Multiply the coefficients of a polynomial with a factor

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multcoeffs(p, c)
multcoeffs(f, <vars>, c)


multcoeffs(p, c) multiplies all coefficients of the polynomial p with the factor c.

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 multiplication with c, the result is converted to an expression.

For a polynomial 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.


Example 1

Some simple examples:

multcoeffs(3*x^3 + x^2*y^2 + 2, 5)

multcoeffs(3*x^3 + x^2*y^2 + 2, c)

multcoeffs(poly(x^3 + 2, [x]), sin(y))

Example 2

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)

delete f:



A polynomial of type DOM_POLY


An arithmetical expression or an element of the coefficient ring of p


A polynomial expression


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

Return Values

Polynomial of type DOM_POLY, or a polynomial expression, or FAIL.

Overloaded By

f, p