<content> Utils </content>

00b99c6b-4da1-497e-a5f2-ede00b704479 60 Alvaro Diaz Falconi 4 5 false false 0 0 decimal

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

Unknowns

<content> Utils </content> <content> Options </content>

O# o# Options Ω# 01 matrix eval : n# 0 : 12 mat ω# o# sys2mat.1 num2str vectorize eval ω# ω# " strrep : n# n# 1 + : 12 mat g# ω# ≡ strsplit : length 1 > f# 1 O# rows range O# augment eval g# 1 el 2 findrows : (0 ≠ (O# f# 1 el 2 el g# 2 el : O# O# g# 1 el g# 2 el augment 11 O# cols range el stack eval : if Ω# Ω# g# 2 el stack eval : 21 line f# O# ω# 1 findrows : (0 ≠ (Ω# Ω# f# 2 el stack eval : Ω# Ω#'NaN stack eval : if if 21 line for Ω# length 1 > o# cols 1 ≡ Ω# Ω# transpose if Ω# 1 el if 31 line :

<content> Example Options </content>

dsol solver Rkadapt steps 100 stepsmax 0 eps 10^{-7} 42 mat :

dsol dummy Options'NaN

dsol solver Rkadapt steps 100 stepsmax 0 eps 10^{-7} 42 mat

dsol steps dummy eps 31 mat Options 100'NaN 10^{-7} 31 mat

dsol steps dummy eps 13 mat Options 100'NaN 10^{-7} 13 mat

dsol steps solver rkfixed ≡ eps 31 mat Options 100 rkfixed 10^{-7} 31 mat

dsol solver rkfixed steps 100 stepsmax 0 eps 10^{-7} 42 mat

dsol Jacobian J# ≡ Options J#

dsol solver rkfixed steps 100 stepsmax 0 eps 10^{-7} Jacobian J# 52 mat

Check inside a procedure

x f dsol dummy x ≡ Options dsol 21 line :

1 f solver rkfixed steps 100 stepsmax 0 eps 10^{-7} Jacobian J# dummy 162 mat

dsol solver rkfixed steps 100 stepsmax 0 eps 10^{-7} Jacobian J# 52 mat

ASCII characters strings. No N\0024\ N\0024\ : N 0123456789ABCDEF : 12 mat k 1 No (range c k : h \ : 12 mat c 0 ≠ m c 16 mod : h N m 1 + 1 substr h concat : c c m - 16 / : 31 line while N\0024\ N\0024\ \ 000015 h strlen - substr h concat concat : 31 line for N\0024\ 31 line :

N\0024\ 210^N\0024\ eval :

It could be 2^16

CSort(M,c) sorts the matrix M by the string elements in the column c. M# C# CSort\0024\ x# k# F# N\0024\ x# k# 1 substr findstr stack 1 el : a# b# C\0024\# A# a# strlen : B# b# strlen : 12 mat k# 1 A# B# 12 mat min range ans# a# k# F# b# k# F# - sign : (0 ≠ break if for ans# 0 ≡ A# B# - sign ans# if 31 line : n# M# rows : v# 1 n# range : r# v# : c# 1 M# cols range : 14 mat V# M# C# col : A# M# : 12 mat k# 2 : k# n# ≤ k# k# 1 + : j# k# : j# 1 > (V# v# j# 1 - el el V# v# j# el el C\0024\# 1 ≡ (& tmp v# j# el : v# j# el v# j# 1 - el : v# j# 1 - el tmp : j# j# 1 - : 14 mat while 21 line for A# r# c# el M# v# r# el c# el : 61 line :

M# CSort\0024\ M# 1 CSort\0024\ 11 line :

E# block2str S# num2str(X#) X# E# strrep str2num : k# 0 : M# 0 : 13 mat S# strlen 11 < (S# 14 substr sys(≠ (| M# S# 11 mat : t# S#, strsplit : n# t# t# rows 1 - el str2num : k# 1 n# range str num2str(el(X#,k#)) X# E# strrep : M# k# el str str2num : 21 line for M# 41 line if 21 line :

