content of a multivariate polynomial
primitive part of a multivariate polynomial
content(a, x, 'pp')
primpart(a, x, 'co')
multivariate polynomial in x
(optional) name or set or list of names
(optional) unevaluated name
If a is an expanded multivariate polynomial in x, content returns the content of a with respect to x, i.e. the greatest common divisor of the coefficients of a with respect to the indeterminate(s) x, and primpart returns a divided by the content of a.
content and primpart are extended to rational functions in normal form multiplicatively:
where f may be content or primpart. Rational functions not in normal form will be normalized first. If the input a is not rational in x, it will result in an error.
The indeterminate(s) x can be a name, or a list or set of names. If x is not specified, then its default value is the set of all indeterminates occurring in a, as determined by indets.
When content is called with a third argument pp, pp is assigned the primitive part of a. Similarly, when primpart is called with a third argument co, co is assigned the content of a.
For all inputs, the primitive part is an expression in rational normal form consisting of a product of polynomial factors each with content 1.
The coefficients in a can be arbitrary expressions independent of x. Any floating point values are left untouched: any floating-point value is assumed to be indivisible with respect to any other value. Other nonpolynomial, nonrational subexpressions get the same treatment unless they are syntactically equal.
The sign is removed from the content, and not removed from the primitive part.
The content of a univariate integer polynomial is the GCD of its coefficients.
The content of a multivariate polynomial a with respect to some of its variable(s) x is the GCD of its coefficients, considering a as a polynomial in the variable(s) x with any remaining variables being part of the coefficient ring. In the example below, a is viewed as a polynomial in x with coefficients that are polynomials in y. The example after that takes the same polynomial, but views it as a multivariate polynomial in x and y with integer coefficients.
The following example computes not just the content, but also the primitive part.
In this example, you can see the effect of calling normal, which happens because the polynomial doesn't have purely numeric coefficients (the coefficient of x is 1a).
Alternatively, if a is included as an indeterminate, the denominator 1a is included in the primpart rather than the content:
Floating point coefficients are considered indivisible with respect to each other -- even if they are equal. As a consequence, the content in the following example is 1.
In the presence of floating-point numbers, other content is still detected. For example, the factor u below.
Non-numeric, nonpolynomial coefficients are also considered indivisible with respect to each other. For example, you could consider 2 to be a common divisor between the two coefficients 10 and 6, but they are considered indivisible with respect to each other for this command and the content is considered to be 1.
The primpart command computes just the primitive part of the expression.
The a parameter was updated in Maple 2023.
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