Talk:Mathematical singularity
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The example of the absolute value function having a singularity at x=0 might not be the best, because the absolute value function is not complex differentiable anywhere.
I don't understand the sentence: The algebraic set defined by y2 = x also has a singularity at (0,0), this time because it has a "corner" at that point.
As a set in the plan (i.e., as an imbedded 1-manifold) it is perfectly well behaved. Thought of as a (multi-valued) function it has an infinite slope.
Per haps "... because it has a vertical tangent at that point."
Maybe I'm missing something, which is why I didn't just make the edit myself.... Better not to be bold and confused at the same time. ;-> Jeff 01:40 Apr 10, 2003 (UTC)
Should we add a fourth kind of singularity in complex analysis -- a branch point? Michael Hardy 02:43 Apr 10, 2003 (UTC)
Are singularities in lower dimensions NOT SO IN THE HIGHER DIMENSIONS?This can be proved in this manner-suppose a curve is given ,then write it's parametric equation.treat the parameter as the new dimension .trace the curve in this new coordinate system .sometimes we see the singularity has vanished in the higher dimension.[user:Preetam ]
Shouldn't this page be merged with Singularity theory ? --Piotr Konieczny aka Prokonsul Piotrus 21:37, 12 Jul 2004 (UTC)
Shouldn't this be at singularity (mathematics)? - Fredrik | talk 19:01, 12 Apr 2005 (UTC)
- It would be better to have that as disambiguation, I think. Singularity of a function would be one alternate name. There is also singularity of a differential equation to think about. Charles Matthews 19:14, 12 Apr 2005 (UTC)
We seem to bw missing singular matricies (determinant zero). I'd like to add a section about one singularity theory in more details (just 1 paragraph). Also should we include a disambig link to Singularity? --Salix alba (talk) 14:36, 24 January 2006 (UTC)
[edit] Connections
A lot of these seem to be closely linked.
Start with a function f : Rm -> Rn. The first derivative dfˈis a linear map or an m by n matrix. f will be singular (in terms of algebraic geometry/singularity theory) when the matrix drops rank. (i.e. is singular).
The commutative algebra ideal's are generilisations of this concept, (think of the ideal generated by the derivatives).
Likewise the singular solutions of ordinary differential equations are simarly linked. --Salix alba (talk) 11:53, 25 January 2006 (UTC)
[edit] Number of Types of Singularities in Complex Analysis
There are more than four types of singularities in Complex Analysis. I will correct this mistake if there is no disagreement on this issue. Furthermore, ranking them is appropriate, as the differences are significant. Tparameter 05:53, 9 December 2006 (UTC)
