Macaulay is freely downloadable with source, and is available for Macintosh, Linux, and Windows.
Macaulay2 is a rewrite of Macaulay and is published under the GPL.
Macaulay: http://www.math.columbia.edu/~bayer/Macaulay/
Macaulay2: http://www.math.uiuc.edu/Macaulay2/
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