<content> plot(data,char,size,clr) </content>

da5196e5-9cb1-48cc-a761-ecbcaa7191a6 131 4 5 false false 0 0 decimal

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

Iterative solve . . . triplet

t0 1 time :

x y z f 2 π * x y + 2 z * - (* cos 2 π * y z + 2 x * - (* cos + 2 π * z x + 2 y * - (* cos + :

The solve bloc is generally ≈ 6 decimals
You can initialise a system ... demo

x 0.3 : z 0.1 : 12 mat

The system solves for y from given [x ... z] ▲
This demo produces two sets of solutions
both valid from the sanity check.
Copy/pate 15 decimals ... either y in initial..
Here, braketing is valid wrt [x ... z]

The two sets of solutionsfrom either selecte y 0.1000006 0.0793387 - 0.0999994 - 31 mat 0.4793298 0.4586691 0.2793298 31 mat 12 mat

r x y z f y 0 0.5 solve : 0.120660701354506 0.279339255953666 21 mat

J 2 :

◄  'y' refine manual trial/error initial x x ≡ y r J el : z z ≡ 31 mat :

ε 103 -^:

x z Clear 1

saved in lexicographic order x y z 31 mat x y z f x y z f x y z f 31 mat initial ε FindRoot : 0.4793298 0.4586691 0.2793298 31 mat

sanity implicit f(x,y,z)≡ 0 x y z f 0.0000001

J r Clear 1

data char size clr plot k 1 data rows range r3 k el char : r4 k el size : r5 k el clr : 13 mat for data r3 r4 r5 augment 21 line :

T 20307180116246311379384421458495497499141 mat :

length _T n 14 :

log vraisemblance α β x L n α β * ln * β 1 - (T i el ln i 1 n sum * + (α T i el β^i 1 n sum * - :

partial derivatives and1rst order conditions. α β x L α diff n α / T i el (β^i 1 n sum - ≡ (0 ≡ α β x L β diff n β / T i el ln i 1 n sum + α T i el (β^(T i el ln * i 1 n sum * - ≡ (0 ≡ 21 sys

system n α / T i el (β^i 1 n sum - 0 ≡ n β / T i el ln i 1 n sum + α T i el (β^(T i el ln * i 1 n sum * - 0 ≡ 21 mat :

init α 0.1 ≡ β 2 ≡ 21 mat :

ε 106 -^:

optimized ▲ trial/error

α β sol system init ε FindRoot :

α β 21 mat α β sol : 55.4246 0.8558 - 21 mat

sanity n α / T i el (β^i 1 n sum - n β / T i el ln i 1 n sum + α T i el (β^(T i el ln * i 1 n sum * - 21 mat : 0.000000 0.000000 21 mat

Weibull  log likelyprobability PDF x β W 1 β 1 el β 2 el * x β 2 el 1 - (^β 1 el x β 2 el^* - exp * (* - eval :

β 1.6286 0.1024 21 mat :

x f x β W :

i 1 T rows range Y i el T i el β W eval : for XY T Y augment : data XY o 4 black plot : 31 line

xy u 16002 range : i 1 u rows range y i el u i el f : for u y augment 31 line :

data xy 2 1 sys

Y X x Clear 1

multisolve a system ...

t1 1 : t2 1.5 : 21 sys

x c 11 - x ≤ cases :

Two parametersreaction curve t R 1 t - t1 / exp - (1 t - t2 / exp - (* :

inflexion @ Deriv(2) = 0roots range [0.5 .. 1] x f x R x 2 diff :

X x f x solve : 0.838906

Y X R : 0.243

t S X R X diff t X - (* X R + :

L X X S 1 - X + (1 S - X S + (/ * - : 0.233

Ω x f Y - x 0.5 0.75 solve : 0.5339059053653

<content> Max/Min Golden ratio </content>

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / iter 21 mat 71 line :

1. All modules/functions
in "Symbolic" optimiz.
2. Once in target:
shrink the range
3. respect the search
y1≥y2≡"max in range"
y1≤y2≡"min in range"

x f x R x 2 diff :

y1 y2 ≤ (min in range ≡

U f 1.5 2 y1 y2 ≤ 1012 -^Extrema 1 el : 1.673

min U f : 0.162 -

Plot arguments ... plot x R x c * x R x 2 diff x c * x S X Y + 200 black 15 mat L 0.4 black 15 mat X 0.4 black 15 mat Ω Y . 4 black 15 mat U min + 50 black 15 mat 81 sys :

plot

plot/solve roots on canvas

Mach parameters x qc p / ≡ (supersonic Pitot ratio ≡ x c 1 k x ≤ (x 10 ≤ (& cases : 31 line

γ 1.4 : (Air isentropic ≡ k 0.88128485 : (Pitot constant ≡ p static pressure ≡ qc dynamic pressure ≡ x Pitot dynamic ratio qc/P ≡ 51 line

