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<div><a href="index.html" title="">Macaulay2Doc</a> > <a href="_matrices.html" title="">matrices</a> > <a href="_random_spand_spgeneric_spmatrices.html" title="">random and generic matrices</a></div>
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<div><h1>random and generic matrices</h1>
<div><h2>random matrices</h2>
To construct a random m by n matrix with entries in a ring R use the function <a href="_random.html" title="get a random element">random</a> by typing <tt>random(R^m,R^n)</tt>.<table class="examples"><tr><td><pre>i1 : R = GF(3^2,Variable => a);</pre>
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<tr><td><pre>i2 : random(R^3,R^4)
o2 = | 1 1 1 -a |
| -a+1 a -1 -a |
| -1 a+1 0 a-1 |
3 4
o2 : Matrix R <--- R</pre>
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Over a polynomial ring, this will select elements in the base ring or field. TO obtain a matrix of (say) linear polynomials, use<table class="examples"><tr><td><pre>i3 : T = R[x,y];</pre>
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<tr><td><pre>i4 : random(T^3,T^{4:-1})
o4 = | (a+1)x+(-a-1)y -ax+(-a-1)y -x+(-a-1)y (a-1)x+(a+1)y |
| (a-1)x+ay -ax+(a+1)y ax+(-a-1)y (-a+1)x-ay |
| -ax+(-a+1)y (-a+1)y ax+ay (-a+1)x+(a+1)y |
3 4
o4 : Matrix T <--- T</pre>
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<h2>matrices of variables</h2>
To build an m by n matrix of variables drawn from the ring R, use <a href="_generic__Matrix.html" title="make a generic matrix of variables">genericMatrix</a>. The syntax is <tt>genericMatrix(R,x,m,n)</tt> where R is the ring, x is the variable where we start and m and n specify the size of the matrix.<table class="examples"><tr><td><pre>i5 : S = R[p..z];</pre>
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<tr><td><pre>i6 : genericMatrix(S,t,3,2)
o6 = | t w |
| u x |
| v y |
3 2
o6 : Matrix S <--- S</pre>
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Note that to use the function genericMatrix the number of variables in the ring R must be at least as large as <tt>m*n</tt>.<h2>genericSymmetricMatrix</h2>
To construct an n by n symmetric matrix whose entries on and above the diagonal are the variables of R use <a href="_generic__Symmetric__Matrix.html" title="make a generic symmetric matrix">genericSymmetricMatrix</a>. The syntax is <tt>genericSymmetricMatrix(R,x,n)</tt> where R is the ring, x is the variable you want to start with and n is the size of the matrix.<table class="examples"><tr><td><pre>i7 : genericSymmetricMatrix(S,s,3)
o7 = | s t u |
| t v w |
| u w x |
3 3
o7 : Matrix S <--- S</pre>
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<h2>genericSkewMatrix</h2>
To construct an n by n skew symmetric matrix whose entries above the diagonal are the variables of R use <a href="_generic__Skew__Matrix.html" title="make a generic skew symmetric matrix of variables">genericSkewMatrix</a>. The syntax is <tt>genericSkewMatrix(R,x,n)</tt> where R is the ring, x is the variable you want to start with and n is the size of the matrix.<table class="examples"><tr><td><pre>i8 : genericSymmetricMatrix(S,u,3)
o8 = | u v w |
| v x y |
| w y z |
3 3
o8 : Matrix S <--- S</pre>
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