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Carl Love

Carl Love

24975 Reputation

25 Badges

10 years, 162 days
Himself
Wayland, Massachusetts, United States
Contact Carl Love
My name was formerly Carl Devore.

MaplePrimes Activity


These are replies submitted by Carl Love

Impressive...

Carl Love 24975
March 13 2023
0 0

@Rouben Rostamian  It's an impressive work, Rouben. I wish that I could give this Answer a 2nd Vote Up.

For x, or for all variables?...

Carl Love 24975
March 12 2023
0 0

Yes, it can be done. But before I tell you how, I'd like to know whether you want the prime to be used for all derivatives or only for those made with respect to a specific variable (of your choosing), such as x.

grid vs numpoints...

Carl Love 24975
March 12 2023
0 0

@vv I vote up. However, I'd change numpoints= n to grid= [i, j] in plot3d commands purely for pedagogical reasons. 

Unwanted, unneeded warning!...

Carl Love 24975
March 11 2023
0 0

[This Comment is unrelated to your undefined issue.] Egads, does this mean that the default is now to show that ugly e warning every time e is used as a variable, even in 1D input? Can't that crap be reserved for the newbies using 2D Input?

Moment of Inertia...

Carl Love 24975
March 11 2023
0 0

@C_R I don't know much about MapleSim---so I don't know if this is relevant---but wouldn't the different moments of inertia between tori and cylinders be significant? I'd guess (just from visual observation) that "standard" train wheels are fairly close to cylinders of uniform density steel. But, for example, I'd suspect that bicycle wheels could be closely modeled by tori.

SI...

Carl Love 24975
March 11 2023
0 0

I suspect that degrees are not an allowed option when you have "system" set to "SI".

Same issue as other Question...

Carl Love 24975
March 10 2023
0 0

@Olesen From your description, especially the black screen part, this is almost certainly the same issue as is discussed in the Question that Preben provided a link to. So, there has been a plague of this just in the last few days.

But just started for me...

Carl Love 24975
March 09 2023
0 0

@nm A weird thing is that this just started happening to me 2 days ago. And now it's happened 4 times. As you probably realize, I use Maple several hours per day, *every* day, for over 20 years.

And it's not only when the computer is coming back from "sleep"; it has happened while I was typing. 

Started yesterday for me...

Carl Love 24975
March 09 2023
0 0

This started happening yesterday for me (about 30 hours ago). I just had my 4th occurence a minute ago. My experience is exactly as you describe. I'm also using Windows 10. The behavior can also happen while on a help page.

Correction...

Carl Love 24975
March 09 2023
0 0

@dharr Yes, here's a few possible corrections:

evalindets(sol, suffixed({_||(Z||(1, 2), B2)}), ()-> n)

or

evalindets(sol, suffixed({_||(Z1, Z2 ,B2)}), ()-> n)

or

evalindets(sol, suffixed({_Z1, _Z2, _B2}), ()-> n)
 

Edited module to modulus...

Carl Love 24975
March 07 2023
0 0

I changed your word "module" to "modulus".

Worksheet with modifications...

Carl Love 24975
March 07 2023
0 0

@vs140580 Here is a worksheet with your requested modifications. I've included your 25 basic metrics and the 4 metrics based on edge weights.
 

29 Graph Metrics

Author: Carl Love <carl.j.love@gmail.com> 2023-Mar-07

> 

restart
:

All are intended for undirected graphs without self loops and work for both weighted and unweighted graphs.

