History of Characteristic polynomials of the monodromy of the simple and unimodal singularities

 Display properties:   number-header: $\Delta_f(t)$-Numbers: []+Numbers:+- params:+    singularity: A1+    n: '1'+  number: t + 1+  comment: $f=x^{2}$, with $\mu=1$; $\Delta_f(t)=\Phi_{2}(t)$.+- params:+    singularity: A1+    n: '2'+  number: t - 1+  comment: $f=x^{2}+y^2$, with $\mu=1$; $\Delta_f(t)=\Phi_{1}(t)$.+- params:+    singularity: A1+    n: '3'+  number: t + 1+  comment: $f=x^{2}+y^2+z^2$, with $\mu=1$; $\Delta_f(t)=\Phi_{2}(t)$.+- params:+    singularity: A2+    n: '1'+  number: t^2 + t + 1+  comment: $f=x^{3}$, with $\mu=2$; $\Delta_f(t)=\Phi_{3}(t)$.+- params:+    singularity: A2+    n: '2'+  number: t^2 - t + 1+  comment: $f=x^{3}+y^2$, with $\mu=2$; $\Delta_f(t)=\Phi_{6}(t)$.+- params:+    singularity: A2+    n: '3'+  number: t^2 + t + 1+  comment: $f=x^{3}+y^2+z^2$, with $\mu=2$; $\Delta_f(t)=\Phi_{3}(t)$.+- params:+    singularity: A3+    n: '1'+  number: t^3 + t^2 + t + 1+  comment: $f=x^{4}$, with $\mu=3$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)$.+- params:+    singularity: A3+    n: '2'+  number: t^3 - t^2 + t - 1+  comment: $f=x^{4}+y^2$, with $\mu=3$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)$.+- params:+    singularity: A3+    n: '3'+  number: t^3 + t^2 + t + 1+  comment: $f=x^{4}+y^2+z^2$, with $\mu=3$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)$.+- params:+    singularity: A4+    n: '1'+  number: t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{5}$, with $\mu=4$; $\Delta_f(t)=\Phi_{5}(t)$.+- params:+    singularity: A4+    n: '2'+  number: t^4 - t^3 + t^2 - t + 1+  comment: $f=x^{5}+y^2$, with $\mu=4$; $\Delta_f(t)=\Phi_{10}(t)$.+- params:+    singularity: A4+    n: '3'+  number: t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{5}+y^2+z^2$, with $\mu=4$; $\Delta_f(t)=\Phi_{5}(t)$.+- params:+    singularity: A5+    n: '1'+  number: t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{6}$, with $\mu=5$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)$.+- params:+    singularity: A5+    n: '2'+  number: t^5 - t^4 + t^3 - t^2 + t - 1+  comment: $f=x^{6}+y^2$, with $\mu=5$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)$.+- params:+    singularity: A5+    n: '3'+  number: t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{6}+y^2+z^2$, with $\mu=5$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)$.+- params:+    singularity: A6+    n: '1'+  number: t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{7}$, with $\mu=6$; $\Delta_f(t)=\Phi_{7}(t)$.+- params:+    singularity: A6+    n: '2'+  number: t^6 - t^5 + t^4 - t^3 + t^2 - t + 1+  comment: $f=x^{7}+y^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{14}(t)$.+- params:+    singularity: A6+    n: '3'+  number: t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{7}+y^2+z^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{7}(t)$.+- params:+    singularity: A7+    n: '1'+  number: t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{8}$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{8}(t)$.+- params:+    singularity: A7+    n: '2'+  number: t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1+  comment: $f=x^{8}+y^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)\,\Phi_{8}(t)$.+- params:+    singularity: A7+    n: '3'+  number: t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{8}+y^2+z^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{8}(t)$.+- params:+    singularity: A8+    n: '1'+  number: t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{9}$, with $\mu=8$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{9}(t)$.+- params:+    singularity: A8+    n: '2'+  number: t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1+  comment: $f=x^{9}+y^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{18}(t)$.+- params:+    singularity: A8+    n: '3'+  number: t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{9}+y^2+z^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{9}(t)$.