreducible, given a certain
tolarence on its coecients. Using the absolutely irreducible criterion due
to Rupport, we are able to nd useful separation bounds, in several norms,
for bivariate polynomials. We consider the problem of factoring a bivariate
polynomial
f(x; y) =
Xm; n
i=0; j=0
ci;jxiyj 2 C[x; y]
where the actual coecients of f are rational or complex numbers and the
C is a eld of complex numbers. The idea is more precisely that we compute
a B(f) 2 R > 0 such that all ~ f 2 C[x; y] with jjf ~ fjj < B(f); and
deg( ~ f) deg(f) must remain absolutely irreducible. If B(f) is not too small,
one can then declare f as a numerically irreducible. The largest possible
B(f) constitutes the distance to the nearest factorizable polynomial and can
be called the radius of irreducibility.