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<head><title>betti(BettiTally) -- view and set the weights of a betti display</title>
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<div><h1>betti(BettiTally) -- view and set the weights of a betti display</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>betti(t, Weights => w)</tt></div>
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<li><span>Function: <a href="_betti.html" title="display degrees">betti</a></span></li>
<li><div class="single">Inputs:<ul><li><span><tt>t</tt>, <span>a <a href="___Betti__Tally.html">Betti tally</a></span></span></li>
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<li><div class="single">Outputs:<ul><li><span><span>a <a href="___Betti__Tally.html">Betti tally</a></span>, different from the input only in its degree weights. If <tt>w</tt> is non-null, then a new betti tally with new weight values is returned</span></li>
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<li><div class="single"><a href="_using_spfunctions_spwith_spoptional_spinputs.html">Optional inputs</a>:<ul><li><span><tt>Weights => </tt><span><span>a <a href="___List.html">list</a></span>, <span>default value null</span>, a list of integers, <tt>w</tt>, with the same degree length as that of <tt>t</tt></span></span></li>
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<div class="single"><h2>Description</h2>
<div><table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d,Degrees=>{2:{1,0},2:{0,1}}];</pre>
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<tr><td><pre>i2 : I = ideal random(R^1, R^{2:{-2,-2},2:{-3,-3}});
o2 : Ideal of R</pre>
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<tr><td><pre>i3 : t = betti res I
0 1 2 3 4
o3 = total: 1 4 13 14 4
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 2 . . .
4: . . . . .
5: . 2 . . .
6: . . 1 . .
7: . . 9 8 1
8: . . 2 4 2
9: . . 1 2 1
o3 : BettiTally</pre>
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<tr><td><pre>i4 : peek t
o4 = BettiTally{(0, {0, 0}, 0) => 1 }
(1, {2, 2}, 4) => 2
(1, {3, 3}, 6) => 2
(2, {3, 7}, 10) => 2
(2, {4, 4}, 8) => 1
(2, {4, 5}, 9) => 4
(2, {5, 4}, 9) => 4
(2, {6, 3}, 9) => 1
(2, {8, 3}, 11) => 1
(3, {4, 7}, 11) => 4
(3, {5, 5}, 10) => 6
(3, {6, 4}, 10) => 2
(3, {8, 4}, 12) => 2
(4, {5, 7}, 12) => 2
(4, {6, 5}, 11) => 1
(4, {8, 5}, 13) => 1</pre>
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The following three displays display the first degree, the second degree, and the total degree, respectively.<table class="examples"><tr><td><pre>i5 : betti(t,Weights=>{1,0})
0 1 2 3 4
o5 = total: 1 4 13 14 4
0: 1 . . . .
1: . 2 2 4 2
2: . 2 5 6 1
3: . . 4 2 .
4: . . 1 . 1
5: . . . 2 .
6: . . 1 . .
o5 : BettiTally</pre>
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<tr><td><pre>i6 : betti(t,Weights=>{0,1})
0 1 2 3 4
o6 = total: 1 4 13 14 4
0: 1 . . . .
1: . 2 2 4 2
2: . 2 5 6 .
3: . . 4 . 2
4: . . . 4 .
5: . . 2 . .
o6 : BettiTally</pre>
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<tr><td><pre>i7 : t1 = betti(t,Weights=>{1,1})
0 1 2 3 4
o7 = total: 1 4 13 14 4
0: 1 . . . .
1: . . . . .
2: . . . . .
3: . 2 . . .
4: . . . . .
5: . 2 . . .
6: . . 1 . .
7: . . 9 8 1
8: . . 2 4 2
9: . . 1 2 1
o7 : BettiTally</pre>
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<tr><td><pre>i8 : peek t1
o8 = BettiTally{(0, {0, 0}, 0) => 1 }
(1, {2, 2}, 4) => 2
(1, {3, 3}, 6) => 2
(2, {3, 7}, 10) => 2
(2, {4, 4}, 8) => 1
(2, {4, 5}, 9) => 4
(2, {5, 4}, 9) => 4
(2, {6, 3}, 9) => 1
(2, {8, 3}, 11) => 1
(3, {4, 7}, 11) => 4
(3, {5, 5}, 10) => 6
(3, {6, 4}, 10) => 2
(3, {8, 4}, 12) => 2
(4, {5, 7}, 12) => 2
(4, {6, 5}, 11) => 1
(4, {8, 5}, 13) => 1</pre>
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