multcoeffs -- multiply the
coefficients of a polynomial with a factor
Introductionmultcoeffs(p, c) multiplies all
coefficients of the polynomial p with the factor
c.
Call(s)multcoeffs(p, c)
multcoeffs(f, <vars,> c)
Parametersp |
- | 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 |
Returnsa polynomial of type DOM_POLY, or a polynomial
expression, or FAIL.
p, f
Related
Functionscoeff, degree, degreevec, lcoeff, ldegree, lterm, nterms, nthcoeff, nthmonomial, nthterm, poly, tcoeff
Detailsf 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.
Example
1Some 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])
Example
2Mathematically, 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: