Singular Manual: extgcd

  | ### 5.1.33 extgcd `Syntax:` `extgcd (` int_expression`,` int_expression `)` `extgcd (` bigint_expression`,` bigint_expression `)` `extgcd (` poly_expression`,` poly_expression `)` `Type:` list of 3 objects of the same type as the type of the arguments `Purpose:` computes extended gcd: the first element is the greatest common divisor of the two arguments, the second and third are factors such that if `list L=extgcd(a,b);` then L[1]=a*L[2]+b*L[3]. `Note:` Polynomials must be univariate (in the same variable) to apply `extgcd`. `Example:`
        extgcd(24,10);
      ==> [1]:
      ==>    2
      ==> [2]:
      ==>    -2
      ==> [3]:
      ==>    5
        ring r=0,(x,y),lp;
        extgcd(x4-x6,(x2+x5)*(x2+x3));
      ==> [1]:
      ==>    x5+x4
      ==> [2]:
      ==>    1/2x2+1/2x+1/2
      ==> [3]:
      ==>    1/2
See gcd; int.

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