Difference between revisions of "ExtendedGCD Command"
From GeoGebra Manual
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;ExtendedGCD( <Polynomial>, <Polynomial> ) | ;ExtendedGCD( <Polynomial>, <Polynomial> ) | ||
:Returns a list containing the polynomial coefficients <math>S(x), T(x)</math> of Bézout's identity for polynomials <math>A(x)S(x) + B(x)T(x) = GCD(A(x), B(x))</math> and the greatest common divisor of the given polynomials. | :Returns a list containing the polynomial coefficients <math>S(x), T(x)</math> of Bézout's identity for polynomials <math>A(x)S(x) + B(x)T(x) = GCD(A(x), B(x))</math> and the greatest common divisor of the given polynomials. | ||
| − | :Results are calculated by applying the [[w:Extended_Euclidean_algorithm]]. | + | :Results are calculated by applying the [[w:Extended_Euclidean_algorithm|Extended Euclidean algorithm]]. |
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{{notes|1=<div> | {{notes|1=<div> | ||
| − | *The GCD of two polynomials is not unique (it's unique up to a scalar multiple) | + | *The GCD of two polynomials is not unique (it's unique up to a scalar multiple). |
*See also [[GCD Command]].</div>}} | *See also [[GCD Command]].</div>}} | ||
Revision as of 09:32, 29 April 2023
CAS Syntax
- ExtendedGCD( <Polynomial>, <Polynomial> )
- Returns a list containing the polynomial coefficients S(x), T(x) of Bézout's identity for polynomials A(x)S(x) + B(x)T(x) = GCD(A(x), B(x)) and the greatest common divisor of the given polynomials.
- Results are calculated by applying the Extended Euclidean algorithm.
Example:
ExtendedGCD(x^2-1,x+4) yields {1,-x+4,15}. (Plugging the result into the Bézout's identity for polynomials we have: 1 \cdot (x^2-1) + (-x+4) \cdot (x+4) = 15.
Notes:
- The GCD of two polynomials is not unique (it's unique up to a scalar multiple).
- See also GCD Command.
