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2019-02-27 16:28:32 -0600 commented answer Calculating Milnor Numbers of Polynomials Using Singular via Sage

You're right, I was wrongly interpreting the error. Thanks!

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2019-02-27 11:03:39 -0600 asked a question Calculating Milnor Numbers of Polynomials Using Singular via Sage

I'm using Singular via Sage Math to calculate the Milnor numbers of a large number of polynomials. For most polynomials, doing polynomial.milnor() works fine, however I am getting a -1 when I have a variable raised to a power times another variable. I have manually calculated the first Milnor number, and it should be 8. For instance:

Works fine:

sage: ring = singular.ring(0,'(x,y,z)','ds')
sage: polynomial = singular('-x2+x3-y3+xy3-z5+xz5')
sage: _=singular.lib('sing.lib')
sage: polynomial.milnor()
8

Returns error:

sage: polynomial2 = singular('y2-x3-z2x2')
sage: polynomial2.milnor()
-1

I am following these documentation pages:

  • Interface to Singular (Sage Interpreter Interfaces)
  • D.6.15.10 milnor (Singular Documentation)

I can't publish links due to low karma, sorry!

By the second page, the -1 would imply that the function is an isolated complete intersection singularity. This function does not have an ICIS to my knowledge, and I have tested several other functions which I can provide. I think that singular is interpreting the polynomial as y2-x3-z^(2x2), instead of the wanted y2-x3-(z2)(x2), but I am new to Sage and unsure of how to fix this (I attempted parentheses and it threw back an error).