8efa99e6-82a2-471a-a623-b65b8b4e6825 30 15 12 decimal

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

Solve/evaluate contour

Incremental discretizer ...
Mesh N  within the bounds L, H L H N xd X 0 : i 1 N range X i el L H L - N / i * + : for X 31 line :

a 816 π * sqrt * : 351.67021

x y Φ 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - 0.005 + :

1. The upper limit

x y XY x y / - :

L 14 : H 14.2455293 : N 29 : 13 mat x L H N xd : 21 line

XY Φ 2 1 sys

n 1 x length range Sols n el y x n el y Φ vectorize y solve at : 11 line for

high x Sols augment :

high high rows row 14.2455293 0.00034955 12 mat

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2. The lower limit

find low limit u 1.7856878 1.7857 1.78569 range :

Explain . . .

0. The solver is implicit-recursive

implicit: in the sense that it solves y given Φ(x,y)=0.

recursive: as it runs on the vectorized discrete x.

1. The low limit is searched first on a practical low range.

2. The upper limit is searched over a generously populated

range, starting from a solvable mid - limit.

3. steps [1, 2] are trial/error.

4. Pairwise solutions aren't true @ the limits.

5. The model document is unique for the given Φ(x,y

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n 1 u length range Sol n el y u n el y Φ vectorize y solve at : 11 line for

low u Sol augment :

low 1 row 1.7856878 0.00094163 12 mat

reasonable zeros
the [2] lobes Xzeros 1.7856878 ± 14.2455293 ± at

Local pairwise solutions

# # at

# # # at

L < u < H ... escape end-points u 10 :

x pairwise user x y Φ y solve : x user 12 mat 21 line :

Draghilev 1.78568577382905 14.24552938284325 21 sys :

pair wise u pairwise 10 4.1749 - 4.1749 21 mat 12 mat

Solving for the green red lobes

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a 816 π * sqrt * : 351.67021

x y f 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - 0.0025 - :

About the Electron function . . .

A closed lobe that has no symbolic expression

of the ± branches. It complicates more familiar

expansion of f(x,y) but delights Smath.

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x y Φ 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - 0.005 + :

x y axes x y / - :

solving 6 values u 5 :

axes Φ f u 25 u 25 - 2 2 mat 14.2455293 5 14.2455293 5 - 2 2 mat 5 1 sys

x green user x y f y solve : x user 12 mat 21 line :

axes Φ f u 25 u 25 - 22 mat 14.24553 5 14.24553 5 - 22 mat 51 sys

pair wise u green 5 19.58772 - 4.029687 - 4.029687 19.58772 41 mat 12 mat

x red user x y Φ y solve : x user 12 mat 21 line :

pair wise u red 5 2.597823 - 2.597823 21 mat 12 mat

===============================================

solving  2 values green lobe ω 10 :

solving 4 values red lobe v 2.5 :

axes Φ f ω v 5 1 sys

y Green user x y f x solve : y user 12 mat 21 line :

pair wise ω Green 10 10.045492 - 10.045492 21 mat 12 mat

y Red user x y Φ x solve : y user 12 mat 21 line :

pair wise v Red 2.5 13.461052 - 4.821716 - 4.821716 13.461052 41 mat 12 mat

r 0.25 - :

given Y [u], solving  X circle u 0.375 :

x y q x 2^y 2^+ r + :

x circle user x y q y solve : user 21 line :

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

pair wise X u circle : 0.330719 - 0.330719 21 mat

xy u X 2 el augment :

f q xy 3 1 sys

x y Clear 1

r 0.25 - : x y c x 2^y 2^+ r + : 21 sys

rejects ? 0.3 0.45 0.31 range

solving  X circle ω 0.31 0.45 0.315 range :

x circle collect x y c y solve : collect 21 line :

pair wise pairs ω circle vectorize : 0.392301 - 0.392301 21 mat 0.388298 - 0.388298 21 mat 0.384187 - 0.384187 21 mat 0.379967 - 0.379967 21 mat 0.375633 - 0.375633 21 mat 51 mat