+- params:+    singularity: A9+    n: '1'+  number: t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{10}$, with $\mu=9$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{5}(t)\,\Phi_{10}(t)$.+- params:+    singularity: A9+    n: '2'+  number: t^9 - t^8 + t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1+  comment: $f=x^{10}+y^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{5}(t)\,\Phi_{10}(t)$.+- params:+    singularity: A9+    n: '3'+  number: t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{10}+y^2+z^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{5}(t)\,\Phi_{10}(t)$.+- params:+    singularity: A10+    n: '1'+  number: t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{11}$, with $\mu=10$; $\Delta_f(t)=\Phi_{11}(t)$.+- params:+    singularity: A10+    n: '2'+  number: t^10 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t + 1+  comment: $f=x^{11}+y^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{22}(t)$.+- params:+    singularity: A10+    n: '3'+  number: t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{11}+y^2+z^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{11}(t)$.+- params:+    singularity: A11+    n: '1'+  number: t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{12}$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{12}(t)$.+- params:+    singularity: A11+    n: '2'+  number: t^11 - t^10 + t^9 - t^8 + t^7 - t^6 + t^5 - t^4 + t^3 - t^2 + t - 1+  comment: $f=x^{12}+y^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{12}(t)$.+- params:+    singularity: A11+    n: '3'+  number: t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t + 1+  comment: $f=x^{12}+y^2+z^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{4}(t)\,\Phi_{6}(t)\,\Phi_{12}(t)$.+- params:+    singularity: A12+    n: '1'+  number: t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t ++    1+  comment: $f=x^{13}$, with $\mu=12$; $\Delta_f(t)=\Phi_{13}(t)$.+- params:+    singularity: A12+    n: '2'+  number: t^12 - t^11 + t^10 - t^9 + t^8 - t^7 + t^6 - t^5 + t^4 - t^3 + t^2 - t ++    1+  comment: $f=x^{13}+y^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{26}(t)$.+- params:+    singularity: A12+    n: '3'+  number: t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t ++    1+  comment: $f=x^{13}+y^2+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{13}(t)$.+- params:+    singularity: D4+    n: '2'+  number: t^4 - t^3 - t + 1+  comment: $f=x^2y+y^{3}$, with $\mu=4$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)$.+- params:+    singularity: D4+    n: '3'+  number: t^4 + t^3 + t + 1+  comment: $f=x^2y+y^{3}+z^2$, with $\mu=4$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)$.+- params:+    singularity: D5+    n: '2'+  number: t^5 - t^4 + t - 1+  comment: $f=x^2y+y^{4}$, with $\mu=5$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{8}(t)$.+- params:+    singularity: D5+    n: '3'+  number: t^5 + t^4 + t + 1+  comment: $f=x^2y+y^{4}+z^2$, with $\mu=5$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{8}(t)$.+- params:+    singularity: D6+    n: '2'+  number: t^6 - t^5 - t + 1+  comment: $f=x^2y+y^{5}$, with $\mu=6$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{5}(t)$.+- params:+    singularity: D6+    n: '3'+  number: t^6 + t^5 + t + 1+  comment: $f=x^2y+y^{5}+z^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{10}(t)$.+- params:+    singularity: D7+    n: '2'+  number: t^7 - t^6 + t - 1+  comment: $f=x^2y+y^{6}$, with $\mu=7$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)\,\Phi_{12}(t)$.+- params:+    singularity: D7+    n: '3'+  number: t^7 + t^6 + t + 1+  comment: $f=x^2y+y^{6}+z^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{12}(t)$.+- params:+    singularity: D8+    n: '2'+  number: t^8 - t^7 - t + 1+  comment: $f=x^2y+y^{7}$, with $\mu=8$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{7}(t)$.