cd80d740-0476-4d30-8bbe-8662250b7f51 9 6 9 decimal

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

arcinv(invx):=solve(inv(x)=invx;x;0;π/2), [Peter,Smath Forum]

x F x tan x - :

x sol xx F x - 0 ≡ xx 1 roots :

x Sol xx F x - 0 ≡ xx 1 - roots :

roots solve for quick plot

x F x sol x Sol 1.16556115 1.16556115 o 10 black 1 5 mat π 2 / 2 π 2 / 0 2 2 mat 5 1 sys

1012 -^sol 0.000144

u 1.16556115 :

u F u sol - 0

u F 1.165561

x q xx F x ≡ xx 0 π 2 / solve :

# # ≠

x Q xx F x ≡ xx π 2 / - 0 solve :

1012 -^q 0.000000048632964

x q x Q 2 1 sys

Granularity is suspected from 'solve', being by nature less accurate than 'roots' ≠ algorithms

x sol x q -

Implicit solve

x f x 2^4 - 2 x * 4 x 2^* - 21 mat :

x f 1 el x f 2 el - x 1 - 2 solve implicit of ≡ x f 1 el x f 2 el - ≡ 0 ≡

x f 1 el x f 2 el x f 1 el x f 2 el - 3 1 sys

r x f 1 el x f 2 el - x 1 - 1.25 solve : 0.716515138721672 - 1.11651513876761 21 mat

Alternately, more accurate roots

R x f 1 el x f 2 el - x 1 - roots x f 1 el x f 2 el - x 1 roots 21 mat :

R 0.716515138991168 - 1.11651513899117 21 mat

solve ... low accuracy

roots ... high accuracy

r 1 el f 1 el r 1 el f 2 el - 2.5 109 -^* -

R 1 el f 1 el R 1 el f 2 el - 0

r 2 el f 1 el r 2 el f 2 el - 2109 -^* -

R 2 el f 1 el R 2 el f 2 el - 1.7 1014 -^*

1. solve => lacks accuracy 2. worst: result depends upon the bracketing

x f x 3^2 x * (2^- 5 + :

a 3 :

b 4 :

x f 0 ≡ x 1.25 - 3.75 solve 1 - 1.38196601125124 3.61803398696977 31 mat

r 1 - 1.3819660112501 3.61803398874989 31 mat :

x Lagrange x r 1 el - (x r 2 el - (* x r 3 el - (* :

x Lagrange 2 1 sys

'c' in ascending order of x^n

c 504 - 141 mat :

c polyroots 1 - 1.3819660112501 3.61803398874989 31 mat