> 

VS25:= proc(G::Graph)
local
   `C+`, `C*`, Csqrt, Cmax, A1, A2, A3, u, N, e:= 0,
    V:= op(4, G), C:= nops~(V), n:= numelems(C), CN, m:= add(C)/2, E:= rtable(1..m),
    Eput:= (_,v)-> (E[++e]:= (u,v))[1],
    Add:= f-> add(f(e), e= E),
    VSprod:= proc(P)
    local T:= table('sparse');
        for e in E do T[P(e)]++ od;
        (mul@op~@[indices])(T, 'pairs')
    end proc
;
    for u,N in V do CN(u):= add(C[[u, N[]]]); select[fold= (Eput, 0)](`<`, N, u) od;
    C:= (max(C)+1) -~ C;
    ((r-> `if`(r::integer[8], r, evalf(r)))~@table)([
        A__0||(1..3)=~ ((A1,A2,A3):= Add~([
            ((u,v)-> (`C+`(u,v):= C[u]+C[v])),
            ((u,v)-> (`C*`(u,v):= C[u]*C[v])),
            `C+`^2
        ])[]),
        A__0||(4..6)=~ Add~([
            `C*`^2, (`C+`-2)^(1/2)/(Csqrt:= `C*`^(1/2)), 2*Csqrt/`C+`
        ])[],
        A__0||(7..9)=~ (2*m*(n-1) - A1, 2*m^2 - A1/2 - A2, A3 - 2*A2),
        'A__10'= Add(m/(m-n+2)/Csqrt),
        A__||(11,12)=~ VSprod~([`C+`,`C*`])[],
        A__||(13..15)=~ Add~([`C+`/`C*`, `C*`/`C+`, `C+`*`C*`])[],
        (N__0||(1..9), N__10)=~ Add~([
            ((u,v)-> (`C+`(u,v):= CN(u)+CN(v))/2),
            ((u,v)-> (`C*`(u,v):= CN(u)*CN(v))/2),
            `C+`^2/4,
            ((u,v)-> 1/(Cmax(u,v):= max(CN(u), CN(v)))),
            `C*`/`C+`, 2/`C+`, 2/`C*`, 4/`C*`^2, Cmax, `C+`/`C*`
        ])[]
    ])
end proc
:

> 

G:= GraphTheory:-SpecialGraphs:-HypercubeGraph(7);

GRAPHLN(undirected, unweighted, ["0000000", "0000001", "0000010", "0000011", "0000100", "0000101", "0000110", "0000111", "0001000", "0001001", "0001010", "0001011", "0001100", "0001101", "0001110", "0001111", "0010000", "0010001", "0010010", "0010011", "0010100", "0010101", "0010110", "0010111", "0011000", "0011001", "0011010", "0011011", "0011100", "0011101", "0011110", "0011111", "0100000", "0100001", "0100010", "0100011", "0100100", "0100101", "0100110", "0100111", "0101000", "0101001", "0101010", "0101011", "0101100", "0101101", "0101110", "0101111", "0110000", "0110001", "0110010", "0110011", "0110100", "0110101", "0110110", "0110111", "0111000", "0111001", "0111010", "0111011", "0111100", "0111101", "0111110", "0111111", "1000000", "1000001", "1000010", "1000011", "1000100", "1000101", "1000110", "1000111", "1001000", "1001001", "1001010", "1001011", "1001100", "1001101", "1001110", "1001111", "1010000", "1010001", "1010010", "1010011", "1010100", "1010101", "1010110", "1010111", "1011000", "1011001", "1011010", "1011011", "1011100", "1011101", "1011110", "1011111", "1100000", "1100001", "1100010", "1100011", "1100100", "1100101", "1100110", "1100111", "1101000", "1101001", "1101010", "1101011", "1101100", "1101101", "1101110", "1101111", "1110000", "1110001", "1110010", "1110011", "1110100", "1110101", "1110110", "1110111", "1111000", "1111001", "1111010", "1111011", "1111100", "1111101", "1111110", "1111111"], Array(1..128, {(1) = {2, 3, 5, 9, 17, 33, 65}, (2) = {1, 4, 6, 10, 18, 34, 66}, (3) = {1, 4, 7, 11, 19, 35, 67}, (4) = {2, 3, 8, 12, 20, 36, 68}, (5) = {1, 6, 7, 13, 21, 37, 69}, (6) = {2, 5, 8, 14, 22, 38, 70}, (7) = {3, 5, 8, 15, 23, 39, 71}, (8) = {4, 6, 7, 16, 24, 40, 72}, (9) = {1, 10, 11, 13, 25, 41, 73}, (10) = {2, 9, 12, 14, 26, 42, 74}, (11) = {3, 9, 12, 15, 27, 43, 75}, (12) = {4, 10, 11, 16, 28, 44, 76}, (13) = {5, 9, 14, 15, 29, 45, 77}, (14) = {6, 10, 13, 16, 30, 46, 78}, (15) = {7, 11, 13, 16, 31, 47, 79}, (16) = {8, 12, 14, 15, 32, 48, 80}, (17) = {1, 18, 19, 21, 25, 49, 81}, (18) = {2, 17, 20, 22, 26, 50, 82}, (19) = {3, 17, 20, 23, 27, 51, 83}, (20) = {4, 18, 19, 24, 28, 52, 84}, (21) = {5, 17, 22, 23, 29, 53, 85}, (22) = {6, 18, 21, 24, 30, 54, 86}, (23) = {7, 19, 21, 24, 31, 55, 87}, (24) = {8, 20, 22, 23, 32, 56, 88}, (25) = {9, 17, 26, 27, 29, 57, 89}, (26) = {10, 18, 25, 28, 30, 58, 90}, (27) = {11, 19, 25, 28, 31, 59, 91}, (28) = {12, 20, 26, 27, 32, 60, 92}, (29) = {13, 21, 25, 30, 31, 61, 93}, (30) = {14, 22, 26, 29, 32, 62, 94}, (31) = {15, 23, 27, 29, 32, 63, 95}, (32) = {16, 24, 28, 30, 31, 64, 96}, (33) = {1, 34, 35, 37, 41, 49, 97}, (34) = {2, 33, 36, 38, 42, 50, 98}, (35) = {3, 33, 36, 39, 43, 51, 99}, (36) = {4, 34, 35, 40, 44, 52, 100}, (37) = {5, 33, 38, 39, 45, 53, 101}, (38) = {6, 34, 37, 40, 46, 54, 102}, (39) = {7, 35, 37, 40, 47, 55, 103}, (40) = {8, 36, 38, 39, 48, 56, 104}, (41) = {9, 33, 42, 43, 45, 57, 105}, (42) = {10, 34, 41, 44, 46, 58, 106}, (43) = {11, 35, 41, 44, 47, 59, 107}, (44) = {12, 36, 42, 43, 48, 60, 108}, (45) = {13, 37, 41, 46, 47, 61, 109}, (46) = {14, 38, 42, 45, 48, 62, 110}, (47) = {15, 39, 43, 45, 48, 63, 111}, (48) = {16, 40, 44, 46, 47, 64, 112}, (49) = {17, 33, 50, 51, 53, 57, 113}, (50) = {18, 34, 49, 52, 54, 58, 114}, (51) = {19, 35, 49, 52, 55, 59, 115}, (52) = {20, 36, 50, 51, 56, 60, 116}, (53) = {21, 37, 49, 54, 55, 61, 117}, (54) = {22, 38, 50, 53, 56, 62, 118}, (55) = {23, 39, 51, 53, 56, 63, 119}, (56) = {24, 40, 52, 54, 55, 64, 120}, (57) = {25, 41, 49, 58, 59, 61, 121}, (58) = {26, 42, 50, 57, 60, 62, 122}, (59) = {27, 43, 51, 57, 60, 63, 123}, (60) = {28, 44, 52, 58, 59, 64, 124}, (61) = {29, 45, 53, 57, 62, 63, 125}, (62) = {30, 46, 54, 58, 61, 64, 126}, (63) = {31, 47, 55, 59, 61, 64, 127}, (64) = {32, 48, 56, 60, 62, 63, 128}, (65) = {1, 66, 67, 69, 73, 81, 97}, (66) = {2, 65, 68, 70, 74, 82, 98}, (67) = {3, 65, 68, 71, 75, 83, 99}, (68) = {4, 66, 67, 72, 76, 84, 100}, (69) = {5, 65, 70, 71, 77, 85, 101}, (70) = {6, 66, 69, 72, 78, 86, 102}, (71) = {7, 67, 69, 72, 79, 87, 103}, (72) = {8, 68, 70, 71, 80, 88, 104}, (73) = {9, 65, 74, 75, 77, 89, 105}, (74) = {10, 66, 73, 76, 78, 90, 106}, (75) = {11, 67, 73, 76, 79, 91, 107}, (76) = {12, 68, 74, 75, 80, 92, 108}, (77) = {13, 69, 73, 78, 79, 93, 109}, (78) = {14, 70, 74, 77, 80, 94, 110}, (79) = {15, 71, 75, 77, 80, 95, 111}, (80) = {16, 72, 76, 78, 79, 96, 112}, (81) = {17, 65, 82, 83, 85, 89, 113}, (82) = {18, 66, 81, 84, 86, 90, 114}, (83) = {19, 67, 81, 84, 87, 91, 115}, (84) = {20, 68, 82, 83, 88, 92, 116}, (85) = {21, 69, 81, 86, 87, 93, 117}, (86) = {22, 70, 82, 85, 88, 94, 118}, (87) = {23, 71, 83, 85, 88, 95, 119}, (88) = {24, 72, 84, 86, 87, 96, 120}, (89) = {25, 73, 81, 90, 91, 93, 121}, (90) = {26, 74, 82, 89, 92, 94, 122}, (91) = {27, 75, 83, 89, 92, 95, 123}, (92) = {28, 76, 84, 90, 91, 96, 124}, (93) = {29, 77, 85, 89, 94, 95, 125}, (94) = {30, 78, 86, 90, 93, 96, 126}, (95) = {31, 79, 87, 91, 93, 96, 127}, (96) = {32, 80, 88, 92, 94, 95, 128}, (97) = {33, 65, 98, 99, 101, 105, 113}, (98) = {34, 66, 97, 100, 102, 106, 114}, (99) = {35, 67, 97, 100, 103, 107, 115}, (100) = {36, 68, 98, 99, 104, 108, 116}, (101) = {37, 69, 97, 102, 103, 109, 117}, (102) = {38, 70, 98, 101, 104, 110, 118}, (103) = {39, 71, 99, 101, 104, 111, 119}, (104) = {40, 72, 100, 102, 103, 112, 120}, (105) = {41, 73, 97, 106, 107, 109, 121}, (106) = {42, 74, 98, 105, 108, 110, 122}, (107) = {43, 75, 99, 105, 108, 111, 123}, (108) = {44, 76, 100, 106, 107, 112, 124}, (109) = {45, 77, 101, 105, 110, 111, 125}, (110) = {46, 78, 102, 106, 109, 112, 126}, (111) = {47, 79, 103, 107, 109, 112, 127}, (112) = {48, 80, 104, 108, 110, 111, 128}, (113) = {49, 81, 97, 114, 115, 117, 121}, (114) = {50, 82, 98, 113, 116, 118, 122}, (115) = {51, 83, 99, 113, 116, 119, 123}, (116) = {52, 84, 100, 114, 115, 120, 124}, (117) = {53, 85, 101, 113, 118, 119, 125}, (118) = {54, 86, 102, 114, 117, 120, 126}, (119) = {55, 87, 103, 115, 117, 120, 127}, (120) = {56, 88, 104, 116, 118, 119, 128}, (121) = {57, 89, 105, 113, 122, 123, 125}, (122) = {58, 90, 106, 114, 121, 124, 126}, (123) = {59, 91, 107, 115, 121, 124, 127}, (124) = {60, 92, 108, 116, 122, 123, 128}, (125) = {61, 93, 109, 117, 121, 126, 127}, (126) = {62, 94, 110, 118, 122, 125, 128}, (127) = {63, 95, 111, 119, 123, 125, 128}, (128) = {64, 96, 112, 120, 124, 126, 127}}), `GRAPHLN/table/11`, 0)

