The set of two variable integral polynomials is undecidable
This program returns the value of x & y if the input is a polynomial with integer values for x & y

Please enter integers in the input fields and press the "DECIDE THE INPUT POLYNOMIAL" button
x3y2 + x2y + xy - = 0

 

 

[ You can try your example equations. If you try   2x3y2 + 4x2y + 2xy - 500 = 0, the program will return 2 as the value of x and 5 as the value of y. If you try   2x3y2 + 4x2y + 2xy - 1032 = 0, the program will return 3 as the value of x and 4 as the value of y. You need to enter only integers as coefficients in the input fields, the rest of the equation is fixed. There are no lower & upper bounds for integral polynomials with 2 or more variables; therefore, the program may run for ever on most examples. One of the undecidable integral polynomial is:     2x3y2 + 4x2y + 2xy - 5 = 0 . Matiyasevich's theorem proves that multivariable integral polynomials are undecidable. ]   Please send comments to:   Pradip Peter Dey ( pdey@nu.edu)

For decidability of one-variable integral polynomials click here

For Rice's Theorem on Undecidability click here

For references click here