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PolynomialQuotient

PolynomialQuotient
gives the quotient of p and q, treated as polynomials in x, with any remainder dropped.
  • With the option Modulus->n, the quotient is computed modulo n.
The quotient of by , with the remainder dropped:
The quotient of by , with the remainder dropped:
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The resulting polynomial will have coefficients that are rational expressions of input coefficients:
PolynomialQuotient also works for rational functions:
Use a prime modulus:
For a polynomial f, , where r is given by PolynomialRemainder:
Use Expand to verify identity:
To get both quotient and remainder use PolynomialQuotientRemainder:
PolynomialReduce generalizes PolynomialQuotient for multivariate polynomials:
Use PolynomialGCD to find a common divisor:
Use PolynomialQuotient to see the resulting factorization:
For rational functions common divisors are not automatically canceled:
Cancel effectively uses PolynomialQuotient to cancel common divisors:
The Cyclotomic polynomials are defined as quotients:
The result depends on what is assumed to be a variable:
The result from PolynomialQuotient depends on recognizing zeros:
This is a hidden zero:
The result is as if the hidden zero was not zero:
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