ce131f78-27bd-4f07-8339-b1f4644bb6c4 32 4 5 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

isolate a 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 13 : H 14.245529 : N 19 : 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 14.24553 0.00002 12 mat

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2. The lower limit

find low limit u 1.7857 2 1.7875 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 Sols n el y u n el y Φ vectorize y solve at : 11 line for

low u Sols augment :

low 1 row 1.7857 0.00008 12 mat

reasonable limits
solving [2] branches xlimits 1.7857 14.245529 at

Local pairwise solutions

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

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

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

RemToDo: solve for the green lobe limits

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

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

x y XY x y / - :

XY Φ φ 3 1 sys

solving 6 values u 5 :

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

pair wise u pairwise 5 19.58772 - 4.029687 - 4.029688 19.58772 41 mat 12 mat

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

pair wise u pairwise 5 2.597824 - 2.597823 21 mat 12 mat