Chalcopyrite Chalcopyrite Chalcopyrite ( ) is a copper iron sulfide mineral that crystallizes in the tetragonal system. It has the chemical formula CuFeS. It has a brassy to golden yellow color and a hardness of 3.5 to 4 on the Mohs scale. Its streak is diagnostic as green tinged black. On exposure to air, chalcopyrite oxidises to a variety of oxides, hydroxides and sulfates. Associated copper minerals include the sulfides bornite (CuFeS), chalcocite (CuS), covellite (CuS), digenite (CuS); carbonates such as malachite and azurite, and rarely oxides such as cuprite (CuO). Chalcopyrite is rarely found in association with native copper. Natural
Ore algebra commutation in the definition makes Ore algebras have a non-commutative generalization theory of Gröbner basis for their left ideals. Ore algebra In computer algebra, an Ore algebra is a special kind of iterated Ore extension that can be used to represent linear functional operators, including linear differential and/or recurrence operators. The concept is named after Øystein Ore. Let formula_1 be a (commutative) field and formula_2 be a commutative polynomial ring (with formula_3 when formula_4). The iterated skew polynomial ring formula_5 is called an Ore algebra when the formula_6 and formula_7 commute for formula_8, and satisfy formula_9, formula_10 for formula_11. Ore