<content> Unknowns </content>

Unknowns in the expression X Xo# Unk s# Xo# num2str : Try with the string of the expression. error try s# s# # ﻼ strrep {(strrep}) strrep : s# s# (F#(strrep ((Π#(strrep),U#)) strrep : s# s# ¬ - strrep - +'NEG#* strrep : k# + * /^& | > ≤ ≥ ≡ ≠ ≈ ≉ ¤ 114 mat s# s# k# < strrep : for k#! 11 mat s# s# k# <Πo#(X#) strrep : for S# s# Π#(< Π#(strrep str2num : SO# 0 : 12 mat SO# num2str S# num2str ≠ S# SO# S# : a# b# < a# b# U# Π# equrep : while s# S# num2str : S# s# < strrep str2num : 12 mat X# U# Π# X# num2str Πo#(findstr 1 - ≡ X# IsDefined num2str 1 ≠ U# U# rows 1 + el X# : if if X# Πo# 21 line : Π1# Π#(X#, : Π2# line(Πo#(Π#(X#,U#), : 12 mat k# 11 s#, findstr stack rows + (range Π1# Π1# X# k# num2str, concat : Π2# Π2# Π#(X# k# num2str,U#), concat : dummy# Π1# U#): Π2# 1,1) concat str2num : 31 line for U# 01 matrix eval : NEG# 1 - : dummy# S# : n# 0 : UO# 0 : 15 mat U# rows 0 ≡ (Xo# IsDefined num2str 1 ≠ (& U# Xo# 11 mat : if u# U# uo# u# num2str : n# 0 ≡ (UO# uo# 1 findrows 0 ≡ (| (Unk Units Options 1 ≡ (uo# 11 substr' ≠ (| UO# n# n# 1 + : el uo# ﻼ # strrep : if if 21 line for n# 0 ≠ UO# UO# CSort\0024\ : UO# UO# str2num vectorize : 12 mat if UO# 171 line :

Unknowns in the expression "X" Xo# Unk\0024\ S# Xo# block2str : M# 0 : 12 mat k# 1 S# length range M# k# el S# k# el Unk : for M# Unk 31 line :

Unk Units 012 mat :

<content> Unknowns Examples </content>

Trivial expressions

3 - π i * + Unk 0

a 3 - π i * + + Unk a 11 mat

Non-Trivial expressions

A a x.2 * + cos 7 Blue * / α - g sin xo α * ~u 4 el h * / * x kg * f (2 -^b - 1 el b 2 el a atan ln * / + x y z cases 12 mat :

A Unknowns transpose ~u a b x x.2 xo y z α 19 mat

Unk Units Options 0

A Unk transpose a b x x.2 xo y z ~u α 19 mat

Unk Units 1 ≡ Options 1

A Unk transpose Blue a b x x.2 xo y z ~u α 110 mat

Undefined units are unknowns.

Unk Units 0 ≡ Options 0

Restore default

B a ~a b c d e f aa bb cc 31 sys h# i j g xx yy zz cases y u i h p 3 el q 4 el p e r 122 mat :

Several unknowns

B Unk transpose a aa b bb c cc d f g h h# j p q r u xx y yy zz ~a 121 mat

Notice that the variable ~a is sorted in different way

B Unknowns transpose ~a a aa b bb c cc d f g h h# j p q r u xx y yy zz 121 mat

Some examples requires assign Unk to a variable U, and others use it as an intermediate steps.
I have not an idea about why.

When num2str fails, it could be neccessary enclose the expression with a Solve Block

Calculus

u v abs f u diff Unk u v 21 mat

u e v^f u int Unk u v 21 mat

U f x a b int Unk : a b f x 41 mat

E X Y * (sum :

U E Unk transpose : X Y 12 mat

x κ α β sum

U E Unk\0024\ transpose : x α β κ 14 mat

Programming

E a b while x 21 line :

U E Unk transpose : x 11 mat

x b > x a + x - a + if

U E Unk\0024\ transpose : a b x 13 mat

Postfix

3 x! a + + Unk a x 21 mat

Factorial is the only one postfix operator that I know in SMath

Logic

x a e b^ltlt Unk transpose a b x 13 mat

a b | (¬ a c | (& Unk transpose a b c 13 mat

Plugins

E H T to P po Water CoolProp_Props :

U E Unk transpose : po to 12 mat

a 0 c 10 f rkfixed

U E Unk\0024\ transpose : a c f 13 mat

U E Unk\0024\ transpose : a b x 13 mat

a b x Dirac * +

Timing

E x a cos * y b sin * + :

M CSort\0024\ M :

Enabling this compare with Unk without sorting

N 100 :

to 0 time : iter 1 N range U E Unk : for 0 time to - 31 line 7.471 s *

to 0 time : iter 1 N range U E Unknowns : for 0 time to - 31 line 0.008 s *

Conslusions

Isn't very fast

Another expression to string function convertion is welcomed. Then all issues could be solved.

Alvaro

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