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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_basic_spcommutative_spalgebra.html" title="">basic commutative algebra</a> > <a href="___M2__Singular__Book.html" title="Macaulay2 examples for the Singular book">M2SingularBook</a></div>
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<div><h1>M2SingularBook -- Macaulay2 examples for the Singular book</h1>
<div><em>M2SingularBook</em> consists of Macaulay2 translations of the examples in the book <em>A Singular introduction to commutative algebra</em><p/>
Each example is numbered as it is in Greuel and Pfister's book. Links to Macaulay2 routines and concepts are also provided. <p/>
</div>
<div><h3>Menu</h3>
<h4>Chapter 1</h4>
<ul><li><span><a href="___Singular_sp__Book_sp1.1.8.html" title="computation in fields">Singular Book 1.1.8</a> -- computation in fields</span></li>
<li><span><a href="___Singular_sp__Book_sp1.1.9.html" title="computation in polynomial rings">Singular Book 1.1.9</a> -- computation in polynomial rings</span></li>
<li><span><a href="___Singular_sp__Book_sp1.1.10.html" title="methods for creating ring maps">Singular Book 1.1.10</a> -- methods for creating ring maps</span></li>
<li><span><a href="___Singular_sp__Book_sp1.2.3.html" title="leading data">Singular Book 1.2.3</a> -- leading data</span></li>
<li><span><a href="___Singular_sp__Book_sp1.2.13.html" title="monomial orderings">Singular Book 1.2.13</a> -- monomial orderings</span></li>
<li><span><a href="___Singular_sp__Book_sp1.3.3.html" title="properties of ring maps">Singular Book 1.3.3</a> -- properties of ring maps</span></li>
<li><span><a href="___Singular_sp__Book_sp1.3.13.html" title="computation in quotient rings">Singular Book 1.3.13</a> -- computation in quotient rings</span></li>
<li><span><a href="___Singular_sp__Book_sp1.3.15.html" title="computing with radicals">Singular Book 1.3.15</a> -- computing with radicals</span></li>
<li><span><a href="___Singular_sp__Book_sp1.4.9.html" title="global versus local rings">Singular Book 1.4.9</a> -- global versus local rings</span></li>
<li><span><a href="___Singular_sp__Book_sp1.5.10.html" title="realization of rings">Singular Book 1.5.10</a> -- realization of rings</span></li>
<li><span><a href="___Singular_sp__Book_sp1.6.13.html" title="normal form">Singular Book 1.6.13</a> -- normal form</span></li>
<li><span><a href="___Singular_sp__Book_sp1.7.10.html" title="standard bases">Singular Book 1.7.10</a> -- standard bases</span></li>
<li><span><a href="___Singular_sp__Book_sp1.7.12.html" title="highest corner">Singular Book 1.7.12</a> -- highest corner</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.1.html" title="ideal membership">Singular Book 1.8.1</a> -- ideal membership</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.2.html" title="linear combination of ideal members">Singular Book 1.8.2</a> -- linear combination of ideal members</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.4.html" title="elimination of variables">Singular Book 1.8.4</a> -- elimination of variables</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.6.html" title="Zariski closure of the image">Singular Book 1.8.6</a> -- Zariski closure of the image</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.7.html" title="solving equations">Singular Book 1.8.7</a> -- solving equations</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.9.html" title="radical membership">Singular Book 1.8.9</a> -- radical membership</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.11.html" title="intersection of ideals">Singular Book 1.8.11</a> -- intersection of ideals</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.13.html" title="quotient of ideals">Singular Book 1.8.13</a> -- quotient of ideals</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.15.html" title="saturation">Singular Book 1.8.15</a> -- saturation</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.18.html" title="kernel of a ring map">Singular Book 1.8.18</a> -- kernel of a ring map</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.19.html" title="algebraic dependence">Singular Book 1.8.19</a> -- algebraic dependence</span></li>
<li><span><a href="___Singular_sp__Book_sp1.8.20.html" title="subalgebra membership">Singular Book 1.8.20</a> -- subalgebra membership</span></li>
</ul>
<h4>Chapter 2</h4>