Mach number ... autosolve on canvas U Clear Clear 'U' from previous use ≡ x Subsonic 2 γ 1 - / (x 1 + (γ 1 - γ /^1 - (* sqrt 0 x ≤ (x k ≤ (& 0 ∞ ≉ cases : x Supersonic U x 1 + (117 U 2^* / - (2.5^* sqrt / k - 0 ≡ U 1 roots k x ≤ 0 ∞ ≉ cases : 31 line

t0 1 time :

show/hide plot arguments x Subsonic x Supersonic x c * k 1 + 20 black 15 mat 31 sys

1 time t0 - 0

plot x Subsonic x Supersonic x c * k 1 + 40 black 15 mat 31 sys :

plot

0 ∞ ≉

trick ▲ to enable X_Y
remove the initial plot
blue return carriage ...
re-plot dot, re-plot solid

plot/solve solve scalar on canvas ...

α β γ t F α β t * - γ t * / ln :

x Clear 1

ε 1012 -^:

α 1 :

β 1 :

γ 1 :

Implicit solve/plot x sol α β γ tt F x - 0 ≡ tt 1 - 1 solve :

α β γ ε F α β γ 1 ε - F 21 mat 27.631021 27.631021 - 21 mat

x Φ α β γ x F 11 line :

x Φ 0 2 1 sys x sol 0 1 0 0 2 2 mat 2 1 sys

x t Clear 1

x f x 2 π * / 2 π * x / tanh * sqrt :

Undocumented root solutions . . .

productive scalar canvas ... slow

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w sol t f w - 0 ≡ t root : w 2 sqrt * π sqrt * - t 2 π * t / tanh * sqrt + 2 sqrt π sqrt * / 0 ≡ t root

λ 20 :

w t argument w 2 sqrt * π sqrt * - t 2 π * t / tanh * sqrt + 2 sqrt π sqrt * / : w t Sol w t argument 0 ≡ t λ - λ solve : x c 10 x ≤ (x λ ≤ (& cases : 31 line

x Nsol2 x t Sol 2 el x c * 11 line :

x Nsol1 x t Sol 1 el x c * 11 line :

0.1785 Nsol1 0.2002 -

x f x Nsol1 x Nsol2 0 0.1785 4 0.1785 4 - 2 2 mat 4 1 sys

x Nsol1 x Nsol2 0 0.1785 4 0.1785 4 - 22 mat 41 sys

x y w Clear 1

Lambert W(x) principal branch x W w w exp * x - 0 ≡ w 1 e / - roots :

Maple LambertW two branches ... x W0 w w exp * x - 0 ≡ w 1 e / - roots : x W1 w w exp * x - 0 ≡ w 2 sqrt - roots : 21 sys

Gumbel PDF μ σ x Gp 1 σ / x μ - x μ - (- σ / exp σ * + (- σ / exp * :

y m σ x Gp - x solve maple m y σ * - LambertW - ln σ * -

μ 1 : σ 0.625 : 12 mat

U 0.375 :

solve Gumbel for two X's Ω μ σ x Gp U ≡ x 02 solve : 0.4873 1.7042 21 mat

Y μ σ 1.125 Gp : 0.578

X μ Y σ * - W - ln σ * - : 1.125

μ σ Ω Gp vectorize 0.375 0.375 21 mat

plot μ x σ * - W0 - ln σ * - μ x σ * - W1 - ln σ * - 21 sys :

plot 1 2 1 sys μ σ x Gp

ζ 0.375 :

μ ζ σ * - W0 - ln σ * - μ ζ σ * - W1 - ln σ * - 21 sys 1.70421695602622 0.487336202878851 21 sys

accurate Scientific

μ σ x Gp ζ - x 04 solve 0.487336 1.704217 21 mat

approxiimate Engineering

Fréchet otherwise ... RootOf

x α β w Clear 1

α β x Fr α β / β x / (α 1 +^* β x / (α^- exp * :

α β x Fr w - x solve maple w β * - α β_Z / (1 α +^* β_Z / (α^- exp * + RootOf

x λ 10 x ≤ (x 5 ≤ (& cases :

w 0.5 :

w a β x sol α β x / (1 α +^* β x / (α^- exp * w β * - :

α 5 : β 1 : 12 mat

X α β x Fr w - 0 ≡ x 05 solve : 0.7597 1.427 21 mat

plot α β x Fr x λ * w X 1 el w + 20 black 15 mat X 2 el w + 20 black 15 mat 41 sys :

plot w 2 1 sys

α β x Fr 1 - x 0 2.5 solve 0.8094 1.2335 21 mat

Fréchet inverse-scanner ...

