Solve polynomial Diophantine equations
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solvelib::pdioe(a
,b
,c
) solvelib::pdioe(aexpr
,bexpr
,cexpr
,x
)
solvelib::pdioe(a, b, c)
returns polynomials u
and
v that satisfy the equation au + bv = c
.
solvelib::pdioe(aexpr, bexpr, cexpr, x)
does
the same after converting the arguments into univariate polynomials a,
b, c
in the variable x
.
The coefficient ring of the polynomials a
, b
,
and c
must be either Expr
, or IntMod(p)
for
some prime p,
or a domain belonging to the category Cat::Field
.
If expressions are passed as arguments, a fourth argument must be provided:
solvelib::pdioe(x, 13*x + 22*x^2 + 18*x^3 + 7*x^4 + x^5 + 3, x^2 + 1, x)
x is not a multiple of the gcd of x + 1 and x^{2}  1. Hence the equation u(x + 1) + v(x^{2}  1) = x has no solution for u and v:
solvelib::pdioe(x + 1, x^2  1, x, x)
If the arguments are polynomials, the fourth argument may be omitted:
solvelib::pdioe(poly(a + 1, [a]), poly(a^2 + 1, [a]), poly(a  1, [a]))

Identifier or indexed identifier 

Univariate polynomials 

Polynomial expressions 
If the equation is solvable, solvelib::pdioe
returns
an expression sequence consisting of two operands of the same type
as the input (expressions or polynomials). If the equation has no
solution, solvelib::pdioe
returns FAIL
.