Computing Singular Points of Projective Plane Algebraic Curves by Homotopy Continuation Methods

Table 1

Results for 𝑓(𝑥,𝑦)=0 in Example 1.

	𝑥	𝑦	𝑧	Mult.	Ord.
𝑄1	0.00000003+0.00000005𝑖	0.00000000+0.00000000𝑖	1.00000000	3	No
𝑄2	−0.89868027+0.41873939𝑖	−0.15046254+1.06341745𝑖	1.00000000	2	Yes
𝑄3	0.36804326−1.20320368𝑖	−0.92239819−0.40178011𝑖	1.00000000	2	Yes
𝑄4	0.36804326+1.20320368𝑖	−0.92239819+0.40178011𝑖	1.00000000	2	Yes
𝑄5	−0.49367385−0.00000000𝑖	0.28024456+0.00000000𝑖	1.00000000	2	Yes
𝑄6	−0.89868027−0.41873939𝑖	−0.15046254−1.06341745𝑖	1.00000000	2	Yes
𝑄7	0.77747393+0.21532054𝑖	−0.56726154−0.66500198𝑖	1.00000000	2	Yes
𝑄8	0.77747393−0.21532054𝑖	−0.56726154+0.66500198𝑖	1.00000000	2	Yes
𝑄9	0.00000000	1.00000000	0	3	No