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Type inference solves type equations through <i>type unification</i>.
Type unification recursively compares the LHS and RHS types of an
equation, where either or both types may be or contain bound type parameters,
and looks for type arguments for those type parameters such that the LHS
and RHS match (become identical or assignment-compatible, depending on
context).

(Y/Z)² = 1 + d(X/Z)²(Y/Z)² // (-X² + Y²)/Z² = 1 + (dX²Y²)/Z⁴ // (-X² + Y²)*Z² = Z⁴ + dX²Y² var lhs, rhs field.Element lhs.Subtract(&YY, &XX).Multiply(&lhs, &ZZ) rhs.Multiply(d, &XX).Multiply(&rhs, &YY).Add(&rhs, &ZZZZ) if lhs.Equal(&rhs) != 1 { t.Errorf("X, Y, and Z do not specify a point on the curve\nX = %v\nY = %v\nZ = %v", p.x, p.y, p.z) } // xy = T/Z lhs.Multiply(&p.x, &p.y) rhs.Multiply(&p.z, &p.t) if lhs.Equal(&rhs) != 1 { t.Errorf("point %d is not valid\nX = %v\nY = %v\nZ = %v", i, p.x, p.y, p.z)...