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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="___The_sp__Macaulay2_splanguage.html" title="">The Macaulay2 language</a> > <a href="_lists_spand_spsequences.html" title="">lists and sequences</a> > <a href="_ranges_spand_sprepetitions.html" title="">ranges and repetitions</a></div>
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<div><h1>ranges and repetitions</h1>
<div><p>In this section we discuss the use of ranges and repetitions.</p>
<h2>ranges</h2>
The operator <a href="_...html" title="a binary operator, used for sequences of consecutive items">..</a> can be used to create sequences of numbers, sequences of subscripted variables, or sequences of those particular symbols that are known to <a href="_vars.html" title="variables">vars</a>, and so on.<table class="examples"><tr><td><pre>i1 : 1 .. 5, y_1 .. y_5, a .. e
o1 = ((1, 2, 3, 4, 5), (y , y , y , y , y ), (a, b, c, d, e))
1 2 3 4 5
o1 : Sequence</pre>
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<h2>repetitions</h2>
The operator <a href="___Z__Z_sp_co_sp__Thing.html" title="repeat an item">ZZ : Thing</a> is used to create sequences by replicating something a certain number of times.<table class="examples"><tr><td><pre>i2 : 12:a
o2 = (a, a, a, a, a, a, a, a, a, a, a, a)
o2 : Sequence</pre>
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Replicating something once results in a sequence of length 1, which cannot be entered by simply typing parentheses.<table class="examples"><tr><td><pre>i3 : 1:a
o3 = 1 : (a)
o3 : Sequence</pre>
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<tr><td><pre>i4 : (a)
o4 = a
o4 : Symbol</pre>
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<h2>ranges and repetitions in lists</h2>
Notice what happens when we try to construct a list using <a href="_...html" title="a binary operator, used for sequences of consecutive items">..</a> or <a href="__co.html" title="a binary operator, uses include repetition; ideal quotients">:</a>.<table class="examples"><tr><td><pre>i5 : z = {3 .. 6, 9, 3:12}
o5 = {(3, 4, 5, 6), 9, (12, 12, 12)}
o5 : List</pre>
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The result above is a list of length 3 some of whose elements are sequences. This may be a problem if the user intended to produce the list <tt>{3, 4, 5, 6, 9, 12, 12, 12}</tt>. The function <a href="_splice.html" title="remove subsequences">splice</a> can be used to flatten out one level of nesting - think of it as removing those pairs of parentheses that are one level inward.<table class="examples"><tr><td><pre>i6 : splice z
o6 = {3, 4, 5, 6, 9, 12, 12, 12}
o6 : List</pre>
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The difference between <a href="_splice.html" title="remove subsequences">splice</a> and <a href="_flatten.html" title="flatten a list by unnesting lists">flatten</a> is, essentially, that <a href="_flatten.html" title="flatten a list by unnesting lists">flatten</a> removes braces one level inward.<table class="examples"><tr><td><pre>i7 : flatten {a,{b,c}}
o7 = {a, b, c}
o7 : List</pre>
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<tr><td><pre>i8 : splice {a,(b,c)}
o8 = {a, b, c}
o8 : List</pre>
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The function <a href="_to__List.html" title="list of elements">toList</a> converts sequences to lists.<table class="examples"><tr><td><pre>i9 : 1..6
o9 = (1, 2, 3, 4, 5, 6)
o9 : Sequence</pre>
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<tr><td><pre>i10 : toList(1..6)
o10 = {1, 2, 3, 4, 5, 6}
o10 : List</pre>
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Many operators and functions will splice lists presented to them. For example, when creating a polynomial ring, the array of variables and the list of degrees are spliced for you.<table class="examples"><tr><td><pre>i11 : QQ[a..c,x_1..x_4, Degrees => { 3:1, 4:2 }]
o11 = QQ[a, b, c, x , x , x , x ]
1 2 3 4
o11 : PolynomialRing</pre>
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<tr><td><pre>i12 : degrees oo
o12 = {{1}, {1}, {1}, {2}, {2}, {2}, {2}}
o12 : List</pre>
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