Design a discrete function inverser  in the L, H span , N points f L H N Inverse ω 0 : dx H L - N / : i 1 N range ω i el L dx - (dx i * + : for j 1 ω rows range vy j el x f ω j el - 0 ≡ x 0.001 12 solve : for ω vy augment 61 line :

data UnestV v data 1 el : j 2 data rows range v v data j el stack : for v 31 line :

x f α β x Fr :

@ 0, Fréchet avoid divide by zero

data f 0.0125 1.874 200 Inverse : U data 2 col : 21 sys

i 1 data rows range N i el data 1 col i el U i el 1 el U i el 2 el augment : for

Triplet N UnestV : blue Triplet 1 col Triplet 2 col augment : red Triplet 1 col Triplet 3 col augment : 31 sys

plot blue red 0.5 - 0.9646 2.25 0.9646 22 mat 31 sys :

plot

Triplet Triplet rows row 1.8647 0.9468 0.9824 13 mat

0.9468 0.9824 + 2 / 0.9646

Solving 'divide by zero' ...

x Vf v f 12 x * g * v 2^/ - exp - sqrt atanh v 2^* g Vf * / :

g 9.8066 :

Vf 10 : v 0.625 : 12 mat

x 01 0.001 range :

zero cnt 1 : j 1 x rows range x j el Vf v f IsDefined 1 ≡ z cnt el x cnt el Vf v f : cnt cnt 1 + : 21 line continue if break try for 21 line z 21 line :

x x 1 zero rows range el :

zero rows 724

data x zero augment :

XY data data rows row : 0.723 0.0745 12 mat

data XY 1 1 el XY 1 2 el + 20 red 1 5 mat 2 1 sys data

Seeded ▼ scanner . . . algo style

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x y z Clear 1

<content> Dual solver algo style ... xd(L,H,N) </content>

U # # f Solve i 1 U rows range data 1 i el U i el y f y solve eval : for v data 1 el : j 2 data cols range v v data j el augment : for v transpose 41 line :

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 :

symmetric decimals 1.78568578 14.24552935 21 sys

t0 1 time :

slightly inner limits L 1.78568578 : H 14.24552935 : N 200 : 13 mat U L H N xd : 21 sys

1.78568577383018 14.2455293828432 21 sys

Optimiz Numeric ... solving the Electron function a 816 π * sqrt * : x y Φ 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - 0.005 + : sols U x y Φ Solve : 31 sys

collect/export both branches branch1 U sols 1 col augment : branch2 U sols 2 col augment : 21 sys

L < u < H ... escape end-points u π :

branch2 branch1 0 3 1 sys

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

pair wise u pairwise 3.141593 1.464026 - 1.464025 21 mat 12 mat

1 time t0 - 4.6 s *

x λ 1 L x ≤ (x H ≤ (& cases :

x spline1 U sols 2 col x cinterp :

x spline2 U sols 1 col x cinterp :

<content> Golden ratio min/max </content>

Code adapted from Valery Ochov Mathcad 11 f a b test TOL Extrema a b G 32 / b * 12 / a * - 12 / 5 sqrt * a b - (* + : y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ x1 a b G eval : y1 x1 f eval : x2 b a G eval : y2 x2 f eval : 41 line iter 0 : iter 1000 < a b - abs TOL ≤ break test b x2 : x2 x1 : y2 y1 : x1 a b G eval : y1 x1 f eval : 51 line a x1 : x1 x2 : y1 y2 : x2 b a G eval : y2 x2 f eval : 51 line if iter iter 1 + : 21 line if while a b + 2 / 71 line :

a b + 2 / iter 21 mat

x spline1 x λ * x spline2 x λ * 0 3 1 sys

y1 y2 ≥ (max in range ≡ y1 y2 ≤ (min in range ≡ 21 sys

ε 1015 -^:

x f x spline1 11 line :

X f 912 y1 y2 ≥ ε Extrema :

X X f 12 mat 9.9916 4.1749 12 mat

8 f 3.8717

x ∫ ω spline1 ω L x int :

x spline1 x L H int 37.2152

H ∫ 37.2152

ω 12 :

track 0 ω ∫ ω ω ∫ ω 032 mat :

ω ω ∫ 12 mat 12 31.1691 12 mat

x ∫ x λ * track 2 1 sys

1 time t0 - min 0.4

<content> Utilities </content>

Generate the symmetric square [U,V] matrix x y f U V Sym r 1 : i 1 U rows range c 1 : j 1 V rows range M r c el U i el V j el f eval : c c 1 + : 21 line for r r 1 + : 31 line for M 31 line :

Mesh U, V  within the bounds L, H L H N xd U 0 : dx H L - N / : i 1 N range U i el L dx i * dx - (+ : for U 41 line :

algo style function: elements wise function over data data algo Vectorise i 1 data rows range j 1 data cols range Fnct i j el data i j el algo eval : for for Fnct 21 line :

M lo hi Scale hi lo - (M M Min - M Max M Min - / (* lo + :

U 15 - 1596 xd :

V U :

x y axes x y / - : a 816 π * sqrt * : level 0.005 : 12 mat x y f 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - level + : 31 line

M x y f U V Sym :

M M 0255 Scale :

