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

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

• ezgcd ezgcd algorithm,
• heugcd heuristic gcd algorithm,
• modgcd modular algorithm,
• psrgcd sub-resultant 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 successfull 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