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5.30.9  Choosing the GCD algorithm of two polynomials: ezgcd heugcd modgcd psrgcd

ezgcd heugcd modgcd psrgcd denote the gcd (greatest common divisor) of two univariate or multivariate polynomials with coefficients in ℤ or ℤ[i] using a specific algorithm:

Input:

ezgcd(x^2-2*x*y+y^2-1,x-y)

or:

heugcd(x^2-2*x*y+y^2-1,x-y)

or:

modgcd(x^2-2*x*y+y^2-1,x-y)

or:

psrgcd(x^2-2*x*y+y^2-1,x-y)

Output:

1

Input:

ezgcd((x+y-1)*(x+y+1),(x+y+1)^2)

or:

heugcd((x+y-1)*(x+y+1),(x+y+1)^2)

or:

modgcd((x+y-1)*(x+y+1),(x+y+1)^2)

Output:

x+y+1

Input:

psrgcd((x+y-1)*(x+y+1),(x+y+1)^2)

Output:

-x-y-1

Input:

ezgcd((x+1)^4-y^4,(x+1-y)^2)

Output:

"GCD not successful Error: Bad Argument Value"

But input:

heugcd((x+1)^4-y^4,(x+1-y)^2)

or:

modgcd((x+1)^4-y^4,(x+1-y)^2)

or:

psrgcd((x+1)^4-y^4,(x+1-y)^2)

Output:

x-y+1

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