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 M

isolate M M :

x mapR 03221 mat 25525521 mat x linterp Floor 0 x ≤ (x 32 ≤ (& 326421 mat 25525521 mat x linterp Floor 32 x ≤ (x 64 ≤ (& 649621 mat 255021 mat x linterp Floor 64 x ≤ (x 96 ≤ (& 9612821 mat 0021 mat x linterp Floor 96 x ≤ (x 128 ≤ (& 12816021 mat 07521 mat x linterp Floor 128 x ≤ (x 160 ≤ (& 16019221 mat 75021 mat x linterp Floor 160 x ≤ (x 192 ≤ (& 19222421 mat 06421 mat x linterp Floor 192 x ≤ (x 224 ≤ (& 22425621 mat 64021 mat x linterp Floor 224 x ≤ (x 256 ≤ (& 0 cases :

x mapG 03221 mat 012821 mat x linterp Floor 0 x ≤ (x 32 ≤ (& 326421 mat 12825521 mat x linterp Floor 32 x ≤ (x 64 ≤ (& 649621 mat 25525521 mat x linterp Floor 64 x ≤ (x 96 ≤ (& 9612821 mat 25520021 mat x linterp Floor 96 x ≤ (x 128 ≤ (& 12816021 mat 2007521 mat x linterp Floor 128 x ≤ (x 160 ≤ (& 16019221 mat 75021 mat x linterp Floor 160 x ≤ (x 192 ≤ (& 19222421 mat 0021 mat x linterp Floor 192 x ≤ (x 224 ≤ (& 22425621 mat 0021 mat x linterp Floor 224 x ≤ (x 256 ≤ (& 0 cases :

x mapB 03221 mat 0021 mat x linterp Floor 0 x ≤ (x 32 ≤ (& 326421 mat 0021 mat x linterp Floor 32 x ≤ (x 64 ≤ (& 649621 mat 0021 mat x linterp Floor 64 x ≤ (x 96 ≤ (& 9612821 mat 06421 mat x linterp Floor 96 x ≤ (x 128 ≤ (& 12816021 mat 6425521 mat x linterp Floor 128 x ≤ (x 160 ≤ (& 16019221 mat 25512821 mat x linterp Floor 160 x ≤ (x 192 ≤ (& 19222421 mat 12812821 mat x linterp Floor 192 x ≤ (x 224 ≤ (& 22425621 mat 128021 mat x linterp Floor 224 x ≤ (x 256 ≤ (& 0 cases :

x algo x mapR : red M algo Vectorise : r red 0255 Scale : r r 0 round vectorize : 41 sys

x algo x mapG : green M algo Vectorise : g green 0255 Scale : g g 0 round vectorize : 41 sys

x algo x mapB : blue M algo Vectorise : b blue 0255 Scale : b b 0 round vectorize : 41 sys

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 r b g 1 3 mat

1 time t0 - min 2.3

u Ω Clear 1

AlgLib Solver for a system of nonlinear equations(Uni) result k 1 x f rows range u k el x k el : for x Jac u f u Jacobian : StepMax 0 : Eps 1014 -^: u X0 StepMax Eps x f x Jac al_nleqsolve : 51 line :

a 816 π * sqrt * : 351.67021

level 0.005 :

U 1.78568577383019 14.2455293828432 21 mat :

x f 1 - 3 / x 1 el (2^x 2 el (2^+ sqrt * exp 2 x 2 el (2^* - x 1 el (2^+ a / * - level + 021 mat :

x y axes x y / - :

range in the ± inner direction of Xrange in the ± inner direction of Y X0 7 - π 21 mat :

result 6.88155957067091 - 3.48860598293442 21 mat

result f 31017 -^* - 021 mat

pairs result 1 el result 2 el result 1 el 022 mat :

x y Ω 1 - 3 / x 2^y 2^+ sqrt * exp 2 y 2^* - x 2^+ a / * - level + :

pairs 6.8816 - 3.4886 6.8816 - 022 mat

X result 1 el num2str : Y result 2 el num2str : 21 sys -688155957067091/100000000000000 174430299146721/50000000000000 21 sys

plot Ω pairs axes pairs 1 el up + pairs 2 el up + 3.488 pairs 3 el dn - pairs 4 el dn - -6.881 23 mat 41 sys :

up 0.5 : dn 0.5 : 12 mat

plot U 1 el 0 . 7 black U 2 el 0 . 7 black 2 5 mat 2 1 sys

You can
1. shift up /dn . . . ▲ ▼
2. space RHS ►
3. can NOT fetche numerical

plot U 1 el 0.7 black U 2 el 0.7 black 25 mat 21 sys

Solving for the roots

X0 1.8 021 mat :

result 1.78568577383019 021 mat

X0 14021 mat :

result 14.2455293828432 021 mat

1.78568577383019 14.2455293828432 21 mat

Discrete differential roots at(3)

x f x 3^:

uu vv axes uu vv / - :

x q x :

at3 1 - 1100 f q algo :

lo hi N f q algo u lo hi lo hi lo - N / + (range : j 1 u length range ρ j el at3 u j el f x - x roots u j el q x - x roots at : for u ρ augment 31 line :