+- params:+    singularity: D8+    n: '3'+  number: t^8 + t^7 + t + 1+  comment: $f=x^2y+y^{7}+z^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{14}(t)$.+- params:+    singularity: D9+    n: '2'+  number: t^9 - t^8 + t - 1+  comment: $f=x^2y+y^{8}$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{16}(t)$.+- params:+    singularity: D9+    n: '3'+  number: t^9 + t^8 + t + 1+  comment: $f=x^2y+y^{8}+z^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{16}(t)$.+- params:+    singularity: D10+    n: '2'+  number: t^10 - t^9 - t + 1+  comment: $f=x^2y+y^{9}$, with $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)\,\Phi_{9}(t)$.+- params:+    singularity: D10+    n: '3'+  number: t^10 + t^9 + t + 1+  comment: $f=x^2y+y^{9}+z^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{6}(t)\,\Phi_{18}(t)$.+- params:+    singularity: D11+    n: '2'+  number: t^11 - t^10 + t - 1+  comment: $f=x^2y+y^{10}$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{4}(t)\,\Phi_{20}(t)$.+- params:+    singularity: D11+    n: '3'+  number: t^11 + t^10 + t + 1+  comment: $f=x^2y+y^{10}+z^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{20}(t)$.+- params:+    singularity: D12+    n: '2'+  number: t^12 - t^11 - t + 1+  comment: $f=x^2y+y^{11}$, with $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{11}(t)$.+- params:+    singularity: D12+    n: '3'+  number: t^12 + t^11 + t + 1+  comment: $f=x^2y+y^{11}+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{22}(t)$.+- params:+    singularity: E6+    n: '2'+  number: t^6 - t^5 + t^3 - t + 1+  comment: $f=x^3+y^4$, with $\mu=6$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{12}(t)$.+- params:+    singularity: E6+    n: '3'+  number: t^6 + t^5 - t^3 + t + 1+  comment: $f=x^3+y^4+z^2$, with $\mu=6$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{12}(t)$.+- params:+    singularity: E7+    n: '2'+  number: t^7 - t^6 + t^4 - t^3 + t - 1+  comment: $f=x^3+xy^3$, with $\mu=7$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{9}(t)$.+- params:+    singularity: E7+    n: '3'+  number: t^7 + t^6 - t^4 - t^3 + t + 1+  comment: $f=x^3+xy^3+z^2$, with $\mu=7$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{18}(t)$.+- params:+    singularity: E8+    n: '2'+  number: t^8 - t^7 + t^5 - t^4 + t^3 - t + 1+  comment: $f=x^3+y^5$, with $\mu=8$; $\Delta_f(t)=\Phi_{15}(t)$.+- params:+    singularity: E8+    n: '3'+  number: t^8 + t^7 - t^5 - t^4 - t^3 + t + 1+  comment: $f=x^3+y^5+z^2$, with $\mu=8$; $\Delta_f(t)=\Phi_{30}(t)$.+- params:+    singularity: P8+    n: '3'+  number: t^8 + t^7 + t^6 - 2*t^5 - 2*t^4 - 2*t^3 + t^2 + t + 1+  comment: $f=x^3+y^3+z^3$, with $\mu=8$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{3}(t)^{3}$.+- params:+    singularity: X9+    n: '2'+  number: t^9 - t^8 - 2*t^5 + 2*t^4 + t - 1+  comment: $f=x^4+y^4$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)^{3}\,\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}$.+- params:+    singularity: X9+    n: '3'+  number: t^9 + t^8 - 2*t^5 - 2*t^4 + t + 1+  comment: $f=x^4+y^4+z^2$, with $\mu=9$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{3}\,\Phi_{4}(t)^{2}$.+- params:+    singularity: J10+    n: '2'+  number: t^10 - t^9 + t^7 - t^6 - t^4 + t^3 - t + 1+  comment: $f=x^3+y^6$, with $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)\,\Phi_{6}(t)^{2}$.+- params:+    singularity: J10+    n: '3'+  number: t^10 + t^9 - t^7 - t^6 - t^4 - t^3 + t + 1+  comment: $f=x^3+y^6+z^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{2}(t)^{2}\,\Phi_{3}(t)^{2}\,\Phi_{6}(t)$.+- params:+    singularity: E12+    n: '2'+  number: t^12 - t^11 + t^9 - t^8 + t^6 - t^4 + t^3 - t + 1+  comment: $f=x^3+y^7$, with $\mu=12$; $\Delta_f(t)=\Phi_{21}(t)$.+- params:+    singularity: E12+    n: '3'+  number: t^12 + t^11 - t^9 - t^8 + t^6 - t^4 - t^3 + t + 1+  comment: $f=x^3+y^7+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{42}(t)$.