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<head><title>dotProduct -- entry by entry dot product of two Betti diagrams</title>
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<div><h1>dotProduct -- entry by entry dot product of two Betti diagrams</h1>
<div class="single"><h2>Synopsis</h2>
<ul><li><div class="list"><dl class="element"><dt class="heading">Usage: </dt><dd class="value"><div><tt>dotProduct(M,lowestDeg,B)</tt><br/><tt>dotProduct(M,B)</tt><br/><tt>dotProduct(B,C)</tt><br/><tt>dotProduct(M,N)</tt></div>
</dd></dl>
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</li>
<li><div class="single">Inputs:<ul><li><span><tt>M</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
<li><span><tt>N</tt>, <span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span></span></li>
<li><span><tt>lowestDeg</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
<li><span><tt>B</tt>, <span>a <a href="../../Macaulay2Doc/html/___Betti__Tally.html">Betti tally</a></span></span></li>
<li><span><tt>C</tt>, <span>a <a href="../../Macaulay2Doc/html/___Betti__Tally.html">Betti tally</a></span></span></li>
</ul>
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</li>
<li><div class="single">Outputs:<ul><li><span><span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span>, the entry by entry dot product</span></li>
</ul>
</div>
</li>
</ul>
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<div class="single"><h2>Description</h2>
<div>In the first version (M, lowestDeg) refers to mat2betti(M, lowestDeg), and in the second version (M,B) refers to (M,0,B).<table class="examples"><tr><td><pre>i1 : d = {0,1,3,4}
o1 = {0, 1, 3, 4}
o1 : List</pre>
</td></tr>
<tr><td><pre>i2 : M = facetEquation(d,1,-5,5)
o2 = | 45 -32 21 -12 |
| 32 -21 12 -5 |
| 21 -12 5 0 |
| 12 -5 0 3 |
| 5 0 -3 4 |
| 0 3 -4 3 |
| 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
| 0 0 0 0 |
11 4
o2 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i3 : B = pureBettiDiagram d
0 1 2 3
o3 = total: 1 2 2 1
0: 1 2 . .
1: . . 2 1
o3 : BettiTally</pre>
</td></tr>
<tr><td><pre>i4 : dotProduct(M,-5,B)
o4 = 6</pre>
</td></tr>
<tr><td><pre>i5 : A = matrix"1,1,0; 0,1,1; 0,1,1"
o5 = | 1 1 0 |
| 0 1 1 |
| 0 1 1 |
3 3
o5 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i6 : B = matrix"0,1,-2;0,0,0;0,0,0"
o6 = | 0 1 -2 |
| 0 0 0 |
| 0 0 0 |
3 3
o6 : Matrix ZZ <--- ZZ</pre>
</td></tr>
<tr><td><pre>i7 : dotProduct(A, B)
o7 = 1</pre>
</td></tr>
<tr><td><pre>i8 : A1 = mat2betti A
0 1 2
o8 = total: 1 3 2
0: 1 1 .
1: . 1 1
2: . 1 1
o8 : BettiTally</pre>
</td></tr>
<tr><td><pre>i9 : B1 = mat2betti B
1 2
o9 = total: 1 -2
0: 1 -2
o9 : BettiTally</pre>
</td></tr>
<tr><td><pre>i10 : dotProduct(A1, B1)
o10 = 1</pre>
</td></tr>
<tr><td><pre>i11 : dotProduct(A, 0, B1)
o11 = 1</pre>
</td></tr>
<tr><td><pre>i12 : dotProduct(A, B1)
o12 = 1</pre>
</td></tr>
</table>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_facet__Equation_lp__List_cm__Z__Z_cm__Z__Z_cm__Z__Z_rp.html" title="The upper facet equation corresponding to (L,i)">facetEquation</a> -- The upper facet equation corresponding to (L,i)</span></li>
<li><span><a href="_pure__Betti__Diagram_lp__List_rp.html" title="pure Betti diagram given a list of degrees">pureBettiDiagram</a> -- pure Betti diagram given a list of degrees</span></li>
</ul>
</div>
<div class="waystouse"><h2>Ways to use <tt>dotProduct</tt> :</h2>
<ul><li>dotProduct(BettiTally,BettiTally)</li>
<li>dotProduct(Matrix,BettiTally)</li>
<li>dotProduct(Matrix,Matrix)</li>
<li>dotProduct(Matrix,ZZ,BettiTally)</li>
</ul>
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