Nat3 at3 eval :

x q x f Nat3 axes 4 1 sys

x q x f Nat3 axes 41 sys

# # # at

dummy

# # at

scalar differetial x a b f Ω b 1 x sin 2^- sqrt * a 1 x cos 2^- sqrt * at :

command line a 1 : b 1 : 12 mat

x a b f π 1 π 1 - 2 2 mat axes 3 1 sys

a b Clear 1

a b f x y * y a : x b : 21 sys at :

0.5 0.5 f 0.25

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

solve at(2) , , , NO real roots
... from too big 'N'

lo 0.499 - : hi 0.499 : N 40 : 13 mat

find low limit ζ lo hi lo hi lo - N / + (range :

C j 1 ζ length range at j el Ω ζ j el y f y solve 2 el at : 11 line for at 21 line :

part ζ C augment :

part part - axes 3 1 sys

C x y N Clear 1

More profitable "roots" at(2) . . . circle solve

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uu vv axes uu vv / - :

r 0.25 - : x y f x 2^y 2^+ r + : u# lo hi lo hi lo - N / + (range : 31 sys

lo 0 : hi 0.5 : N 99 : 13 mat

u# rows 100

C j 1 u# length range rho j el ρ u# j el y f y roots at : 11 line for rho 21 line :

C C eval :

u# C augment u# C - augment u# - C augment u# - C - augment axes 5 1 sys

u# C augment u# C - augment u# - C augment u# - C - augment axes 51 sys

C rows 100

Otherwise profitable Discrete-Difference "roots" at(3) . . .

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r 0.125 - :

x y u data Clear 1

x y Γ x 2^y 2^+ r + :

r sqrt abs 0.3536

x y Ω 1 x 4^(* 2 x 2^* y * + 3 x * y 2^* - 1 y 3^(* + :

Ω Γ 0.3536 0.0525 - 1 2 mat 0.3536 0.25 0.3536 0.5 - 2 2 mat 4 1 sys

Intersection limit

lo 0.35 : hi 0.36 : N 1000 : 13 mat

find low limit u lo hi lo hi lo - N / + (range :

last value "on error" ... NO real root. data j 1 u length range rho j el System u j el y Ω y roots u j el y Γ y roots at : break try for rho 21 line :

data data rows row 0.0525 11 mat

data rows 356

data rows 356 ≡

data data rows row 0.0525 ≡

k a r Clear 1

DE Verhulst [Logistic]

a k t f 1 y a y - (* / y int k t int ≡ y solve maple :

a k t f a k t * a * exp * 1 - k t * a * exp + /

a k t f a k t * a * exp * 1 k t * a * exp + / :

a k y0 t f1 1 u a u - (* / u y0 y int k u 0 t int ≡ y solve maple :

a k y0 t f1 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + /

a k y0 t f1 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + / :

k y0 to t f2 1 u 1 u - (* / u y0 y int k u to t int ≡ y solve maple :

k y0 to t f2 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + /

yo r t to - (* exp * 1 yo - yo r t to - (* exp * + / 111 yo / 1 - (r t to - (* - exp * + / ≡

NOT from Smath

a k y0 to t f3 1 u a u - (* / u y0 y int k u to t int ≡ y solve maple :

a k y0 to t f3 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + /

r to yo t Logistic 111 yo / 1 - (r t to - (* - exp * + / :

yo yo - 1 + (r t to - (* - exp * + yo /

a k y0 t f1 y0 a * k t * a * exp * a y0 1 - k t * a * exp + (* + / :

r 1 : yo 0.5 : to 0 : ε 1.5 : 14 mat

a k t f a k t * a * exp * 1 k t * a * exp + / :

r to yo x Logistic r to ε - yo x Logistic r to ε + yo x Logistic to yo . 7 blue 1 5 mat 4 1 sys 1.25 0.5 x f 1.25 0.75 x f 1.25 1 x f 3 1 sys 1.25 0.5 0.025 x f1 1.25 0.75 0.025 x f1 1.25 1 0.025 x f1 3 1 sys

k y0 to t f2 y0 k t to - (* exp * 1 y0 1 - k t to - (* exp + (* + / :

a k y0 to t f3 y0 a * k a * t to - (* exp * a y0 1 - k a * t to - (* exp + (* + / :

a 1.5 : k 1 : y0 0.5 : to 0 : λ .875 : ζ 0.25 : 16 mat

k y0 to λ x * ζ + f2 a k y0 to x f3 0 2 0 0 2 2 mat 3 1 sys

k y0 to λ x * ζ + f2 a k y0 to x f3 020022 mat 31 sys

ζ

k y0 to λ x * ζ + f2 a k y0 to x f3 - x 0 roots 0.2007

shifted differential system dual command-line

a b α β Clear 1

x Γ b a at

command-line

shift 0.5 :

x Γ b a at a Γ b Γ -

f a x sin * :

q b x shift + sin * :

