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PolynomialRemainder

PolynomialRemainder
gives the remainder from dividing p by q, treated as polynomials in x.
MORE INFORMATION
  • 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.
EXAMPLESCLOSE ALL
Basic Examples   (1)
Find the remainder after dividing one polynomial by another:
Find the remainder after dividing one polynomial by another:
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Click for copyable input
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Scope   (2)
The resulting polynomial will have coefficients that are rational expressions of input coefficients:
PolynomialRemainder also works for rational functions:
Options   (1)
Use a prime modulus:
Applications   (1)
Euclid's algorithm for the greatest common divisor:
Divide by the leading coefficient:
Properties & Relations   (3)
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:
Possible Issues   (1)
The variable assumed for the polynomials matters:
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