> 

interface(rtablesize= 25):
> 

sort(<entries(CodeTools:-Usage(VS25(G)), pairs)>, key= lhs);

memory used=2.13MiB, alloc change=0 bytes, cpu time=15.00ms, real time=23.00ms, gc time=0ns

Vector(25, {(1) = `#msub(mi("A"),mi("01"))` = 896, (2) = `#msub(mi("A"),mi("02"))` = 448, (3) = `#msub(mi("A"),mi("03"))` = 1792, (4) = `#msub(mi("A"),mi("04"))` = 448, (5) = `#msub(mi("A"),mi("05"))` = 0, (6) = `#msub(mi("A"),mi("06"))` = 448, (7) = `#msub(mi("A"),mi("07"))` = 112896, (8) = `#msub(mi("A"),mi("08"))` = 400512, (9) = `#msub(mi("A"),mi("09"))` = 896, (10) = `#msub(mi("A"),mi("10"))` = 623.3043478, (11) = `#msub(mi("A"),mi("11"))` = 896, (12) = `#msub(mi("A"),mi("12"))` = 448, (13) = `#msub(mi("A"),mi("13"))` = 896, (14) = `#msub(mi("A"),mi("14"))` = 224, (15) = `#msub(mi("A"),mi("15"))` = 896, (16) = `#msub(mi("N"),mi("01"))` = 25088, (17) = `#msub(mi("N"),mi("02"))` = 702464, (18) = `#msub(mi("N"),mi("03"))` = 1404928, (19) = `#msub(mi("N"),mi("04"))` = 8, (20) = `#msub(mi("N"),mi("05"))` = 12544, (21) = `#msub(mi("N"),mi("06"))` = 8, (22) = `#msub(mi("N"),mi("07"))` = .2857142857, (23) = `#msub(mi("N"),mi("08"))` = 0.1822157434e-3, (24) = `#msub(mi("N"),mi("09"))` = 25088, (25) = `#msub(mi("N"),mi("10"))` = 16})

> 

VSdist:= proc(G::Graph)
uses GT= GraphTheory;
local
    d:= GT:-AllPairsDistance(G), n:= op([1,1], d),
    (D,D__min):= (op@[max,min]@rhs~@op)(2, d), B, A:= GT:-AdjacencyMatrix(G)
;
    table(
        [B__||(1..4)]=~
            if D=infinity then [D, undefined$2, 0]
            else [
                -(B:= -add(d)/2), (B+= D*(n*= (n-1)/2)), B+D__min*n,
                map['reduce'= `+`](x-> `if`(x=0, 0, 1/x), (D-~d)*~A)/2
            ]
            fi
    )
end proc
:        
> 

B:= sort(<entries(CodeTools:-Usage(VSdist(G)), pairs)>, key= lhs);

memory used=5.42MiB, alloc change=0 bytes, cpu time=47.00ms, real time=37.00ms, gc time=0ns

Vector(4, {(1) = `#msub(mi("B"),mi("1"))` = 28672, (2) = `#msub(mi("B"),mi("2"))` = 28224, (3) = `#msub(mi("B"),mi("3"))` = 36352, (4) = `#msub(mi("B"),mi("4"))` = 224/3})

> 

 


 

Download 29GraphMetrics.mw

Vote up...

Carl Love 24975
March 06 2023
0 0

@vv I vote up also. I know you're aware of this; I only point it out for other readers: Your analysis only applies to real solutions. There are numerous nonreal solutions for which not all the variables are equal.

Combined Answer...

Carl Love 24975
March 05 2023
0 0

I combined my Answer for this with my Answer regarding your 15 "A" values and posted it as an Answer to that Question.

Why weighted?...

Carl Love 24975
March 04 2023
0 0

Not a single one of your 15 functions make use of the weights. What am I missing? 

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