multcoeffs
-- multiply the
coefficients of a polynomial with a factormultcoeffs(
p, c)
multiplies all
coefficients of the polynomial p
with the factor
c
.
multcoeffs(p, c)
multcoeffs(f, <vars,> c)
p |
- | a polynomial of type
DOM_POLY |
c |
- | an arithmetical expression
or an element of the coefficient ring of p |
f |
- | a polynomial expression |
vars |
- | a list of indeterminates of the polynomial: typically, identifiers or indexed identifiers |
a polynomial of type DOM_POLY
, or a polynomial
expression, or FAIL
.
p
, f
coeff
, degree
, degreevec
, lcoeff
, ldegree
, lterm
, nterms
, nthcoeff
, nthmonomial
, nthterm
, poly
, tcoeff
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
multiplication with c
, the result is converted to an
expression.f
, the factor
c
may be any arithmetical
expression. For a polynomial p
of type DOM_POLY
, the factor c
must be convertible to an element of the coefficient ring of
p
.multcoeffs
is a function of the system kernel.Some simple examples:
>> multcoeffs(3*x^3 + x^2*y^2 + 2, 5)
3 2 2 15 x + 5 x y + 10
>> multcoeffs(3*x^3 + x^2*y^2 + 2, c)
3 2 2 2 c + 3 c x + c x y
>> multcoeffs(poly(x^3 + 2, [x]), sin(y))
3 poly(sin(y) x + 2 sin(y), [x])
Mathematically, multcoeffs(
f,
c)
is the same as f*c
. However,
multcoeffs
produces an expanded form of the product which
depends on the indeterminates:
>> f := 3*x^3 + x^2*y^2 + 2: multcoeffs(f, [x], c), multcoeffs(f, [y], c), multcoeffs(f, [z], c)
3 2 2 2 2 3 2 c + 3 c x + c x y , c x y + c (3 x + 2), 3 2 2 c (3 x + x y + 2)
>> delete f: