plotG(vx,vy,a,b,c)

1900ea6c-a8b0-4821-9915-7fe39a4535dc 11 4 5 decimal

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

1 D Matrix

A a c g 13 mat :

A matrix type maple true

A array type maple true

A table type maple true

A indexed type maple false

A eval maple a c g 13 mat

A indices maple [1 1] [1 2] [1 3] 31 mat

A transpose set convert maple Error, improper op or subscript selector

A set convert maple Error, improper op or subscript selector

This is what this convert command looks like in the Maple Tools Log:

So the maple_convert function has turned the array which we can make in Smath Studio, into a set, which is very hard to do in Smath because {} cannot be accessed easily. Please note, if we check the type, maple_type confirms we have a set present.

A set convert set type maple true

A transpose a c g 31 mat

A transpose list convert maple Error, (in convert/list) can't convert array of dimension > 1 ans

We are meant to be able to get a 1D array to be able to be converted intoa list, but at the moment this does not work.

2 D Matrix

B 1234562345678933 mat :

B matrix type maple true

B array type maple true

B table type maple true

B indexed type maple false

B eval maple 1234562345678933 mat

B indices maple [1 2] [1 3] [2 1] [2 2] [2 3] [3 1] [3 2] [3 3] [1 1] 91 mat

B set convert maple Error, improper op or subscript selector

This is what this convert command looks like in the maple tools log:

[INFO ] [->] convert(smath_mat(123456,2,3,4,5,6,7,8,9,3,3),set)

{2, 3, 4, 5, 6, 7, 8, 9, 123456}

B set convert set type maple true

convert 2D array into a list of lists. B listlist convert maple Pile vide.

convert evaluated 2D array into a list of lists. B eval listlist convert maple Pile vide.

But this is what Maple Tools log records:

1234562345678933 smath_mat eval listlist convert

1234562345678933 smath_mat listlist convert

[[123456, 2, 3], [4, 5, 6], [7, 8, 9]]

So we do get three lists of lists as expected by the Maple V learning guide page 48.

We can create a 1 member array, and this will work with maple_convert to list function

9 list convert maple [9]

j 3 list convert maple : [3]

j #

If we hover the mouse over j, we can see [3], but Smath will not let us see it.

In the log file, we see: \[REGION[b7a5f680a05148b1a9284802c981d20f]]\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

and next line: [3]

Test j to see if it contains a list. j list type maple true

We can create a 1 member array using standard Smath way, and this will work with maple_convert to list function

D 711 mat :

711 smath_mat list convert

j D list convert maple : Error, (in convert/list) can't convert array of dimension > 1 ans

this time j contains nothing.

Test j to see if it contains a list. j list type maple false

Create lists and sets as strings and try to get Maple to recognize them as lists and sets.

create list within a string P [1,2,3,4] : [1,2,3,4]

Q [2,4] :

P [1,2,3,4]

maple thinks a string is not a set, which is correct. p set type maple false

Now use maple_parse function

P parse maple Pile vide.

[1,2,3,4] parse

[1, 2, 3, 4]

Maple thinks a string that holds a list is a list. Success...

P parse list type maple true

So now we can use our maple 'list' as if it is a maple list!

P parse array convert maple 123441 mat

P parse array convert set convert maple Error, improper op or subscript selector

[1,2,3,4] parse array convert set convert

{1, 2, 3, 4}

We have created a list within a string, then converted it to a set via maple commands!

set1 set2 member maple set1 set2 member

1 P parse array convert set convert member maple true

Does not appear to work... set1 set2 intersect maple set1 set2 intersect

P parse array convert set convert Q parse array convert set convert intersect maple 123424 intersect

maple does not seem to activate intersect command: 'intersect({1, 2, 3, 4}, {2, 4})

set1 set2 union maple set1 set2 union

P parse array convert set convert Q parse array convert set convert union maple 123424 union

maple does not seem to activate union command: \[REGION[e1bc72ab84de4699990aef622dcb884c]]\123424union

R {a,b,c,f} :

maple does not recognize curly brackets even with string to set trick R parse maple a b c f 41 mat

R {a,b,c,f} {ε,d,g,h} {p,k,m,n} 31 mat :

j 3 :

Parse R j el parse maple : p k m n 41 mat

Parse i 1 R rows range parse i el R i el parse maple : for parse 21 line :

Parse transpose a b c f 14 mat ε d g h 14 mat p k m n 14 mat 13 mat

R does not look like a maple set according to Maple Tools log: \[REGION[15e8b397af524163b6a962d475b019cc]]\(a,b,c,f)parse

[INFO ] [<-] mat(a,b,c,f,4,1)

Conclusion We can create lists via strings, then convert them to sets if we need sets. Note there are quite a few maple functions that work with lists and sets.

A t 000 t 000 t 33 mat :

A exponential maple t exp 000 t exp 000 t exp 33 mat

A eigenvalues maple t t t 31 mat

B 13 - 10 - 211622 mat :

B t exponential maple 15 t exp * 142 t * exp * - 102 t * exp * - 10 t exp * + 212 t * exp * 21 t exp * - 14 t exp * - 152 t * exp * + 22 mat

B dn_LinAlgEigenvalues 1221 mat

Smath
f(x) menu B dn_LinAlgEigenvectors 0.5812 - 0.5547 0.8137 0.8321 - 22 mat

p x 4^9 x 3^* + 2 x 2^* + 17 x * + 5 + :

q z 3^19 z * - 30 - :

p x companion maple 0005 - 10017 - 0102 - 0019 - 44 mat

q z companion maple 0030101901033 mat

A bit unclear interesting

A 21 - 321401 - 261 - 534 mat :

A rref maple 100 5.667 010 1.667 - 001 3.667 - 34 mat

PROGRAM: 2: Read DATA : YEAR / MONTH / DATE  in String Format 
and VALS in Number Format.. VECTORIZE FUNCTION IS USED data Process_Str_Data data eval a data 1 col : (String column ≡ b data 2 col : (Numerical column ≡ x nn F2 x / strsplit nn el str2num vectorize : a 3 F2 a 1 F2 a 2 F2 b augment 51 line :

Courtesy NDTMA

This vectorize function splits strings at "/" and converts entire matrix to numbers

a 1/3/1960 / strsplit : 13196031 mat

Example

a 1 el 1

a 2 el 3

a 3 el 1960

a 3 el str2num 1960

Data Str_data 1/1/1960 7.9 1/2/1960 34.5 1/3/1960 23.3 1/4/1960 1.5 1/5/1960 0 1/6/1960 0.1 1/7/1960 3.3 1/8/1960 10.1 1/9/1960 5.1 1/10/1960 21.8 1/11/1960 14.9 1/12/1960 6.6 122 mat :

Using PROGRAM 2 Str_data Process_Str_Data 196011 7.9 196012 34.5 196013 23.3 196014 1.5 1960150196016 0.1 196017 3.3 196018 10.1 196019 5.1 1960110 21.8 1960111 14.9 1960112 6.6 124 mat

plotG(vx,vy,a,b,c)

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 :

Fibonnacci incremental algorithm λ Fib set Exponential threshold data n 1 + el MCD ORIGIN 0 ≡ 21 sys n 1 λ range Fib n 1 + el 15 sqrt + 2 / (n^15 sqrt - 2 / (n^- (5 sqrt 5 / * : idx n 1 + el n : 21 line for idx Fib 0 round vectorize augment 31 line :

Vect(sizechar,n)... Vect(colorchar,n) size n Vect n 1 ≡ size ct 1 : j 1 n range a ct 1 el size : ct ct 1 + : 21 line for v a 1 el : k 2 a rows range v v a k el stack : for v 51 line if :

15 sqrt + 2 / (n^15 sqrt - 2 / (n^- (5 sqrt 5 / * 15 sqrt + (n^15 sqrt - (n^- 5 sqrt 2 n^* / ≡

13 Fib transpose 01234567891011121301123581321345589144233214 mat

λ 10 :

λ Fib transpose 012345678910011235813213455211 mat

Fibonnacci infinitesimal sequence
OPTIMIZ  ... Numeric vx λ Fib 1 col : vy λ Fib 2 col : 12 mat x f vx vy x cinterp : x c 11 x ≤ (x λ 1 + ≤ (& cases : data vx vy . 14 black plotG : 41 sys

nodes λ Fib 1 col : NodesLabel nodes var2str vectorize : X vx : Y vy : 12 mat n X rows : Graph nodes Y augment : 51 line

plot symbol converted2Numbers

symbol color

nodes_label X Y NodesLabel 10 n Vect red n Vect augment :

you can sequence nodes otherwise nodes transpose 012345678910111 mat

x f x c * data 1 25 1 25 - 2 2 mat nodes_label 4 1 sys

Graph 001121324355687138219341055112 mat

plot arguments x f x c * data 125125 - 22 mat nodes_label 41 sys

Create new companion vector

plotG(vx,vy,a,b,c)

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 :

Fibonnacci incremental algorithm I λ Fib set Exponential threshold data n 1 + el MCD ORIGIN 0 ≡ cont 0 : 31 sys n I λ range cont cont 1 + : Fib cont el 15 sqrt + 2 / (n^15 sqrt - 2 / (n^- (5 sqrt 5 / * : idx cont el n : 31 line for idx Fib 0 round vectorize augment 31 line :

V(sizechar,n)... V(colorchar,n) var n V n 1 ≡ var ct 1 : j 1 n range b ct 1 el var : ct ct 1 + : 21 line for U b 1 el : k 2 b rows range U U b k el stack : for U 51 line if :

3035 Fib transpose 303132333435 8.3204 105^* 1.346269 106^* 2.178309 106^* 3.524578 106^* 5.702887 106^* 9.227465 106^* 26 mat

range Fibonnacci ... Carlos [012520] I 30 : λ 35 : 12 mat

I λ Fib transpose 303132333435 8.3204 105^* 1.346269 106^* 2.178309 106^* 3.524578 106^* 5.702887 106^* 9.227465 106^* 26 mat

