gives the quotient of p and q, treated as polynomials in x, with any remainder dropped.
Details and Options
- With the option Modulus->n, the quotient is computed modulo n.
Examplesopen allclose all
Basic Examples (3)
PolynomialQuotient also works for rational functions:
Use PolynomialGCD to check that divides :
Properties & Relations (4)
For a polynomial f, f==gq+r, where r is given by PolynomialRemainder:
Use Expand to verify identity:
To get both quotient and remainder use PolynomialQuotientRemainder:
Use PolynomialGCD to find a common divisor:
Use PolynomialQuotient to see the resulting factorization:
The Cyclotomic polynomials are defined as quotients:
Possible Issues (2)
The result from PolynomialQuotient depends on recognizing zeros:
Wolfram Research (1988), PolynomialQuotient, Wolfram Language function, https://reference.wolfram.com/language/ref/PolynomialQuotient.html (updated 2023).
Wolfram Language. 1988. "PolynomialQuotient." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2023. https://reference.wolfram.com/language/ref/PolynomialQuotient.html.
Wolfram Language. (1988). PolynomialQuotient. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/PolynomialQuotient.html