α 0.5 :

β 2 :

rx α x sin * β x shift + sin * - x 1 - 0 solve : 0.6524 -

r b x shift + sin * x 2 roots : 2.6416

plot f a 0.5 ≡ at q b 2 ≡ at axes rx 1 rx 1.5 - 22 mat r 0.5 black 15 mat 51 sys :

command-line

<content> hatch, scale </content>

You need that one for scaling grayscale image M lo hi Scale hi lo - (M M Min - M Max M Min - 106 -^+ / (* lo + :

Erzeugt eine Matrix für die Darstellung vertikaler Linien zwischen den Funktionen f(x) und g(x) im Bereich von x1 bis x2 mit 2*n Linien. Generates a matrix for 2*N vertical lines (hatching) between functions f(x) and g(x) in x-range from x1 to x2 f g x.1 x.2 N hatch dx x.2 x.1 - N / (: h x.1 x.1 f x.1 x.1 g 22 mat : x x.1 x.2 dx - x.1 dx + range h h x dx 2 / + x dx 2 / + g x dx 2 / + x dx 2 / + f x dx + x dx + f x dx + x dx + g 42 mat stack : for h 41 line :

plot

x λ1 f a 1.25 ≡ at 11 line : 5 x sin * 4 /

x λ2 q b 4 ≡ at 11 line : 412 x * + 2 / sin *

x f x λ2 :

x g x λ1 :

Hatch f g 0.65 - 2.49 7 hatch :

x λ1 x λ2 Hatch axes 4 1 sys

x λ1 x 0.65 - 2.49 int 1.99

x λ2 x 0.65 - 2.49 int 7.91

1 time t0 - min 3.8

Lambert(W) for Smath ...

w u v Clear 1

Maple style LambertW two branches ... x W0 w w exp * x - 0 ≡ w 1 e / - roots : x W1 w w exp * x - 0 ≡ w 2 sqrt - roots : x W w w exp * x - 0 ≡ w 1 e / - roots : 31 sys

u v axes u v / - :

cmmand line solution X 0.25 - :

e W 1.000000000000000

X W0 X W1 21 mat 0.357403 - 2.153292 - 21 mat

plot x W0 x W1 1 e / - 11 e / - 5 - 22 mat X 1 X 3 - 22 mat 0.5 - 1 - 01 - 22 mat axes 71 sys :

plot

more algebraic u 2^e u^- 0 ≡ a b v * + c 10 v -^* ≡ a b v * + c e v -^* ≡ 3 x^x 2^≡ α α exp * 1 e / - ≡ a x^b x * + c + 0 ≡ 2 t^5 t * - 0 ≡ x t^z - 0 ≡ z z b log * a - 0 ≡ 91 sys

y 1 υ e υ^* + ≡ υ solve maple y υ υ e υ^* + υ υ e υ^* - / ≡ υ solve maple y 1 υ e υ^* + 1 υ e υ^* - / ≡ υ solve maple 31 mat 1 - y + LambertW 1 - y + 1 y + / ln 1 - y + 1 y + / LambertW 31 mat

υ 2^e υ^- 0 ≡ υ solve maple 212 / - LambertW * - 212 / LambertW * - 21 mat

a b v * + c e v -^* ≡ v solve maple c a b / exp * b / LambertW b * - a + b / -

a b v * + c 10 v -^* ≡ v solve maple 10 ln c * 10 ln a * b / exp * b / LambertW b * - 10 ln a * + b 10 ln * / -

a xx^b xx * + c + 0 ≡ xx solve maple a ln a ln c * b / - exp * b / LambertW b * a ln c * + b a ln * / -

3 xx^xx 2^≡ xx solve maple 23 ln 2 / - LambertW * 3 ln / - 23 ln 2 / LambertW * 3 ln / - 21 mat

a Clear 1

a a exp * 1 e / - ≡ a solve maple 1 -

2 tt^5 tt * - 0 ≡ tt solve maple 2 ln 5 / - LambertW 2 ln / - 1 - 2 ln 5 / - LambertW 2 ln / - 21 mat

xx tt^z - 0 ≡ tt solve maple z ln xx ln /

xx tt^z - 0 ≡ xx solve maple z ln tt / exp

xx tt^z - 0 ≡ z solve maple xx tt^

z z log * a - 0 ≡ z solve maple a a LambertW /

MCD 11 a 10 ln a 10 ln * W / *

a 0.25 :

b 5 :

a a W / a b ln a b ln * W / * 21 mat 1.226161251 1.34785908 21 mat

L H N xd U 0 : dx H L - N 1 - / : 12 mat i 1 N range U i el L dx - (dx i * + eval : for U 31 line :

