MultivariatePolynomial
The domain constructor
MultivariatePolynomial is
similar to Polynomial except that it
specifies the variables to be used.
Polynomial are available for
MultivariatePolynomial.
The abbreviation for
MultivariatePolynomial is
MPOLY. The type expressions
MultivariatePolynomial([x,y],Integer)
and
MPOLY([x,y],INT)
refer to the domain of multivariate polynomials in the variables x and y
where the coefficients are restricted to be integers. The first variable
specified is the main variable and the display of the polynomial reflects
this. This polynomial appears with terms in descending powers of the
variable x.
It is easy to see a different variable ordering by doing a conversion.
You can use other, unspecified variables, by using
Polynomial in the coefficient type of
MPOLY.
Conversions can be used to re-express such polynomials in terms of the
other variables. For example, you can first push all the variables into a
polynomial with integer coefficients.
Now pull out the variables of interest.
Restriction: Axiom does not allow you to create types where
MultivariatePolynomial is
contained in the coefficient type of
Polynomial. Therefore,
MPOLY([x,y],POLY INT)
is legal but this is not:
POLY MPOLY([x,y],INT)n
Multivariate polynomials may be combined with univariate polynomials to
create types with special structures.
This is a polynomial in x whose coefficients are quotients of polynomials
in y and z. Use conversions for the structural rearrangements. z does not
appear in a denominator and so it can be made the main variable.
Or you can make a multivariate polynomial in x and z whose coefficients
are fractions in polynomials in y
A conversion like
q::MPOLY([x,y],FRAC UP(z,INT))
is not possible in this example because y appears in the denominator of
a fraction. As you can see, Axiom provides extraordinary flexibility in
the manipulation and display of expressions via its conversion facility.
For more information on related topics, see
Polynomial,
UnivariatePolynomial, and
DistributedMultivariatePolynomial.
Issue the system command
to display the full list of operations defined by
MultivariatePolynomial.