# Questions tagged [diophantine-equations]

Questions on the use of Mathematica to find integer/rational solutions to equations.

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### Computing Ehrhart's polynomial for a convex polytope

Is there a Mathematica implementation for computing the Ehrhart polynomial of a convex polytope which is specified either by its vertices or by a set of inequalities? I am interested in knowing this ...
295 views

### Solving Thue equations

A Thue equation is a 2-variable homogeneous integer polynomial of degree at least 3. It's well-known that such equations have only finitely many solutions over the integers. I'm trying to solve some ...
64 views

### Never terminating when solving linear Diophantine systems

Say I have: $(1):$ Set of Diophantine systems where each defines a (possibly unbounded) polyhedron. This is solvable with existing algorithms: $(*):$ The $(1)$ can be solved in SageMath with ...
73 views

### Introducing constraints in FrobeniusSolve

I have a knapsack problem. Say I have N possible items $x_i$. I would like to know: $\sum_{i=0}^{2} c_i x_i = W$ With the following constraint: $c_i=3 \lor 4$ As an example suppose the set \$x_i=...
191 views

### How to test solvability of a Diophantine equation?

When applying the BRC theorem I need to test if an equation has a non-zero solution in integers. The equation is of form: $$x^2 + by^2 + cz^2 = 0$$ We could try to directly check if this equation ...