Example: solving a DE

L 0 : H 10 : N 200 : 13 mat vu L H N xd : 21 line

t C t diff Vm t C * - Km t C + / ≡

C0 1 :

Vm 2 :

Km 3 :

solution borrowed from Mathematica "ProductLog" DE i 1 N range p i el vu i el Vm Km / * (- C0 C0 Km / exp * ln Km / + exp eval : d i el Km p i el W0 * : 21 line for d 21 line :

DEsol vu DE augment :

Title 1.5 1.5 DE solution in Pharmacology 12 red 15 mat :

DEsol Title 2 1 sys

a b c x K T Clear 1

T ln b K ln - (c / + (T ln b K ln - c / (+ exp * x ≡ T solve maple b K ln - c x LambertW * - c / - exp

T ln b K ln - (c / + (T ln b K ln - c / (+ exp * x ≡ K solve maple b T ln c * + c x LambertW * - exp

u 0 x ≤ : b 0.75 : c 1 : K 15 : T 10 : 14 mat x equilibrium_T b K ln - c x W * - c / - exp : x equilibrium_K b T ln c * + c x W * - exp : 41 sys

x equilibrium_T x equilibrium_K 0.946 12.2474 + 40 black 1 5 mat 3 1 sys

◄ does NOT solve
over solve dependent

NO solver wrt Lambert jnct 0.94596452 :

jnct equilibrium_T jnct equilibrium_K - 0.0000000

jnct equilibrium_T 12.24745

0 equilibrium_T 0 equilibrium_K 21 mat 7.0855 21.17 21 mat

1 time t0 - min 3.9

a b c d H Clear 1

Diophantine chemical balance

f 2 a * 2 c * ≡ 4 a * c e + ≡ 6 a * 2 b * + 4 c * d + 4 e * + ≡ 2 b * 2 d * 2 e * + ≡ 41 mat :

seed a 1 ≡ b 1 ≡ c 1 ≡ d 1 ≡ 41 mat :

expeiment/observe ε 1015 -^:

external seed e 3 :

a b c d 41 mat f seed ε FindRoot : 1.000000000000000 7.000000000000000 1.000000000000000 4.000000000000000 41 mat

a b c d e 51 mat 1714351 mat

2 a * 2 c * - 4 a * c e + (- 6 a * 2 b * + 4 c * d + 4 e * + (- 2 b * 2 d * 2 e * + (- 41 mat 0.000000000000000 0.000000000000000 0.000000000000000 0.000000000000000 41 mat

e Clear 1

e 2.7183

Difficult chemical ... doctored Radovan

Coefficients pertaining to the "Equilibrium solution" k1 10 6.3 -^: (1rst dissociation constant carbonic acid ≡ k2 10 10.3 -^: (2nd dissociation constant carbonic acid ≡ kw 1014 -^: kh 10 1.5 -^: PCO2 10 3.5 -^: 13 mat 31 line

balance H OH * kw ≡ CO2 kh PCO2 * ≡ H HCO3 * k1 CO2 * ≡ H CO3 * k2 HCO3 * ≡ H HCO3 2 CO3 * + OH + ≡ 51 mat :

ionisation of water: equilibrium expression Henry's law CO2: equilibrium gas/liquid equilibrium expression for bicarbonate HCO3 equilibrium expression for carbonate CO3 charge balance 51 mat

balance H OH * 1100000000000000 / ≡ CO2 1100000 / ≡ H HCO3 * CO2 1010 nthroot (63^/ ≡ H CO3 * HCO3 1010 nthroot (103^/ ≡ H HCO3 OH + 2 CO3 * + ≡ 51 mat :

H CO2 OH HCO3 CO3 51 mat balance H CO2 OH HCO3 CO3 51 mat roots (: 2.241 106 -^* 1105 -^* 4.4623 109 -^* 2.2364 106 -^* 5.0017 1011 -^* 51 mat

sanity H OH * kw - CO2 kh PCO2 * - H HCO3 * k1 CO2 * - H CO3 * k2 HCO3 * - H HCO3 2 CO3 * + OH + (- 51 mat : 61022 -^* 011021 -^* 71022 -^* 11015 -^* - 51 mat

H 2.241 106 -^*

alkalinity H log10 - 5.65

Export/enable ▼ this section

x y f 3 x 2^* 4 y * - 7 - :

x y f n isolve maple Pile vide.

x y f n isolve maple y 1 - 6 n * 1 - 2 n * + (* + = x 14 n * - = y 56 n * 3 - 2 n * + (* + = x 34 n * - = 21 mat ≡

n 2 - :

yxyx n Sol 1 - 6 n * 1 - 2 n * + (* + 14 n * - 56 n * 3 - 2 n * + (* + 34 n * - 41 mat :

Diophantine Segments XY n Sol 2 el n Sol 4 el 21 mat n Sol 1 el n Sol 3 el 21 mat augment :

