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PolynomialExtendedGCD

PolynomialExtendedGCD
gives the extended GCD of and treated as univariate polynomials in x.
PolynomialExtendedGCD[poly1, poly2, x, Modulus->p]
gives the extended GCD over the integers mod prime p.
Compute the extended GCD:
The second part gives coefficients of a linear combination of polynomials that yields the GCD:
Compute the extended GCD:
In[1]:=
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In[2]:=
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Out[2]=
The second part gives coefficients of a linear combination of polynomials that yields the GCD:
In[3]:=
Click for copyable input
Out[3]=
Polynomials with numeric coefficients:
Polynomials with symbolic coefficients:
Relatively prime polynomials:
Extended GCD over the integers:
Extended GCD over the integers modulo 2:
Given polynomials , , and , find polynomials and such that :
A solution exists if and only if is divisible by :
The extended GCD of and is , such that and :
is equal to PolynomialGCD up to a factor not containing :
r and s are uniquely determined by the following Exponent conditions:
Use Cancel or PolynomialRemainder to prove that divides and :
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