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<head><title>matrix(BettiTally,ZZ,ZZ) -- Betti diagram to matrix</title>
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<div><h1>matrix(BettiTally,ZZ,ZZ) -- Betti diagram to matrix</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>matrix B</tt><br/><tt>matrix(B,lowDegree)</tt><br/><tt>matrix(B,lowDegree,highDegree)</tt></div>
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<li><span>Function: <a href="../../Macaulay2Doc/html/_matrix.html" title="make a matrix">matrix</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>B</tt>, <span>a <a href="../../Macaulay2Doc/html/___Betti__Tally.html">Betti tally</a></span></span></li>
<li><span><tt>lowDegree</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
<li><span><tt>highDegree</tt>, <span>an <a href="../../Macaulay2Doc/html/___Z__Z.html">integer</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="../../Macaulay2Doc/html/___Matrix.html">matrix</a></span>, The Betti diagram as a matrix</span></li>
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<li><div class="single"><a href="../../Macaulay2Doc/html/_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><a href="../../Macaulay2Doc/html/_matrix_lp__List_rp.html">Degree => ...</a>, -- create a matrix from a doubly-nested list of ring elements or matrices</span></li>
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<div class="single"><h2>Description</h2>
<div>If either lowDegree or highDegree is not given, then they are inferred from the Betti diagram itself. The result matrix has highDegree-lowDegree+1 rows, corresponding to these (slanted) degrees. <table class="examples"><tr><td><pre>i1 : B = pureBettiDiagram {0,1,4,7}
0 1 2 3
o1 = total: 9 14 7 2
0: 9 14 . .
1: . . . .
2: . . 7 .
3: . . . .
4: . . . 2
o1 : BettiTally</pre>
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<tr><td><pre>i2 : matrix B
o2 = | 9 14 0 0 |
| 0 0 0 0 |
| 0 0 7 0 |
| 0 0 0 0 |
| 0 0 0 2 |
5 4
o2 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i3 : matrix(B,-2)
o3 = | 0 0 0 0 |
| 0 0 0 0 |
| 9 14 0 0 |
| 0 0 0 0 |
| 0 0 7 0 |
| 0 0 0 0 |
| 0 0 0 2 |
7 4
o3 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i4 : matrix(B,-2,5)
o4 = | 0 0 0 0 |
| 0 0 0 0 |
| 9 14 0 0 |
| 0 0 0 0 |
| 0 0 7 0 |
| 0 0 0 0 |
| 0 0 0 2 |
| 0 0 0 0 |
8 4
o4 : Matrix ZZ <--- ZZ</pre>
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This function is essentially the inverse of <a href="_mat2betti_lp__Matrix_cm__Z__Z_rp.html" title="matrix to Betti diagram">mat2betti</a>.<table class="examples"><tr><td><pre>i5 : R = ZZ/101[a..e];</pre>
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<tr><td><pre>i6 : I = ideal borel monomialIdeal"abc,ad3,e4";
o6 : Ideal of R</pre>
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<tr><td><pre>i7 : B = betti res I
0 1 2 3 4 5
o7 = total: 1 56 182 232 135 30
0: 1 . . . . .
1: . . . . . .
2: . 5 6 2 . .
3: . 51 176 230 135 30
o7 : BettiTally</pre>
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<tr><td><pre>i8 : C = matrix B
o8 = | 1 0 0 0 0 0 |
| 0 0 0 0 0 0 |
| 0 5 6 2 0 0 |
| 0 51 176 230 135 30 |
4 6
o8 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i9 : B == mat2betti C
o9 = true</pre>
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If the lowest degree of the matrix is not 0, then this information must be supplied in order to obtain the inverse operation.<table class="examples"><tr><td><pre>i10 : B = pureBettiDiagram {-2,0,1,2,5}
0 1 2 3 4
o10 = total: 5 42 70 35 2
-2: 5 . . . .
-1: . 42 70 35 .
0: . . . . .
1: . . . . 2
o10 : BettiTally</pre>
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<tr><td><pre>i11 : C = matrix B
o11 = | 5 0 0 0 0 |
| 0 42 70 35 0 |
| 0 0 0 0 0 |
| 0 0 0 0 2 |
4 5
o11 : Matrix ZZ <--- ZZ</pre>
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<tr><td><pre>i12 : mat2betti(C,-2)
0 1 2 3 4
o12 = total: 5 42 70 35 2
-2: 5 . . . .
-1: . 42 70 35 .
0: . . . . .
1: . . . . 2
o12 : BettiTally</pre>
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<div class="single"><h2>Caveat</h2>
<div>Currently, the error messages are not that illuminating. The [lowDegree, highDegree], if given, must be as large as the actual degree range</div>
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<div class="single"><h2>See also</h2>
<ul><li><span><a href="_mat2betti_lp__Matrix_cm__Z__Z_rp.html" title="matrix to Betti diagram">mat2betti</a> -- matrix to Betti diagram</span></li>
<li><span><a href="_lowest__Degrees_lp__Betti__Tally_rp.html" title="list of lowest degree shifts">lowestDegrees</a> -- list of lowest degree shifts</span></li>
<li><span><a href="_highest__Degrees_lp__Betti__Tally_rp.html" title="list of highest degree shifts">highestDegrees</a> -- list of highest degree shifts</span></li>
<li><span><a href="_is__Pure_lp__Betti__Tally_rp.html" title="is a Betti diagram pure?">isPure</a> -- is a Betti diagram pure?</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>
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