<p> plotG(vx,vy,a,b,c) </p>

93fe4dd6-9f50-4be2-ae12-66f08d668bf4 26 6 9 decimal

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

vx vy a b c plotG a char ≡ b size ≡ c color ≡ 13 mat n vx length : plot vx 1 el vy 1 el a b c augment : i 2 n range plot plot vx i el vy i el a b c augment stack : for plot 51 line :

Tr φ 36 Tr / 42 Tr ln * + 35 - Tr 6^- : Tr Ψ 0.0364 Tr φ * Tr log10 - : Tc Pc α T Pvap 10 Pc log10 0.1183 T Tc / φ * - 7 T Tc / log10 * + α 7 - (T Tc / Ψ * -^: 31 line

t0 1 time :

Tc 433.8 556.4 553562 619.6 51 mat :

Pc 31.6 4540 48.6 3851 mat 101.33 * :

α 6.771 6.742 6.844 6.848 7.330 51 mat :

z 0.35 0.1 0.1 0.1 0.35 51 mat :

P 101.33 : T 350 : 12 mat T P Tc Pc α U Tc Pc α T Pvap P / : 21 line

optional k n el 1 - (z n el * k n el 1 - (Φ * 1 + / (n 1 z length sum 11 line :

i 1 Tc length range k i el T P Tc i el Pc i el α i el U : for

Φ f k n el 1 - (z n el * k n el 1 - (Φ * 1 + / (n 1 z length sum :

x Low 2 - : δ 1.1636 : 21 line

0 f 1 f 21 mat 1.708323 1.864072 - 21 mat

δ f 7445.470396

0 x ≤ x 1.5 ≤ & x f rejected if δ 200 δ 200 - 2 2 mat x Low 3 1 sys

Given f(x) => solve for 'x'

This document is Smath 5346. Other Smath build may need the "line local" in f(Φ). This solver is "recursive" wrt the variate Φ=>[x] on the range ω of 38 visible values in "Sol". Observe: N = 35 produces the visible 0.1 increments in "Sol" on the range 1.7 .. -1.8 N+3 in ω extends the range 1.7 .. -2

f L H N Inverse dx H L - N / : i 1 N 3 + range ω i el L dx - (dx i * + : for j 1 ω rows range sol j el x f ω j el - 0 ≡ x 0 1.05 solve eval : for ω sol augment 41 line :

'x' range is 0..1, thus range the upper limit of the solver > 1 ... kind of "solve contract".

An "InverseFnct" is a solving function ... it consists in solving for 'x' that gives f(x). For some given value on the plot f(x), we look for 'x' that gives f(x). The proposed "inverser" solves "recursively" for the 38 values given by ω[j]. It is not seeded, it restarts each 'solve cycle' from 0. On a long range 'x', it may fail. A seeded inverser would start each next cycle from the solution of the previous one. The "Sanity" proves the robustness of Smath in this example.

Sol f 1.7 1.8 - 35 Inverse :

Sol 1.7 0.001 1.6 0.009 1.5 0.019 1.4 0.03 1.3 0.042 1.2 0.055 1.1 0.07 1 0.088 0.9 0.107 0.8 0.13 0.7 0.155 0.6 0.185 0.5 0.22 0.4 0.261 0.3 0.307 0.2 0.36 0.1 0.419 0 0.482 0.1 - 0.545 0.2 - 0.606 0.3 - 0.662 0.4 - 0.711 0.5 - 0.754 0.6 - 0.792 0.7 - 0.824 0.8 - 0.851 0.9 - 0.875 1 - 0.895 1.1 - 0.914 1.2 - 0.929 1.3 - 0.944 1.4 - 0.956 1.5 - 0.967 1.6 - 0.978 1.7 - 0.987 1.8 - 0.995 1.9 - 1.003 2 - 1.01 382 mat

1 time t0 - 6.4 sec *

Working range of f(Φ)

0 x ≤ ( x 1 ≤ ( & x f rejected if 1.1636 2 1.1636 2 - 2 2 mat 2 1 sys

vx Sol 1 col : vy Sol 2 col : sol vx vy . 9 black plotG : 31 line

Global solution => think modelling

sol 2 - 2 2 - 0.5 - 2 2 mat 1.7 0.5 1.7 0.5 - 2 2 mat 3 1 sys

Sanity of "Sol" wrt support points Φ f 1.7 ≡ Φ 0 0.1 solve Φ f 1 ≡ Φ 0 0.1 solve Φ f 0 ≡ Φ 0.4 0.6 solve Φ f 1 - ≡ Φ 0.8 1 solve Φ f 2 - ≡ Φ 0.95 1.05 solve 51 mat 0.001 0.088 0.482 0.895 1.01 51 mat

User on-line "solve/collect" Φo OnLine 1.8 - Φo ≤ 1.7 ≤ Φ Φ f Φo ≡ Φ 0 1.1636 solve eval : i 1 z length range x i el z i el k i el 1 - (Φ * 1 + / : y i el k i el x i el * : 21 line for header Φo Φsol x.....y 13 mat : header Φo Φ x y augment 13 mat stack 51 line :

Φo 1.25 - :

Φo OnLine Φo Φsol x.....y 1.25 - 0.9367 0.0544 0.37 0.0996 0.1 0.1115 0.0992 0.1099 0.0993 1.7955 0.2524 52 mat 23 mat

In mathematics, Horner's method (also known as Horner scheme in the UK or Horner's rule in the U.S.[1][2]) is either of two things: an algorithm for calculating polynomials, which consists of transforming the monomial form into a computationally efficient form;[2] or a method for approximating the roots of a polynomial.[3] The latter is also known as Ruffini–Horner's method.[4] These methods are named after the British mathematician William George Horner, although they were known before him by Paolo Ruffini[5] and, six hundred years earlier, by the Chinese mathematician Qin Jiushao.[6]

maple parfrac z 2 el 1 - k 2 el + (* 1 x 1 - k 1 el + (* + (* z 1 el 1 - k 1 el + (* 1 x 1 - k 2 el + (* + (* + 1 x 1 - k 1 el + (* + (1 x 1 - k 2 el + (* + (* / ≡