d6744263-50e3-40ff-9eb5-c91949832fa2 10 15 12 decimal

&[DATE] &[TIME] - &[FILENAME]

from cubic solver(s) r 0.4915 1.6194 i * + 0.4915 1.6194 i * - 6.983 - 31 mat :

Lagrange roots style x L x r n el - (n 13 product :

a 204 - 6114 mat transpose :

a polyroots 0.4915 1.6194 i * + 0.4915 1.6194 i * - 6.983 - 31 mat

Lagrange canonic x canonic a 1 el a 2 el x * + a 3 el x 2^* + a 4 el x 3^* + :

x c 16 - x ≤ (x 2 ≤ (& cases :

x L x c * x canonic 2 1 sys

Otherwise encountered x f 204 x * - 6 x 2^* + x 3^+ :

x expr x f op maple :

x 1 :

coeffs x expr :

coeffs 204 - 6141 mat

coeffs polyroots 0.4915 1.6194 i * + 0.4915 1.6194 i * - 6.983 - 31 mat

r 0.4915 1.6194 i * + 0.4915 1.6194 i * - 6.983 - 31 mat :

===== Lagrange roots styles =====

Lagrange roots style x L x r n el - (n 13 product :

Lagrange roots style x Labs x r n el abs - (n 13 product :

Lagrange roots style x Lre x r n el Re - (n 13 product :

Lagrange roots style x Lim x r n el Im - (n 13 product :

x L x Labs x Lre 5 x Lim * 4 1 sys

a 1 el a 2 el x * + a 3 el x 2^* + x 3^+ canonic format ≡

a 204 - 613 mat transpose :

# 204 - 6114 mat transpose ≡

for polyroots, x^3 is silent

S1 36 a 2 el * a 3 el * 108 a 1 el * - 8 a 3 el (3^* - 1212 a 2 el (3^* 3 a 2 el (2^* a 3 el (2^* - 54 a 1 el * a 2 el * a 3 el * - 81 a 1 el (2^* + 12 a 1 el * a 3 el (3^* + (12 /^* + (13 /^:

q 13 / a 2 el * 19 / a 3 el (2^* - :

q 5.3333 -

S1 9.3391 -

Z 16 / S1 * 6 q S1 / * - 13 / a 3 el * - 1 - 12 / S1 * 3 q S1 / * + 13 / a 3 el * - i 3 sqrt 2 / * 16 / S1 * 6 q S1 / * + (* + 1 - 12 / S1 * 3 q S1 / * + 13 / a 3 el * - i 3 sqrt 2 / * 16 / S1 * 6 q S1 / * + (* - 31 mat :

a Z 12 mat 204 - 631 mat 6.983 - 0.4915 1.6194 i * + 0.4915 1.6194 i * - 31 mat 12 mat

Cubic roots invariants

Z 1 el Z 2 el * Z 3 el * abs 20

q 3^r 2^+ 0 > q 3^r 2^+ 0 ≡ q 3^r 2^+ 0 < 31 mat 1 real pair complex conjugate all real roots, at least TwoEqual all real roots 31 mat ≡

[1]

Z 1 el Z 2 el * Z 1 el Z 3 el * + Z 2 el Z 3 el * + 4 -

Z 1 el Z 2 el + Z 3 el + (- 6

x f 3 x 3^* 2 x * - :

x f 0 ≡ x 10 - 10 solve 0.816496580927726 - 0 0.816496580927726 31 mat

x Clear 1

x f 0 ≡ x solve maple 06 sqrt 3 / 6 sqrt 3 / - 31 mat