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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_rings.html" title="">rings</a></div>
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<div><h1>rings</h1>
<div>Macaulay2 differs from other computer algebra systems such as Maple and Mathematica, in that before making a polynomial, you must create a ring to contain it, deciding first the complete list of indeterminates and the type of coefficients permitted. Recall that a ring is a set with addition and multiplication operations satisfying familiar axioms, such as the distributive rule. Examples include the ring of integers (<a href="___Z__Z.html" title="the class of all integers">ZZ</a>), the ring of rational numbers (<a href="___Q__Q.html" title="the class of all rational numbers">QQ</a>), and the most important rings in Macaulay2, polynomial rings.<p/>
The sections below describe the types of rings available and how to use them.<p/>
For additional common operations and a comprehensive list of all routines in Macaulay2 which return or use rings, see <a href="___Ring.html" title="the class of all rings">Ring</a>.</div>
<div><h3>Menu</h3>
<h4>Rings</h4>
<ul><li><span><a href="_basic_springs_spof_spnumbers.html" title="">basic rings of numbers</a></span></li>
<li><span><a href="_integers_spmodulo_spa_spprime.html" title="">integers modulo a prime</a></span></li>
<li><span><a href="_finite_spfields.html" title="">finite fields</a></span></li>
<li><span><a href="_polynomial_springs.html" title="">polynomial rings</a></span></li>
<li><span><a href="_monoid.html" title="make or retrieve a monoid">monoid</a> -- make or retrieve a monoid</span></li>
<li><span><a href="_monomial_sporderings.html" title="">monomial orderings</a></span></li>
<li><span><a href="_graded_spand_spmultigraded_sppolynomial_springs.html" title="">graded and multigraded polynomial rings</a></span></li>
<li><span><a href="_quotient_springs.html" title="">quotient rings</a></span></li>
<li><span><a href="_manipulating_sppolynomials.html" title="">manipulating polynomials</a></span></li>
<li><span><a href="_factoring_sppolynomials.html" title="">factoring polynomials</a></span></li>
</ul>
<h4>Fields</h4>
<ul><li><span><a href="_fraction_spfields.html" title="">fraction fields</a></span></li>
<li><span><a href="_finite_spfield_spextensions.html" title="">finite field extensions</a></span></li>
</ul>
<h4>Other algebras</h4>
<ul><li><span><a href="_exterior_spalgebras.html" title="">exterior algebras</a></span></li>
<li><span><a href="_symmetric_spalgebras.html" title="">symmetric algebras</a></span></li>
<li><span><a href="_tensor_spproducts_spof_springs.html" title="">tensor products of rings</a></span></li>
<li><span><a href="___Weyl_spalgebras.html" title="">Weyl algebras</a></span></li>
<li><span><a href="_associative_spalgebras.html" title="">associative algebras</a></span></li>
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