<ul><li><span><a href="___Singular_sp__Book_sp2.1.6.html" title="matrix operations">Singular Book 2.1.6</a> -- matrix operations</span></li>
<li><span><a href="___Singular_sp__Book_sp2.1.7.html" title="maps induced by Hom">Singular Book 2.1.7</a> -- maps induced by Hom</span></li>
<li><span><a href="___Singular_sp__Book_sp2.1.10.html" title="Submodules of A^n">Singular Book 2.1.10</a> -- Submodules of A^n</span></li>
<li><span><a href="___Singular_sp__Book_sp2.1.13.html" title="kernel, image and cokernel of a module homomorphism">Singular Book 2.1.13</a> -- kernel, image and cokernel of a module homomorphism</span></li>
<li><span><a href="___Singular_sp__Book_sp2.1.20.html" title="sum, intersection, module quotient">Singular Book 2.1.20</a> -- sum, intersection, module quotient</span></li>
<li><span><a href="___Singular_sp__Book_sp2.1.24.html" title="submodules, presentation of a module">Singular Book 2.1.24</a> -- submodules, presentation of a module</span></li>
<li><span><a href="___Singular_sp__Book_sp2.1.26.html" title="computation of Hom">Singular Book 2.1.26</a> -- computation of Hom</span></li>
<li><span><a href="___Singular_sp__Book_sp2.1.34.html" title="minimal presentations, prune">Singular Book 2.1.34</a> -- minimal presentations, prune</span></li>
<li><span><a href="___Singular_sp__Book_sp2.2.15.html" title="graded rings and modules">Singular Book 2.2.15</a> -- graded rings and modules</span></li>
<li><span><a href="___Singular_sp__Book_sp2.3.10.html" title="normal form">Singular Book 2.3.10</a> -- normal form</span></li>
<li><span><a href="___Singular_sp__Book_sp2.3.12.html" title="standard bases">Singular Book 2.3.12</a> -- standard bases</span></li>
<li><span><a href="___Singular_sp__Book_sp2.4.12.html" title="resolution and Betti numbers">Singular Book 2.4.12</a> -- resolution and Betti numbers</span></li>
<li><span><a href="___Singular_sp__Book_sp2.4.15.html" title="homogeneous resolution and graded Betti numbers">Singular Book 2.4.15</a> -- homogeneous resolution and graded Betti numbers</span></li>
<li><span><a href="___Singular_sp__Book_sp2.5.5.html" title="syzygies">Singular Book 2.5.5</a> -- syzygies</span></li>
<li><span><a href="___Singular_sp__Book_sp2.5.18.html" title="Schreyer resolution">Singular Book 2.5.18</a> -- Schreyer resolution</span></li>
<li><span><a href="___Singular_sp__Book_sp2.6.3.html" title="diagonal form">Singular Book 2.6.3</a> -- diagonal form</span></li>
<li><span><a href="___Singular_sp__Book_sp2.6.11.html" title="cyclic decomposition">Singular Book 2.6.11</a> -- cyclic decomposition</span></li>
<li><span><a href="___Singular_sp__Book_sp2.6.15.html" title="Jordan normal form">Singular Book 2.6.15</a> -- Jordan normal form</span></li>
<li><span><a href="___Singular_sp__Book_sp2.7.5.html" title="tensor product of maps">Singular Book 2.7.5</a> -- tensor product of maps</span></li>
<li><span><a href="___Singular_sp__Book_sp2.7.9.html" title="tensor product of modules">Singular Book 2.7.9</a> -- tensor product of modules</span></li>
<li><span><a href="___Singular_sp__Book_sp2.7.14.html" title="tensor product of rings">Singular Book 2.7.14</a> -- tensor product of rings</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.1.html" title="module membership">Singular Book 2.8.1</a> -- module membership</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.3.html" title="elimination of module components">Singular Book 2.8.3</a> -- elimination of module components</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.5.html" title="intersection of modules">Singular Book 2.8.5</a> -- intersection of modules</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.6.html" title="quotient of modules">Singular Book 2.8.6</a> -- quotient of modules</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.7.html" title="radical, zerodivisors of modules">Singular Book 2.8.7</a> -- radical, zerodivisors of modules</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.8.html" title="annihilator and Fitting ideal">Singular Book 2.8.8</a> -- annihilator and Fitting ideal</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.9.html" title="kernel of a module homomorphism">Singular Book 2.8.9</a> -- kernel of a module homomorphism</span></li>
<li><span><a href="___Singular_sp__Book_sp2.8.10.html" title="solving linear equations">Singular Book 2.8.10</a> -- solving linear equations</span></li>
</ul>
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