+- params:+    singularity: E13+    n: '2'+  number: t^13 - t^12 + t^10 - t^9 + t^7 - t^6 + t^4 - t^3 + t - 1+  comment: $f=x^3+xy^5$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{5}(t)\,\Phi_{15}(t)$.+- params:+    singularity: E13+    n: '3'+  number: t^13 + t^12 - t^10 - t^9 + t^7 + t^6 - t^4 - t^3 + t + 1+  comment: $f=x^3+xy^5+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{10}(t)\,\Phi_{30}(t)$.+- params:+    singularity: E14+    n: '2'+  number: t^14 - t^13 + t^11 - t^10 + t^8 - t^7 + t^6 - t^4 + t^3 - t + 1+  comment: $f=x^3+y^8$, with $\mu=14$; $\Delta_f(t)=\Phi_{6}(t)\,\Phi_{12}(t)\,\Phi_{24}(t)$.+- params:+    singularity: E14+    n: '3'+  number: t^14 + t^13 - t^11 - t^10 + t^8 + t^7 + t^6 - t^4 - t^3 + t + 1+  comment: $f=x^3+y^8+z^2$, with $\mu=14$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{12}(t)\,\Phi_{24}(t)$.+- params:+    singularity: Z11+    n: '2'+  number: t^11 - t^10 + t^6 - t^5 + t - 1+  comment: $f=x^3y+y^5$, with $\mu=11$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{3}(t)\,\Phi_{15}(t)$.+- params:+    singularity: Z11+    n: '3'+  number: t^11 + t^10 - t^6 - t^5 + t + 1+  comment: $f=x^3y+y^5+z^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{6}(t)\,\Phi_{30}(t)$.+- params:+    singularity: Z12+    n: '2'+  number: t^12 - t^11 - t + 1+  comment: $f=x^3y+xy^4$, with $\mu=12$; $\Delta_f(t)=\Phi_{1}(t)^{2}\,\Phi_{11}(t)$.+- params:+    singularity: Z12+    n: '3'+  number: t^12 + t^11 + t + 1+  comment: $f=x^3y+xy^4+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{22}(t)$.+- params:+    singularity: Z13+    n: '2'+  number: t^13 - t^12 + t^7 - t^6 + t - 1+  comment: $f=x^3y+y^6$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{9}(t)\,\Phi_{18}(t)$.+- params:+    singularity: Z13+    n: '3'+  number: t^13 + t^12 + t^7 + t^6 + t + 1+  comment: $f=x^3y+y^6+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{9}(t)\,\Phi_{18}(t)$.+- params:+    singularity: W12+    n: '2'+  number: t^12 - t^11 + t^8 - t^6 + t^4 - t + 1+  comment: $f=x^4+y^5$, with $\mu=12$; $\Delta_f(t)=\Phi_{10}(t)\,\Phi_{20}(t)$.+- params:+    singularity: W12+    n: '3'+  number: t^12 + t^11 + t^8 - t^6 + t^4 + t + 1+  comment: $f=x^4+y^5+z^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{5}(t)\,\Phi_{20}(t)$.+- params:+    singularity: W13+    n: '2'+  number: t^13 - t^12 + t^9 - t^8 + t^5 - t^4 + t - 1+  comment: $f=x^4+xy^4$, with $\mu=13$; $\Delta_f(t)=\Phi_{1}(t)\,\Phi_{8}(t)\,\Phi_{16}(t)$.+- params:+    singularity: W13+    n: '3'+  number: t^13 + t^12 + t^9 + t^8 + t^5 + t^4 + t + 1+  comment: $f=x^4+xy^4+z^2$, with $\mu=13$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{8}(t)\,\Phi_{16}(t)$.+- params:+    singularity: Q10+    n: '3'+  number: t^10 + t^9 + t^8 - t^6 - t^5 - t^4 + t^2 + t + 1+  comment: $f=x^3+y^4+yz^2$, with $\mu=10$; $\Delta_f(t)=\Phi_{3}(t)\,\Phi_{24}(t)$.+- params:+    singularity: Q11+    n: '3'+  number: t^11 + t^10 + t^9 + t^2 + t + 1+  comment: $f=x^3+y^2z+xz^3$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{3}(t)\,\Phi_{6}(t)\,\Phi_{18}(t)$.+- params:+    singularity: Q12+    n: '3'+  number: t^12 + t^11 + t^10 + t^7 + t^6 + t^5 + t^2 + t + 1+  comment: $f=x^3+y^5+yz^2$, with $\mu=12$; $\Delta_f(t)=\Phi_{3}(t)^{2}\,\Phi_{15}(t)$.+- params:+    singularity: S11+    n: '3'+  number: t^11 + t^10 + t^9 + t^8 + t^3 + t^2 + t + 1+  comment: $f=x^4+y^2z+xz^2$, with $\mu=11$; $\Delta_f(t)=\Phi_{2}(t)\,\Phi_{4}(t)\,\Phi_{16}(t)$.+- params:+    singularity: S12+    n: '3'+  number: t^12 + t^11 + t^10 + t^9 + t^8 + t^7 + t^6 + t^5 + t^4 + t^3 + t^2 + t ++    1+  comment: $f=x^2y+y^2z+xz^3$, with $\mu=12$; $\Delta_f(t)=\Phi_{13}(t)$.+- params:+    singularity: U12+    n: '3'+  number: t^12 + t^11 + t^10 + 2*t^9 + t^8 + t^7 + 2*t^6 + t^5 + t^4 + 2*t^3 + t^2+    + t + 1+  comment: $f=x^3+y^3+z^4$, with $\mu=12$; $\Delta_f(t)=\Phi_{2}(t)^{2}\,\Phi_{4}(t)^{2}\,\Phi_{6}(t)\,\Phi_{12}(t)$.