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<head><title>newCoordinateSystem -- change variables</title>
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<div><h1>newCoordinateSystem -- change variables</h1>
<div class="single"><h2>Description</h2>
<div><tt>newCoordinateSystem(S,m)</tt> -- takes a one-rowed matrix <tt>m</tt> of independent linear forms over a ring <tt>R</tt> and returns a pair <tt>(f,g)</tt>, where <tt>f</tt> is a ring map given by some linear change of coordinates from <tt>R</tt> to <tt>S</tt> which sends the last variables of <tt>R</tt> to the forms in <tt>m</tt>, and <tt>g</tt> is the inverse of <tt>f</tt>.<p/>
The ring <tt>S</tt> should have the same number of variables as <tt>S</tt>.<table class="examples"><tr><td><pre>i1 : R = ZZ/101[a..d]
o1 = R
o1 : PolynomialRing</pre>
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<tr><td><pre>i2 : S = ZZ/101[p..s]
o2 = S
o2 : PolynomialRing</pre>
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<tr><td><pre>i3 : (f,g) = newCoordinateSystem(S,matrix{{a+2*b,3*c-d}});</pre>
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<tr><td><pre>i4 : f
o4 = map(S,R,{50p, 3r, p + 2q, 3r - s})
o4 : RingMap S <--- R</pre>
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<tr><td><pre>i5 : g
o5 = map(R,S,{-2a, a - 50c, 34b, b - d})
o5 : RingMap R <--- S</pre>
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<div class="waystouse"><h2>Ways to use <tt>newCoordinateSystem</tt> :</h2>
<ul><li>newCoordinateSystem(PolynomialRing,Matrix)</li>
</ul>
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