Diophantine solutions wrt 'n' n Sol 2 el n Sol 4 el 21 mat n Sol 1 el n Sol 3 el 21 mat f 36324321 mat

n Sol 599891141 mat

XY 959118922 mat

x Interp XY 1 col XY 2 col x cinterp :

x XY 11 el 1 + : 10

x Interp 74

xy x x Interp augment : 107412 mat

plot f XY xy 31 sys :

XY 959118922 mat

xy 107412 mat

p vx 15 - 15 14.8 - range : ii 1 vx rows range vy ii el 0.75 vx ii el 2^* eval : for vx vy augment 31 line :

As you paste in new WS,
this freak survives

plot p 0 0 + 1000 red 1 5 mat 3 1 sys

XY 1 row xy XY 2 row 31 mat 95912 mat 107412 mat 118912 mat 31 mat

x y Clear 1

Trace0 transparent ≡

Trace1 solid red 5 ≡

Trace2 symbol dot 6 black ≡

Trace3 l blue ≡

Implicit solve matrix

x y z f 5 x * 6 y z + (* - 8 - 3 x y - (* 2 z * + 6 + x y + z + 2 - 31 mat :

sol x y z f x y z 31 mat roots : 1.818182 2.363636 2.181818 - 31 mat

x y z 31 mat sol 1 el sol 2 el sol 3 el 31 mat : 1.818 2.364 2.182 - 31 mat

sanity 13 decimals x y z f 0.0000000000000 0.0000000000000 0.0000000000000 31 mat

Solve an hypersurface isocurve
Export/Enable

x y Clear 1

c 1 :

t0 1 time :

f 2 c * y * 3 x 2^* y 2^* y 4^- c 2^x 2^y 2^+ (* - 4 c 4^* + (* x cos * y sinh * 2 c * y * x 4^3 y 2^* x 2^* - c 2^x 2^y 2^+ (* - 4 c 4^* - (* x sin * y cosh * x y * x 2^y 2^+ (y 2^x 2^- 2 c 2^* + (* (* 2 c * sin * 31 mat :

x y f f 1 el f 2 el + f 3 el + :

level_0 0 : level_1 1 : level_2 2 : 13 mat

y x f0 x y f level_0 + : y x f1 x y f level_1 + : y x f2 x y f level_2 + : 31 sys

r 1 : a 1 : b 1 : 13 mat y x circle a x * (2^b y * (2^+ r - : 21 sys

"FindRoot" needs the two algorithmsin explicit form. eq_1 x y f1 : eq_2 a x * (2^b y * (2^+ r - : 21 sys

The system is set for f1(x,y)
initialised accordingly.

roots accuracy ε 1012 -^:

guess wisely ... init 0.25 - 1 - 21 mat 1 - 0.5 - 21 mat 0.25 121 mat 1 0.5 21 mat 14 mat :

roots j 123414 mat : ct 1 : j j sol j el eq_1 eq_2 21 mat init 1 j el ε FindRoot : ct ct 1 + : 21 line for all sol 1 el transpose sol 2 el transpose sol 3 el transpose sol 4 el transpose stack : 41 line :

roots roots eval : 0.1832 - 0.9831 - 0.8628 - 0.5056 - 0.1832 0.9831 0.8628 0.5056 42 mat

roots circle f0 f1 f2 5 1 sys

You are at liberty to select
oblate/prolate ellipse ...
Check initials !

roots circle f0 f1 f2 51 sys

1 time t0 - min 0.1

<content> sol(f,L,H,N,level) </content>

f L H N level sol Roots range typical ± 100 X 0 : dx H L - N / : 12 mat i 1 N range X i el L dx - (dx i * + : for j 1 X rows range Sol j el y X j el f level - y roots eval : j j 1 + : 21 line for X Sol augment 51 line :

Explore an hypersurface

The governing hypersurface parameter 1 ≤ 'c' c 1 :

f 2 c * y * 3 x 2^* y 2^* y 4^- c 2^x 2^y 2^+ (* - 4 c 4^* + (* x cos * y sinh * 2 c * y * x 4^3 y 2^* x 2^* - c 2^x 2^y 2^+ (* - 4 c 4^* - (* x sin * y cosh * x y * x 2^y 2^+ (y 2^x 2^- 2 c 2^* + (* (* 2 c * sin * 31 mat :

level 0.125 :

x y f f 1 el f 2 el + f 3 el + :

Iso_1 f 1.5 - 1.5 199 level sol :

r 1 : a 1 : b 1 : 13 mat y x circle a x * (2^b y * (2^+ r - : 21 sys

Iso_2 f 1.5 - 1.5 199 level sol :

Iso_3 f 1.5 - 1.5 199 level sol :

iso Iso_1 Iso_1 1 row 1 - (* stack :

Iso_1 circle 2 1 sys iso 1 x 2 ^ - sqrt ± 2 1 sys

Suite ▼ Next

Solve EDU 30405 HYPERSURFACE.sm
from there, Smath crashes

jmG: 20231221