Fibonnacci infinitesimal sequence
OPTIMIZ  ... Numeric vx I λ Fib 1 col : vy I λ Fib 2 col : 12 mat x f vx vy x cinterp : x c 1 I x ≤ (x λ 1 + ≤ (& cases : data vx vy . 14 black plotG : 41 sys

nodes I λ Fib 1 col : NodesLabel nodes var2str vectorize : X vx : Y vy : 12 mat n X rows : Graph nodes Y augment : 51 line

plot symbol converted2Numbers

symbol color

Nodes_label X Y NodesLabel 10 n V red n V augment :

nodes transpose 30313233343516 mat

Typical "Unary cost" of 'λ' polluants ...

x f x c * data 30 832040 + 100 green 1 5 mat Nodes_label 4 1 sys

Graph 30 8.32 105^* 31 1.35 106^* 32 2.18 106^* 33 3.52 106^* 34 5.7 106^* 35 9.23 106^* 62 mat

Pad a Matrix

x y φ x y * :

Ω 812 φ matrix maple :

Ω 12345678910111224681012141618202224369121518212427303336481216202428323640444851015202530354045505560612182430364248546066727142128354249566370778481624324048566472808896812 mat

M nc nr Pad A M : insert 'nc' cols in 'A' i 1 A rows range j 1 nc range vert i j el 0 : for for a A 1 A rows 1 A cols 2 / Floor submatrix : b A 1 A rows A cols 2 / Floor 1 + A cols submatrix : S a vert b augment transpose : insert 'nr' rows in the transpose 'S' i 1 S rows range j 1 nr range horiz i j el 0 : for for a S 1 S rows 1 S cols 2 / Floor submatrix : b S 1 S rows S cols 2 / Floor 1 + S cols submatrix : S a horiz b augment transpose : 111 line :

Numeric

P Ω 33 Pad :

P 123456000789101112246810120001416182022243691215180002124273033364812162024000283236404448000000000000000000000000000000000000000000000510152025300003540455055606121824303600042485460667271421283542000495663707784816243240480005664728088961115 mat

del row/col f(x)"vminor"

B 28 - 3 - 56 - 3315 - 4426861 - 8893 - 5 - 6 - 873 - 8097 - 8607 - 41 - 266 mat :

confusing ...same symbol

vminor f(x) menu # # # vminor

Minor palette 
or f(x) minor # # # minor

f(x) ... vminor B 23 vminor 28 - 56 - 3681 - 8893 - 6 - 873 - 897 - 86041 - 255 mat

V 134791215601733 mat :

Cofactor matrix N V 33 minor : 12 -

Cofactor matrix
Determinant of vminor N V 23 minor : 15

13156022 mat det 15

137922 mat det 12 -

vminor
f(x) menu V 23 vminor 13156022 mat

Smath rref solving conventional invertible matrix M rref U M 1 M rows range 1 M rows range el : V M M cols col : sol U 1 -^V * : out U rows identity sol augment : 41 line :

uu 1545423945518725426262571955 mat :

vv 8749851 mat :

uu 1 -^vv * 1.9787 1.3394 0.0266 0.1054 0.3273 - 51 mat

'U' is invertible

M 154548239457518725442626925719856 mat :

M rref 10000 1.9787 01000 1.3394 00100 0.0266 00010 0.1054 00001 0.3273 - 56 mat

M rref maple 10000 1.9787 01000 1.3394 00100 0.0266 00010 0.1054 00001 0.3273 - 56 mat

N M 14 range 15 range el :

N rref 1000 1.7897 0100 2.3452 - 0010 0.4643 - 0001 3.1587 45 mat

The Risteski-Korobov solver

solving a singular matrix . . .

chemical mass balance

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The Reaction Matrix A 7000001 - 0018240010 - 6 - 001824008 - 6 - 01 - 011100 3.99 - 0001100001 - 00202300 2.97 - 0000012 - 00000011424 - 01 - 00000710 - 002 - 99 mat :

PseudoInverse  Mass balance
Courtesy: Viktor Korobov {Mathcad 11] x r A rank : I A rows identity : a 1 el A tr - : B 1 el A a 1 el I * + : n 2 r range B n el A B n 1 - el * A B n 1 - el * tr - n / I * + : a n el A B n 1 - el * tr - n / : n n 1 + : 31 line for Ω A B r 1 - el (2^* a r el (2^/ : i 1 A rows range u i el 1 : for I Ω A * - (u * 81 line :

Difficult to find C 209279 x * :

Mass balance

fractional . . . components . . . integer

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Fractional
mass balance x 0.189 2.431 1.378 1.476 1.167 0.583 1.325 3.809 1.167 91 mat

Yb C N Cs Ru F H Pt O 91 mat

Integer 
mass balance C 3960050873528846530882824418612209327720079720024418691 mat