genpoly
Create a polynomial using badic expansion
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genpoly(n
, b
, x
)
genpoly(n, b, x)
creates a polynomial p
in the
variable x
from the b
adic expansion
of n
, such that p(b)
= n. The integer coefficients
of the resulting polynomial are greater than and
less than or equal to .
The badic
expansion of an integer n is
defined by ,
such that the c_{i} are
symmetric remainders modulo b,
i.e., for
all i (see mods
). From this expansion
the polynomial is
created. The polynomial is defined over the coefficient ring Expr
.
If the first argument of genpoly
is a (multivariate) polynomial, then it must be defined over
the coefficient ring Expr
and must have only integer coefficients.
The third argument x
must not be a variable of
the polynomial. In this case each integer coefficient is converted
into a polynomial in x
as described above. The
result is a polynomial in the variable x
, followed
by the variables of the given polynomial. (x
is
the main variable of the returned polynomial.)
The first argument n
may also be a polynomial expression.
In this case, it is converted into a polynomial using poly
, then genpoly
is
applied as described above, and the result is again converted into
a polynomial expression.
If the first argument is an integer or a polynomial, then the
result is a polynomial of domain type DOM_POLY
; otherwise it
is a polynomial expression.
We create a polynomial p
in the indeterminate x
such
that p(7) = 15
. The coefficients of p
are
between 3
and 3
:
p := genpoly(15, 7, x)
p(7)
Here is an example with a polynomial expression as input:
p := genpoly(15*y^2  6*y + 3*z, 7, x)
The return value has the same type as the first argument:
p := genpoly(poly(15*y^2 + 8*z, [y, z]), 7, x)
We check the result:
p(7, y, z)

An integer, a polynomial of type 

An integer greater than 1 

The indeterminate: an identifier 
polynomial if the first argument is a polynomial or an integer. Otherwise, a polynomial expression.
genident
 indets
 int2text
 interpolate
 mods
 numlib::g_adic
 poly
 text2int