4c3bf459-858a-4d30-8b5d-fed68e64d65f 18 6 9 decimal

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

∞ # ± # #^# (# abs # sqrt # # nthroot 17 mat

complex 1 i + : i imaginary by default ≡

complex abs 1.414214

# # # # # # # # # 33 mat # det # transpose # # # alg # # # minor # # † 16 mat

# # ≡ # # < # # > # # ≤ # # ≥ # ¬ # ≠ # ¬ # # & # # | # # ¤ 110 mat

# # # # sum # sum # # # # product # # diff # # n diff # # int # # # # int z ∫ z integrand z int : # # # # 41 sys 19 mat

# # range # # # range # # # for # # # # for # # # if # # while # # # 31 line break continue 19 mat

24 matrix 0000000024 mat

# # # # # # coma to add backspace to delete 18 mat

Cntrl+M # # # # # # # # # 33 mat ≡ customise rows/cols ≡

# # # coma to add backspace to delete 51 line

i # # range # for

i # # # range # for

x # # # range : i 1 x rows range # for # 31 line

The "for loop counter inclusive"

3D plot M 5003 matrix : k 1 : k M rows ≤ k k 1 + : M k 1 el k cos 1 * eval : M k 2 el 2 k * sin 0.5 * eval : 21 line for 21 line

2D plot [points ,line] m 5002 matrix : k 1 : k m rows ≤ k k 1 + : m k 1 el k cos 1 * eval : m k 2 el 2 k * sin 0.5 * eval : 21 line for 21 line

The centered XY system x y XY x y / - :

m XY 2 1 sys M 0 m 2 1 sys M

As it looks, the 'x' 3D default plot is not pure angle ... not nice.

The Lissajous Project

vx vy char size color plotG n vx length : plot vx 1 el vy 1 el char size color augment : i 2 n range plot plot vx i el vy i el char size color augment stack : for plot 41 line :

t 0 : move points by some π factor ≡

Lissajous, discrete plot L typical Classroom demo x 02 π * 0.01 range : i 1 x rows range cos i el x i el cos eval : sin i el 2 x i el * sin 0.5 * eval : 21 line for cos sin augment 41 line :

Equipolar points on Lissajous Lpts x 02 π * 2 π 12 / * t + (range : i 1 x rows range cos i el x i el cos eval : sin i el 2 x i el * sin 0.5 * eval : 21 line for cos sin augment 31 line :

vx Lpts 1 col : vy Lpts 2 col : V vx vy . 10 black plotG : 31 line

a 1 :

x y L 22 x 2^* a 2^- (2^* a 2 y * a - (2^* y a + (* - :

0 L V 3 1 sys L

p 512 : q 3 : 21 line

2D plot [points ,line] N p 2 matrix : k 1 : k N rows ≤ k k q + : N k 1 el k cos 1 * eval : N k 2 el 2 k * sin 0.5 * eval : 21 line for 21 line

0 N 2 1 sys

The centered XY system x y XY x y / - :

m XY L 3 1 sys

data select ListCollect collects index list ct 1 : i select a ct el data i 1 el : b ct el data i 2 el : ct ct 1 + : 31 line for a b augment 41 line :

XW 0.175 317.303 0.3325 217.0355 0.525 130.1479 0.7 61.3415 0.875 32.4856 1.05 47.5163 1.225 90.6788 1.4 143.2053 1.575 173.5314 1.75 155.6779 1.925 105.1301 2.1 56.8338 2.275 34.1471 2.45 51.1141 2.625 114.8755 2.8 214.0454 2.975 306.0658 3.15 341.7215 3.325 304.952 3.5 214.1093 3.675 111.3089 3.85 42.8756 4.025 15.8375 4.2 7.5659 242 mat :

coma to add point
backspace to delete
shuffle at will select 12357916 mat :

data XW select ListCollect :

p 399 : q 8 : q-> 1,2,3.. ≡ 21 line

data 0.175 317.303 0.3325 217.0355 0.525 130.1479 0.875 32.4856 1.225 90.6788 1.575 173.5314 62 mat

2D plot [points ,line] m p 2 matrix : k 1 : k m rows ≤ k k q + : m k 1 el k 2 π * / cos 1 * eval : m k 2 el k 2 π * / sin 1 * eval : 21 line for 21 line

0 m 2 1 sys

Deca sequence: p:=399, q:=8 p:= 1 => line circle.