e857f0ae-8189-4ebe-a4e7-827c000702ed 38 4 5 decimal

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

The famous 'mtp" construct algo

t0 1 time :

Reproduces Mathcad "mtp" in Smath code

1. mtp "unirange"

f L H N mtp i 1 N range x i el L i 1 - N / H L - (* + : y i el x i el f : 21 line for x y 21 mat 21 line :

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

x f x sqrt x 1 + ln x cos 1 x 0.001 + / 14 mat :

L 0 : H 3 π * : N 100 : 13 mat

Explode the project X f L H N mtp 1 el : Ys f L H N mtp 2 el sys2mat : Y Ys UnestRow : 31 line

1. add/insert fnct: place holder on the fuct => coma to add a fill-in place holder. 2. remove fnct: place holder on that fnct, delete [done] 3. To blank a trace: "" in "collect".

Collect the projet for plotting collect X Y 1 col augment X Y 2 col augment X Y 3 col augment X Y 4 col augment 41 sys :

collect

1 time t0 - 5.6 s *

x π - π π - 0.01 + (range :

V x x mwsin augment :

x x Clear :

x 1

2. mtp "Asymmetric range"

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

t0 1 time :

x F 0.1 1 x 2^+ / :

x q 0.125 x sin * :

x S 0.05 x sqrt * :

Note the transit variate x <= u

Plot_1 5 - 5 4.95 - u F inc :

Plot_2 π - π π - 0.05 + (u q inc :

Plot_3 05 0.05 u S inc :

P Plot_1 Plot_2 Plot_3 31 sys :

1 time t0 - 0.8 s *

Plot range, collect global

Plot_1 rows Plot_2 rows Plot_3 rows 31 mat 20112610131 mat

3. mtp "any range, any 'N' "

x f x0 x1 xmesh Xmesh clear U from previous U 0 : count 1 : i 1 xmesh range x i el x0 i xmesh / x1 x0 - (* + : U count el x i el f : count count 1 + : 31 line for x U augment 51 line :

x F 11 x 2^+ / :

x q 0.01 x 3^(* :

Fncts u F 8 - 8200 Xmesh u q 5 - 5200 Xmesh 21 sys :

Fncts

Extract/Export

Fncts 1 el to extract ≡

Fncts 2 el to extract ≡

4. Smart QuickPlot range simple

x F 11 x 2^+ / :

t0 1 time :

U 5 - 5 4.99 - range :

U rows 1001

x fnct Quick i 1 U rows range vy i el U i el fnct : 11 line for U vy augment 21 line :

Scalar autorange on canevas

x F

Discrete plot external pilot 'U'

x F Quick 0 2 1 sys

2. 2D symmetric/asymmetric, any 'N'

t0 1 time :

Mostly used for image display. Smath does not plot matrix.

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

L 1 - : H 1 : N 40 : 13 mat

U L H N xd :

V U :

x y f 255 x 2^y 2^+ (- 0.25 / exp * :

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 :

Matrix vx vy f U V Sym :

Matrix rows 41

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1 time t0 - 5 s *

α 10 :

x y f α 10 x * sin * α 10 y * cos * + :

Matrix vx vy f U V Sym :

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x y f x cos y cos * :

α 1 :

x y f α 1 x * sin * α 1 y * cos * + :