MaplePrimes Questions

1) the two cylinders are centered on the x and z axis respectively

2) any two intersecting cylinders

Hi everyone,
Please I need your help, if anyone has idea of using Perturbation Theory to Solve the following Logistic Fractional Equation and ploting with iteration. Thanks

Restart

u(t):=1/(m)(u(t)-(u^(2)(t))/(k));

NULL

uu(t):=(k*u_0)/((u_0+(u_0)*k)*(e)^(-t/(m)))

NULL

u(0) = u_0

NULL

Hi,

I want to define the functions 10 and 11 and then put them in the eq equation, then simplify them and get the unknown values after the solve command, but there are error.

And value the function psi ?

NULL

NULL

restart

with(student)

NULL

"U(xi[n]):=a[0]+sum(-a[i]*psi^(i)(xi[n]),i=1..1)+sum(-b[i]*psi^(-i)(xi[n]),i=1..1)+sum(-c[i]*((diff(psi,xi[n])^(i)))/(psi^(i)(xi[n])),i=1..1);"

Error, empty script base

Typesetting:-mambiguous(Typesetting:-mrow(Typesetting:-mi("U", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo("≔", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("a", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mn("0", mathvariant = "normal"), open = "[", close = "]", mathvariant = "normal"), Typesetting:-mo("+", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("sum", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("a", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal"), Typesetting:-mo("⋅", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msup(Typesetting:-mi("ψ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("=", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo("+", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("sum", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("b", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal"), Typesetting:-mo("⋅", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-msup(Typesetting:-mi("ψ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic")), superscriptshift = "0"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo(",", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("=", accent = "false", fence = "false", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mo(".", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", mathvariant = "normal")), mathvariant = "normal"), Typesetting:-mo("+", accent = "false", fence = "false", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("sum", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mo("&uminus0;", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.2222222em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mi("c", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo("⋅", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mfrac(Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("diff", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ψ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mo(",", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("ξ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mambiguous(Typesetting:-msup(Typesetting:-merror("?"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-merror("empty script base"))), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mrow(Typesetting:-msup(Typesetting:-mi("ψ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), superscriptshift = "0"), Typesetting:-mfenced(Typesetting:-mrow(Typesetting:-mi("ξ", font_style_name = "2D Input", fontstyle = "normal", mathvariant = "normal"), Typesetting:-mfenced(Typesetting:-mi("n", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), open = "[", close = "]", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal")), bevelled = "false", denomalign = "center", linethickness = "1", numalign = "center"), Typesetting:-mo(",", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.3333333em", separator = "true", stretchy = "false", symmetric = "false"), Typesetting:-mi("i", font_style_name = "2D Input", fontstyle = "italic", mathvariant = "italic"), Typesetting:-mo("=", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2777778em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(".", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mo(".", accent = "false", fence = "false", font_style_name = "2D Input", largeop = "false", lspace = "0.2222222em", mathvariant = "normal", movablelimits = "false", rspace = "0.0em", separator = "false", stretchy = "false", symmetric = "false"), Typesetting:-mn("1", font_style_name = "2D Input", mathvariant = "normal")), font_style_name = "2D Input", mathvariant = "normal"), Typesetting:-mo(";", accent = "false", fence = "false", largeop = "false", lspace = "0.0em", mathvariant = "normal", movablelimits = "false", rspace = "0.2777778em", separator = "true", stretchy = "false", symmetric = "false")))

 

NULL

U(xi[n+1]) := U(xi[n]+d)

U(xi[n]+d)

(1)

U(xi[n-1]) := U(xi[n]-d)

U(xi[n]-d)

(2)

NULL

eq := c*(diff(U, xi[n]))*(U(xi[n])+u(xi[n-1]))*(U(xi[n])+u(xi[n+1]))-(2*(u(xi[n-1])-u(xi[n+1])))*(U(xi[n])^2)(1-U(xi[n])^2)

-2*(u(xi[n-1])-u(xi[n+1]))*(U(xi[n]))(1-U(xi[n])^2)^2

(3)

NULL

Download abs.mw

What am I doing wrong, why cant I get the result correct?

 

 

proc(U::Matrix);

proc (U::(Matrix(i .. m, j .. m))) local m, i, j; m := LinearAlgebra:-Dimension(U); if modp(i+j, 2) = 0 then U[i, j] := 1 else U[i, j] := 0 end if end proc

``

(1)

Hello! I've made these procedures but it doesn't result give me the result i want. Can someone please tell me where it is I made a mistake?

 

Hello

I have programs below for the cases n=3 and n=4. If n is increasing by 1, then there is one loop more. As you can see, that additional loop has always the structure:

x[i+1] from ceil(((n-2)*24-d[i])/(n-i)) to x[i]

whereas d[i] is the sum of the values of x before.

Now I want to write "nequaln":=proc(k), which goes through all the values for n from 3 to k and produces a list [a_3,a_4,a_5,...,a_n].

I guess that I need to program a kind of dynamical loop, but I failed completely. May someone help me? That would be very kind.

 

nequal3:=proc()
    local u,v,a_3;
    a_3:=0;
    for u from ceil((3-2)*24/(3-0)) to (3-2)*24-3+1 do
        for v from ceil(((3-2)*24-u)/(3-1)) to u do
            if (3-2)*24-u-v>=1 then
                a_3:=a_3+1;
            end if;
        end do;
    end do;
    print(a_3);
end proc:

 

nequal4:=proc()
    local u,v,w,a_4;
    a_4:=0;
    for u from ceil((4-2)*24/(4-0)) to (4-2)*24-4+1 do
        for v from ceil(((4-2)*24-u)/(4-1)) to u do
            for w from ceil(((4-2)*24-u-v)/(4-2)) to v do
                if (4-2)*24-u-v-w>=1 then
                    a_4:=a_4+1;
                end if;
            end do;
        end do;
    end do;
    print(a_4);
end proc:

The old question "Longest distance in a graph via Maple code" offers some general methods to find longest paths in a given graph, while for directed acyclic graphs, the longest paths can be found much more directly via built-in functions. However, it apprears that even for small dags, Maple cannot solve this in an acceptable time. In the following example, I'd like to count the number of nodes that on longest paths for certain source and target vertexes.
 

restart;

_seed := 1234

Warning, the use of _seed is deprecated.  Please consider using one of the alternatives listed on the _seed help page.

 

G := GraphTheory:-RandomGraphs:-RandomNetwork(200, .2, 'acyclic', 'weights' = 0. .. 2)

