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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_ideals.html" title="">ideals</a> > <a href="_sums_cm_spproducts_cm_spand_sppowers_spof_spideals.html" title="">sums, products, and powers of ideals</a></div>
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<div><h1>sums, products, and powers of ideals</h1>
<div>Arithmetic for ideals uses the standard symbols. Below are examples of the basic arithmetic functions for ideal.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d]/(b*c-a*d,c^2-b*d,b^2-a*c);</pre>
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For more information about quotient rings see <a href="_quotient_springs.html" title="">quotient rings</a>.<table class="examples"><tr><td><pre>i2 : I = ideal (a*b-c,d^3);
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : J = ideal (a^3,b*c-d);
o3 : Ideal of R</pre>
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<tr><td><pre>i4 : I+J
3 3
o4 = ideal (a*b - c, d , a , a*d - d)
o4 : Ideal of R</pre>
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<tr><td><pre>i5 : I*J
4 3 2 3 3 4 4
o5 = ideal (a b - a c, a b*d - a*b*d - a*c*d + c*d, a d , a*d - d )
o5 : Ideal of R</pre>
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<tr><td><pre>i6 : I^2
3 2 3 3 6
o6 = ideal (a c - 2a d + b*d, a*b*d - c*d , d )
o6 : Ideal of R</pre>
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For more information see <a href="___Ideal_sp_pl_sp__Ideal.html" title="sum of ideals">Ideal + Ideal</a>, <a href="___Ideal_sp_st_sp__Ideal.html" title="product of ideals">Ideal * Ideal</a>, and <a href="___Ideal_sp^_sp__Z__Z.html" title="power">Ideal ^ ZZ</a>.</div>
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