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based on an earlier version of the Wolfram Language.
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gives the remainder from dividing p by q, treated as polynomials in x.
  • The degree of the result in x is guaranteed to be smaller than the degree of q.
  • With the option Modulus->n, the remainder is computed modulo n.
Find the remainder after dividing one polynomial by another:
Find the remainder after dividing one polynomial by another:
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The resulting polynomial will have coefficients that are rational expressions of input coefficients:
PolynomialRemainder also works for rational functions:
Use a prime modulus:
Euclid's algorithm for the greatest common divisor:
Divide by the leading coefficient:
For a polynomial , , where is given by PolynomialQuotient:
Use Expand to verify identity:
To get both quotient and remainder use PolynomialQuotientRemainder:
PolynomialReduce generalizes PolynomialRemainder for multivariate polynomials:
The variable assumed for the polynomials matters:
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