G__0 := applyop(`-`, -1, G)``

GRAPHLN(directed, weighted, [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200], Array(1..200, {(1) = {2, 3, 4}, (2) = {5}, (3) = {4, 5}, (4) = {5}, (5) = {6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18}, (6) = {11, 12, 13, 14, 15, 17, 18, 19, 21}, (7) = {9, 10, 11, 16, 17, 20, 22}, (8) = {12, 14, 16, 17, 19, 20, 21, 22, 23}, (9) = {11, 14, 21, 23}, (10) = {11, 13, 18, 19, 20, 21, 23}, (11) = {14, 15, 16, 17, 18, 21, 23}, (12) = {13, 15, 18, 19, 20, 22}, (13) = {14, 15, 16, 17, 21}, (14) = {19, 20, 22}, (15) = {19, 20, 22, 23}, (16) = {17, 18, 21}, (17) = {19, 20, 23}, (18) = {19, 20, 21}, (19) = {20, 24, 25}, (20) = {22, 23, 25}, (21) = {23, 24, 25}, (22) = {23, 24, 25}, (23) = {24, 25}, (24) = {26, 27, 29}, (25) = {27, 28, 29}, (26) = {28, 29, 30}, (27) = {28, 29, 31, 32, 33}, (28) = {32, 33}, (29) = {32, 33}, (30) = {34, 35, 38, 39}, (31) = {32, 37, 38, 39}, (32) = {33, 36, 37, 38}, (33) = {35, 36, 39}, (34) = {36, 38, 39}, (35) = {37, 39}, (36) = {37, 39}, (37) = {39, 40}, (38) = {39, 40}, (39) = {40}, (40) = {41, 42}, (41) = {43, 44, 47, 48, 49}, (42) = {44, 45, 46, 47, 48, 49}, (43) = {47, 49, 50, 55, 56, 57}, (44) = {45, 48, 50, 51, 52, 53, 54, 56}, (45) = {46, 47, 49, 50, 52, 56}, (46) = {47, 48, 49, 50, 51, 52, 53, 56, 57}, (47) = {49, 50, 51, 52, 54, 56, 57}, (48) = {49, 51, 52, 53, 54, 55, 56, 57}, (49) = {50, 52, 53, 54, 57}, (50) = {51, 57}, (51) = {53, 54, 57}, (52) = {53, 55, 57}, (53) = {54, 56}, (54) = {56, 58}, (55) = {58}, (56) = {58}, (57) = {58}, (58) = {59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75}, (59) = {60, 61, 66, 68, 70, 71, 74, 75, 76, 77}, (60) = {61, 63, 67, 68, 70, 72, 73, 77}, (61) = {62, 66, 69, 70, 71, 72, 73, 75, 76, 77}, (62) = {65, 68, 75, 76, 77}, (63) = {65, 66, 69, 70, 72, 73, 76, 77}, (64) = {65, 67, 68, 69, 70, 71, 73, 77}, (65) = {66, 70, 72, 73, 74, 76}, (66) = {68, 70, 71, 72, 73, 74, 75, 76, 77}, (67) = {69, 70, 71, 74, 76}, (68) = {73, 74}, (69) = {71, 76, 77}, (70) = {71, 73, 77}, (71) = {72, 76, 77}, (72) = {75}, (73) = {75, 76}, (74) = {76}, (75) = {76}, (76) = {77, 78, 79, 80, 81, 82, 83, 85, 86}, (77) = {79, 80, 82, 84, 85}, (78) = {79, 83, 85, 87}, (79) = {81, 82, 83, 85, 86, 87}, (80) = {83, 86}, (81) = {83, 84, 87}, (82) = {87}, (83) = {85, 86, 87}, (84) = {85, 87}, (85) = {87}, (86) = {87}, (87) = {88, 89}, (88) = {90, 91, 92, 93, 94}, (89) = {90, 91, 93, 94, 95}, (90) = {96, 97, 99, 101, 103, 104, 107, 108, 109, 110, 112, 115, 117, 118, 120}, (91) = {92, 94, 96, 97, 98, 100, 101, 102, 105, 106, 107, 110, 113, 116, 117, 118, 120}, (92) = {95, 97, 98, 99, 101, 103, 106, 107, 108, 111, 112, 113, 115, 117, 119, 120}, (93) = {95, 96, 98, 100, 104, 106, 109, 111, 112, 113, 116, 118, 119, 120}, (94) = {95, 99, 100, 102, 103, 104, 106, 108, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120}, (95) = {97, 98, 99, 100, 102, 103, 104, 105, 107, 108, 109, 111, 112, 113, 114, 115, 116, 117, 118, 120}, (96) = {98, 100, 102, 103, 104, 106, 107, 110, 111, 114, 119, 120, 121}, (97) = {99, 100, 102, 104, 106, 107, 108, 109, 111, 114, 118, 119}, (98) = {102, 103, 107, 110, 