### 2.25.12 Solving au+bv=c over polynomials: `abcuv`

`abcuv` solves the polynomial equation

where *A*,*B*,*C* are given polynomials and *U* and *V* are unknown
polynomials. *C* must be a multiple of the gcd of *A* and *B*
for a solution to exist. `abcuv` takes 3 expressions as argument,
and an optional variable specification (which defaults to *x*)
and returns a list of 2 expressions (*U* and *V*). Alternatively, the
polynomials *A*,*B*,*C* may be entered as list-polynomials.

Input :

`abcuv(x``^`

`2+2*x+1 ,x``^`

`2-1,x+1)`

Output :

`[1/2,1/-2]`

Input :

`abcuv(x``^`

`2+2*x+1 ,x``^`

`2-1,x``^`

`3+1)`

Output :

`[1/2*x``^`

`2+1/-2*x+1/2,-1/2*x``^`

`2-1/-2*x-1/2]`

Input :

`abcuv([1,2,1],[1,0,-1],[1,0,0,1])`

Output :

`[poly1[1/2,1/-2,1/2],poly1[1/-2,1/2,1/-2]]`