mapcoeffs
Apply a function to the coefficients of a polynomial
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mapcoeffs(p
,F
, <a1, a2, …
>) mapcoeffs(f
, <vars
>,F
, <a1, a2, …
>)
mapcoeffs(p, F, a1, a2, ...)
applies the
function F
to the polynomial p
by
replacing each coefficient c
in p
by F(c,
a1, a2, ...)
.
For a polynomial p
of type DOM_POLY
generated
by poly
, the
function F
must accept arguments from the coefficient
ring of p
and must produce corresponding results.
A polynomial expression f
is first converted
to a polynomial with the variables given by vars
.
If no variables are given, they are searched for in f
.
See poly
about
details of the conversion. FAIL
is returned if f
cannot
be converted to a polynomial. After applying the function F
,
the result is converted to an expression.
mapcoeffs
evaluates its arguments. Note,
however, that polynomials of type DOM_POLY
do not evaluate
their coefficients for efficiency reasons. Cf. Example 4.
The function sin
is
mapped to the coefficients of a polynomial expression in the indeterminates x
and y
:
mapcoeffs(3*x^3 + x^2*y^2 + 2, sin)
The following call makes mapcoeffs
regard
this expression as a polynomial in x
. Consequently, y
is
regarded as a parameter that becomes part of the coefficients:
mapcoeffs(3*x^3 + x^2*y^2 + 2, [x], sin)
The system function _plus
adds its arguments. In the following
call, it is used to add 2 to
all coefficients by providing this shift as an additional argument:
mapcoeffs(c1*x^3 + c2*x^2*y^2 + c3, [x, y], _plus, 2)
The function sin
is
mapped to the coefficients of a polynomial in the indeterminates x
and y
:
mapcoeffs(poly(3*x^3 + x^2*y^2 + 2, [x, y]), sin)
In the following call, the polynomial has the indeterminate x
.
Consequently, y
is regarded as a parameter that
becomes part of the coefficients:
mapcoeffs(poly(3*x^3 + x^2*y^2 + 2, [x]), sin)
A userdefined function is mapped to a polynomial:
F := (c, a1, a2) > exp(c + a1 + a2): mapcoeffs(poly(x^3 + c*x, [x]), F, a1, a2)
delete F:
We consider a polynomial over the integers modulo 7:
p := poly(x^3 + 2*x*y, [x, y], Dom::IntegerMod(7)):
A function to be applied to the coefficients must produce values in the coefficient ring of the polynomial:
mapcoeffs(p, c > c^2)
The following call maps a function which converts its argument
to an integer modulo 3. Such
a return value is not a valid coefficient of p
:
mapcoeffs(p, c > Dom::IntegerMod(3)(expr(c)))
delete p:
Note that polynomials of type DOM_POLY
do not evaluate
their arguments:
delete a, x: p := poly(a*x, [x]): a := PI: p
Evaluation can be enforced by the function eval
:
mapcoeffs(p, eval)
We map the sine function
to the coefficients of p
. The polynomial does not
evaluate its coefficient sin(a)
to 0
:
mapcoeffs(p, sin)
The composition of sin
and eval
is mapped to the
coefficients of the polynomial:
mapcoeffs(p, eval@sin)
delete p, a:

A polynomial of
type 
 

Additional parameters for the function 
 

A list of indeterminates of the polynomial: typically, identifiers or indexed identifiers 
f
, p