| Classify |
| Coding |
| Deformations |
| Equidim Part |
| Existence |
| Finite Groups |
| Flatness |
| Genus |
| Hilbert Series |
| Membership |
| Monodromy |
| Normalization |
| Primdec |
| Puiseux |
| Plane Curves |
| Solving |
| Space Curves |
| Spectrum |
Task: Using MuPAD, plot the variety given by the ideal
I=(y2 z5 -x2 y2 z2 +y2 z4 -z6 -z5 +x4 -x2 z2 ,-y3 z3 +yz4 +x2 yz).
| Step | 0: | Load the (MuPAD) library sing.mu
and define I:>> read("sing.mu"):>> Ideal:=Dom::Ideal(Dom::DistributedPolynomial([x,y,z],Dom::Rational)):>> Id:=Ideal([poly(...,[x,y,z]),poly(...)]):
|
| Step | 1: | Calculate a primary decomposition of I using Singular. |
>> primDec:=sing::primdecGTZ(Id)):>> primeComps:=map(primDec, op, 2); |
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[[x^2-y^2*z^2+z^3],[x^4,z],[y,x^2-z^2-z^3]] |
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| Step | 2: | For each prime component, calculate the normalization of the radical, i.e., a parametrization using Singular. |
>> paramComps:=map(primeComps, sing::parametrize) |
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[[s^2*t-t^3,s,s^2-t^2],
[0,s,0], [s^3-s,0,s^2-1]] |
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| Step | 3: | Plot the parametrizations using MuPAD. |
>>
plot3d([Mode=Surface,paramComps[1],s=[-2..2],t=[-2..2]]); |