111, 112, 113, 114, 116, 117, 119, 120, 121}, (99) = {101, 102, 104, 106, 107, 112, 117, 120}, (100) = {101, 104, 105, 106, 109, 110, 116, 117, 119, 120, 121}, (101) = {102, 105, 109, 110, 111, 112, 113, 114, 115, 117, 118, 119, 120}, (102) = {103, 106, 107, 108, 110, 112, 113, 114, 117, 118, 119}, (103) = {104, 105, 107, 108, 109, 110, 111, 113, 115, 116, 119, 120, 121}, (104) = {105, 106, 109, 110, 114, 115, 116, 118, 119}, (105) = {106, 108, 109, 110, 113, 114, 116, 117}, (106) = {107, 108, 109, 112, 114, 117, 118, 119, 121}, (107) = {110, 114, 116, 119, 120}, (108) = {111, 112, 113, 114, 118, 119, 120, 121}, (109) = {113, 116, 117, 118, 121}, (110) = {111, 113, 117, 119, 120, 121}, (111) = {112, 113, 115, 118, 120}, (112) = {113, 114, 116, 117, 118, 119, 120}, (113) = {116, 117, 119, 121}, (114) = {115, 116, 117, 121}, (115) = {116, 120}, (116) = {119, 121}, (117) = {118, 119, 121}, (118) = {121}, (119) = {121}, (120) = {121}, (121) = {122, 123, 124, 125, 126}, (122) = {123, 124, 125, 126, 127}, (123) = {126}, (124) = {126, 127}, (125) = {127}, (126) = {127}, (127) = {128, 129}, (128) = {130}, (129) = {130}, (130) = {131, 132}, (131) = {132, 133, 135}, (132) = {134, 135}, (133) = {134, 136, 137, 138, 140, 141, 142}, (134) = {135, 136, 139, 140, 141}, (135) = {136, 137, 139, 140, 141, 142}, (136) = {145, 146, 147}, (137) = {139, 141, 143, 145, 147, 148}, (138) = {139, 140, 143, 144, 145, 148}, (139) = {141, 143, 145}, (140) = {143, 145, 146, 147, 148}, (141) = {142, 144, 145, 146, 147}, (142) = {143, 144, 146, 148}, (143) = {145, 146, 147, 148}, (144) = {146, 149}, (145) = {147}, (146) = {149}, (147) = {149}, (148) = {149}, (149) = {150, 151, 152, 153, 154, 155, 156, 157, 158}, (150) = {152, 153, 155, 157, 158}, (151) = {152, 153, 159}, (152) = {154, 158}, (153) = {154, 155, 156}, (154) = {156, 158, 159}, (155) = {158}, (156) = {157, 158, 159}, (157) = {158}, (158) = {159}, (159) = {160, 161, 162, 163}, (160) = {161, 163, 166, 167}, (161) = {165, 166, 167}, (162) = {163, 165}, (163) = {164, 166, 167}, (164) = {166}, (165) = {166, 168, 169}, (166) = {169}, (167) = {168}, (168) = {169, 170, 171, 172, 173, 174, 177, 178, 179, 180, 182}, (169) = {170, 171, 172, 173, 174, 175, 176, 177, 178, 180, 181, 182}, (170) = {172, 173, 174, 175, 176, 180, 182, 183, 185}, (171) = {172, 174, 176, 177, 181, 182, 185}, (172) = {175, 176, 177, 183, 185}, (173) = {175, 176, 178, 183, 185}, (174) = {175, 180, 181, 183, 184, 185}, (175) = {181, 182, 183, 185}, (176) = {177, 178, 179, 182}, (177) = {178, 179, 184, 185}, (178) = {179, 180, 182, 183, 184}, (179) = {180, 182, 185}, (180) = {181, 182}, (181) = {184}, (182) = {185}, (183) = {187, 188, 190}, (184) = {187, 188, 189}, (185) = {186, 188, 190}, (186) = {187, 188, 190, 191, 193, 194, 196}, (187) = {188, 190, 192, 193, 194, 195}, (188) = {189, 190, 191, 192, 194}, (189) = {190, 191, 196}, (190) = {191, 192, 195, 196}, (191) = {193, 196, 199}, (192) = {194, 196, 198, 199}, (193) = {197, 199}, (194) = {195, 196, 197}, (195) = {196, 198, 199}, (196) = {198, 199}, (197) = {198}, (198) = {199, 200}, (199) = {200}, (200) = {}}), `GRAPHLN/table/1`, )

