c599a6c2-1bd7-4927-863f-a8454e047127 18 6 5 decimal

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1. Maple symbolic solve

2. Numerical issue [complex]

3. Complete LaceLoop plot

4. Submitted Smath Forum [2018-10-31]

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Low step High x f inc U Low High step range : i 1 U rows range f i el U i el f eval : for U f augment 31 line :

x y f x 4^2 x 2^* y * + 3 x * y 2^* - y 3^+ :

<= observe the construction y sol y x f 0 ≡ y solve allvalues maple :

x c 1 x 0.625 ≤ cases :

x f1 x sol 1 el Re : x f2 x sol 2 el Re : x f3 x sol 3 el Re : x f4 x sol 4 el Re : 41 sys

3 appVersion 0.98.6179 ≡ Timing ~ 1.5 min ≡ 21 mat

Observe . . .

The 4 branches are real but evaluate with

residual imaginary [ie-16], to be removed.

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x u 1 0.21 - x ≤ (x 0 ≤ (& cases :

Discretize/collect b1 0.25 - 0.245 - 0.625 x f1 inc : b2 0.5 - 0.49 - 0.625 x f2 inc : b3 0.21 - 0.205 - 0 x f3 inc : b4 0.21 - 0.205 - 0 x f4 inc : 41 sys

x f1 x c * x f2 x c * x f3 x u * x f4 x u * 4 1 sys x sol 1 el x c * x sol 2 el x c * x sol 3 el x u * x sol 4 el x u * 4 1 sys b1 b2 b3 b4 4 1 sys

x 0.21 - :

x sol 3 el Re x sol 4 el Re - 0.000000000000000

x 0.625 :

x sol 1 el Re x sol 2 el Re - 51015 -^*

x 0.1875 - :

x sol 3 el 0.262604 - 1.685943 1016 -^* i * +

x sol 3 el is not complex ≡

64 nthroot 64 nthroot 43 nthroot x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot * x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot 43 nthroot * 8 x * - (* 16 x 2^* 13 x * + (* + x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot / sqrt * - 43 nthroot x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot * x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot 43 nthroot * 8 x * - (* 16 x 2^* 13 x * + (* + x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot / sqrt 43 nthroot x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot * x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot 43 nthroot * 16 x * + (* 16 x 2^* 13 x * + (* + (* 6 sqrt * 216 x 2^* 4 sqrt * x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot * + x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot 43 nthroot x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot * x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot 43 nthroot * 8 x * - (* 16 x 2^* 13 x * + (* + x 3^1699 x * + (* 32 nthroot (3^x 7^32 x 107256 x * - (* + (* sqrt * + 3 nthroot / sqrt * / - sqrt + (* 1246 nthroot * /