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| What does facstd(ideal) actually do? https://www.singular.uni-kl.de/forum/viewtopic.php?f=10&t=2919 |
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| Author: | rambiz [ Sun Aug 09, 2020 7:44 pm ] |
| Post subject: | What does facstd(ideal) actually do? |
Hi all, a) I am looking for reference(s) elaborating on the factorizing Groebner basis algorithm. I want to know what it exactly does and how to possibly have a look at the code to see how it is implemented. b) I had a look at https://www.singular.uni-kl.de/Manual/4 ... htm#SEC282. Do I understand it correctly that if facstd(ideal_1, ideal_2) is called with two arguments, then the union of the solutions to the output ideals contains all solutions of ideal_1 for which all members of ideal_2! are strictly non-zero?! Let's have a look at the example provided in the link above: Code: ring r=32003,(x,y,z),(c,dp); ideal I=xyz,x2z; facstd(I); ==> [1]: ==> _[1]=z ==> [2]: ==> _[1]=x So far,so good. I can see that the variety of I is the union of the x-y-plane and the y-z-plane. But now: Code: facstd(I,x); ==> [1]: ==> _[1]=z The answer is the x-y-plane which obviously contains (x=0, y, z=0). So it includes the whole y-axis for which x=0! So am I right or wrong or am I?! |
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