<p> Construct demo circle </p>

d0891160-489c-483d-8fe6-761b1abf2330 29 4 5 decimal

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

Polar Notation

x y xy2pol z x i y * + : z abs z arg 12 mat 21 line :

x 1 : y 1 : 12 mat

U 00 x y 0032 mat :

Y x 0 x y x 032 mat :

r ∠ 12 mat x y xy2pol (: 1.4142 0.7854 12 mat

U Y 2 1 sys

metric r m * ∠'rad * 21 mat : 1.4142 m * 0.7854'rad * 21 mat

∠ ° 45

xy2pol("1:argument", "2:argument") Converts the rectangular coordinates of a point in 2D space to polar coordinates.

Universal version  [Smath 6179]. It supports "data" sets from 
source ... data sets subject to be decimated from auxilliary
module Decimate(data,n)... reasonably fast on primitive PC. 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 :

--------
radius circle
-------- Y0 02031 mat :

setup system t0 0 : t1 2 π * : N 11 : 31 sys

<p> Construct demo circle </p>

Rename: Y => .. else variable name t u D u 2 el u 3 el 1 u 1 el (2^- (* u 2 el * (u 1 el - 031 mat :

'Rkadapt' the most accurate s Y0 t0 t1 N t u D Rkadapt :

X s 2 col : Y s 3 col : XY X Y augment : 31 line

polar XY . 10 black plot :

polar XY 2 1 sys

j 9 :

X j el 1.9796 -

Clockwise Angles wrt origin [0 0]

V Unest v V 1 el : j 2 V rows range v v V j el stack : for v 31 line :

cplx j 1 XY rows 1 - (range cplx j el X j el i Y j el * + : for cplx 21 line :

x y j xy2pol z cplx j el : z abs z arg ° / 12 mat 21 line :

j 1 cplx rows range : N x y j xy2pol vectorize : Ω N Unest : 31 sys

polar XY 2 1 sys

cplx 2 i * 1.081 1.683 i * + 1.819 0.831 i * + 1.98 0.285 i * - 1.511 1.31 i * - 0.563 1.919 i * - 0.563 - 1.919 i * - 1.511 - 1.31 i * - 1.98 - 0.285 i * - 1.819 - 0.831 i * + 1.081 - 1.683 i * + 111 mat

N 29012 mat 2 57.273 12 mat 2 24.545 12 mat 2 8.182 - 12 mat 2 40.909 - 12 mat 2 73.636 - 12 mat 2 106.364 - 12 mat 2 139.091 - 12 mat 2 171.818 - 12 mat 2 155.455 12 mat 2 122.727 12 mat 111 mat

Ω 2902 57.273 2 24.545 2 8.182 - 2 40.909 - 2 73.636 - 2 106.364 - 2 139.091 - 2 171.818 - 2 155.455 2 122.727 112 mat

Trigonometric style ... 15 D accuracy

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 :

x N Ω Clear 1

r 1.25 :

x circle r 2^x 2^- sqrt ± :

n 11 :

roots x n^1 - 0 ≡ x solve maple r * :

P roots Re roots Im augment :

rootsP P . 14 black plot :

x circle rootsP r 0 + 100 green 1 5 mat 3 1 sys

P 1.25 0 1.0516 0.6758 0.5193 1.137 0.1779 - 1.2373 0.8186 - 0.9447 1.1994 - 0.3522 1.1994 - 0.3522 - 0.8186 - 0.9447 - 0.1779 - 1.2373 - 0.5193 1.137 - 1.0516 0.6758 - 112 mat

roots 1.25 1.0516 0.6758 i * + 0.5193 1.137 i * + 0.1779 - 1.2373 i * + 0.8186 - 0.9447 i * + 1.1994 - 0.3522 i * + 1.1994 - 0.3522 i * - 0.8186 - 0.9447 i * - 0.1779 - 1.2373 i * - 0.5193 1.137 i * - 1.0516 0.6758 i * - 111 mat

n 11

x y j xy2pol z roots j el : z abs z arg ° / 12 mat 21 line :

◄ optional 90 z arg ° / -

j 1 roots rows range : N x y j xy2pol vectorize : Ω N Unest : 31 sys

90 32.727 - 57.273

29012 mat 2 57.273 12 mat 2 24.545 12 mat 2 8.182 - 12 mat 2 40.909 - 12 mat 2 73.636 - 12 mat 2 106.364 - 12 mat 2 139.091 - 12 mat 2 171.818 - 12 mat 2 155.455 12 mat 2 122.727 12 mat 111 mat

N 1.25 012 mat 1.25 32.727 12 mat 1.25 65.455 12 mat 1.25 98.182 12 mat 1.25 130.909 12 mat 1.25 163.636 12 mat 1.25 163.636 - 12 mat 1.25 130.909 - 12 mat 1.25 98.182 - 12 mat 1.25 65.455 - 12 mat 1.25 32.727 - 12 mat 111 mat

Ω 1.25 0 1.25 32.7272727272728 1.25 65.4545454545455 1.25 98.1818181818182 1.25 130.909090909091 1.25 163.636363636364 1.25 163.636363636364 - 1.25 130.909090909091 - 1.25 98.1818181818182 - 1.25 65.4545454545455 - 1.25 32.7272727272728 - 112 mat