(1)

t, s := combinat:-randcomb(GraphTheory:-Vertices(G__0), 5^2), combinat:-randcomb(GraphTheory:-Vertices(G__0), integermul2exp(5, 2))

[12, 13, 22, 23, 41, 65, 70, 80, 88, 97, 105, 119, 124, 127, 129, 132, 135, 138, 146, 150, 165, 170, 189, 193, 199], [6, 13, 28, 29, 31, 41, 42, 49, 55, 85, 98, 104, 136, 141, 162, 166, 167, 168, 192, 199]

(2)

"DataFrame((`M__1`:=CodeTools:-Usage(Matrix(numelems(s),numelems(t),(i,j)->numelems((GraphTheory:-BellmanFordAlgorithm(`G__0`,s[i],t[j]))[1]),datatype=integer[2]))),'columns'=t,'rows'=s)"

memory used=7.99GiB, alloc change=0 bytes, cpu time=5.74m, real time=5.63m, gc time=22.55s

 

module DataFrame () description "two-dimensional rich data container"; local columns, rows, data, binder; option object(BaseDataObject); end module

(3)

"DataFrame((`M__2`:=CodeTools:-Usage(Matrix(numelems(s),numelems(t),proc(i::posint,j::posint,` $`)::nonnegint;  uses ListTools,GraphTheory; local ts::list(posint):=TopologicSort(`G__0`,'output'='permutation'),q::posint:=Search(t[j],ts),p::posint:=Search(s[i],ts); if  p>q then 0 elif q=p then 1 else numelems(BellmanFordAlgorithm(`G__0`,s[i],t[j])[1]) fi end,datatype=integer))),':-columns'=t,':-rows'=s)"

memory used=4.34GiB, alloc change=32.00MiB, cpu time=3.26m, real time=3.19m, gc time=14.34s

 

module DataFrame () description "two-dimensional rich data container"; local columns, rows, data, binder; option object(BaseDataObject); end module

(4)

EqualEntries(M__ || (1 .. 2))

true

(5)

 


 

Download longest_paths_in_a_DAG.mw

Unfortunately, I have to wait for almost four minutes in the above instance. Can this task be done in 0.4s?

In the Grading Quiz, it is possible for students to indicate whether the answer is correct or incorrect. In the context menu, it is also possible to add an icon instead of the text.

For some reason, I can't get this to work! If I assign an icon to the correct answer, the same icon is transferred to the incorrect answer.

Is there a way that I'm missing that can show two different icons rather than the same one?

 


How to force Maple to prove equality (2) under conditions cond.

 

restart:

# Given
#     0 < u < 1
#     0 < v < 1
#     theta > 1
#
# let F the function defined by:

F := (u, v) -> exp(-((-ln(u))^theta+(-ln(v))^theta)^(1/theta))

proc (u, v) options operator, arrow; exp(-((-ln(u))^theta+(-ln(v))^theta)^(1/theta)) end proc

(1)

# How to prove this equality for any n > 0?

'F(u^(1/n), v^(1/n))^n' = 'F(u, v)'

F(u^(1/n), v^(1/n))^n = F(u, v)

(2)

cond := u > 0, u < 1, v > 0, v < 1, theta > 1, n > 1:

simplify(F(u^(1/n), v^(1/n))^n - F(u, v)) assuming cond;

(exp(-(((-ln(u))^theta+(-ln(v))^theta)*n^(-theta))^(1/theta)))^n-exp(-((-ln(u))^theta+(-ln(v))^theta)^(1/theta))

(3)

 

 

Download Stable.mw


Thanks for your help.

Hi, I am using ArchLinux and used Maple's official installer to install it. Whenever I export my Maple files as PDF all my "-" symbols are converted to "K" for some reason. Has anyone else had this issue or have an idea on how to fix it?

Below is a screenshot of what I mean. "-" has been replaced with "K"

Hi! Do you know how can I plot revolution of this curve:

plot(1 + 1/4*sin(8*(1 + 1/8*sin(16*(1 + 1/16*sin(32*t))))), t = 0 .. 2*Pi, coords = polar)

to get a wrinkled torus like this:

Abelprijs 2015 voor John Nash en Louis Nirenberg - NEMO Kennislink

Do u have any idea? (I've tried to convert this polar curve to cartesian coords but I don't get it)

map won't work with left quotes

L:=[2,"foo",4]

Hello

I have a list with n positive integer numbers and a positive integer k.

I would like to write a Malple programm, that calculates, in how many ways k can be written as a sum of numbers in the list.

Easy examles: let the list be [2,3,6,9].

k=9 can be written in 4 ways: 9=9, 9=6+3, 9=3+3+3, 9=3+2+2+2. The result therefore shoud be 4.

k=8 can be written in 3 ways: 8=6+2, 8=3+3+2, 8=2+2+2+2. The result therefore shoud be 3.

Thank you very much your help!

I cannot get this to work:

Print all the non-string entries in a list:

L := [1, 2, "abc", "a", 7.0, infinity]:

for x in L do
    if type(x, 'string') then
        next;
    end if;
    print(x);
end do;

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