i1 : R = CC[x,y,z]; |
i2 : F = {x^2+y^2+z^2-1, y-x^2, z-x^3}; |
i3 : s = solveSystem F o3 = {{.540536-1.03152*ii, -.771845-1.11514*ii, -1.5675+.193395*ii}, ------------------------------------------------------------------------ {-.737353, .543689, -.400891}, {.540536+1.03152*ii, -.771845+1.11514*ii, ------------------------------------------------------------------------ -1.5675-.193395*ii}, {-.540536-1.03152*ii, -.771845+1.11514*ii, ------------------------------------------------------------------------ 1.5675+.193395*ii}, {-.540536+1.03152*ii, -.771845-1.11514*ii, ------------------------------------------------------------------------ 1.5675-.193395*ii}, {.737353, .543689, .400891}} o3 : List |
i4 : realPoints s o4 = {{-.737353, .543689, -.400891}, {.737353, .543689, .400891}} o4 : List |
i5 : R = CC[x,y,z]; |
i6 : sph = x^2+y^2+z^2-1; |
i7 : I = ideal {x*sph*(y-x^2), sph*(z-x^3)}; o7 : Ideal of R |
i8 : numericalIrreducibleDecomposition I o8 = a numerical variety with components in dim 1: (dim=1,deg=1) (dim=1,deg=3) dim 2: (dim=2,deg=2) o8 : NumericalVariety |
Basic types (such as Point and WitnessSet) are defined in the package NAGtypes.
Version 1.4 of this package was accepted for publication in volume 3 of the journal The Journal of Software for Algebra and Geometry: Macaulay2 on 2011-05-20, in the article Numerical Algebraic Geometry. That version can be obtained from the journal or from the Macaulay2 source code repository, svn://svn.macaulay2.com/Macaulay2/trunk/M2/Macaulay2/packages/NumericalAlgebraicGeometry.m2, release number 13254.