Solve polynomial Diophantine equations
This functionality does not run in MATLAB.
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.
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 x2 - 1. Hence the equation u(x + 1) + v(x2 - 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
a, b, c
aexpr, bexpr, cexpr
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.