11.2.6 Choosing the GCD algorithm of two polynomials
The ezgcd,
heugcd,
modgcd and
psrgcd
commands compute the gcd (greatest common divisor) of two
univariate or multivariate polynomials with coefficients in
ℤ or ℤ[i] with different algorithms.
-
ezgcd, heugcd, modgcd and
psrgcd take two arguments:
P and Q, two polynomials.
- ezgcd(P,Q) returns the gcd of P and Q
computed with the ezgcd algorithm.
- heugcd(P,Q) returns the gcd
of P and Q computed with the heuristic algorithm.
- modgcd(P,Q) returns the gcd
P and Q computed with the modular algorithm.
- psrgcd(P,Q) returns the gcd
of P and Q computed with the sub-resultant algorithm.
Examples
| 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) |
| 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) |
| psrgcd((x+y-1)*(x+y+1),(x+y+1)^2) |
| ezgcd((x+1)^4-y^4,(x+1-y)^2) |
|
| |
GCD not successful Error: Bad Argument Value
| | | | | | | | | | |
|
But:
| 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) |