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MaplePrimes Questions

Can ImportGraph read a specified range of lines fr...

Asked by: lcz 1039
April 22 2023
1  4

We can read all the graphs in a file at once, or we can use an iterative approach. But can I specify a certain number of lines to read? 

with(GraphTheory):
g:=ImportGraph("E:/5cc3free.txt", graph6, output=list)

The contents of 5cc3free.txt are as follows (all 5-vertex C_3 free connected graphs).  There are 6 lines.

D?{
D@s
DBw
DFw
DDW
DqK

The reason for wanting this kind of operation is that sometimes there are tens of thousands of graphs stored in a single file, and I want to read them in batches. For example, I want to extract the graph data from lines 1-2, 3-4, and 5-6 in batches. How can I accomplish this?

In the previous example, a small dataset was used for demonstration purposes. In the following example, which involves all 8-vertex connected graphs (see the attachment graph8c.txt), I want to extract the graphs from lines 200-300. 

I found that readline always starts reading from the first line of a file, so the efficiency may not be very high.

equivalent seq loop...

Asked by: Christopher2222 6030
matrix seq do-loop
April 22 2023
0  4

For example - I have a for loop acting on a Matrix

a:=Matrix(20,20,rand(0..1.)

for i from 1 to 20 do
  for j from 1 to 20 do
    if a[i,j]<0.2 then a[i,j]:=0 end if:
  end do:
end do:

Is there an equivalent sequence loop?  I tried to set up a double seq to set the values in the matrix but this fails

seq(seq(`if`(a[i,j]<0.2,a[i,j]:=0,a[i,j]),i=1..20),j=1..20)

How to Randomly Shuffle a list of list of huge dat...

Asked by: vs140580 495
user-error list
April 22 2023
0  1

I have list of lists I looking to Shuffle the entire List of lists in a very very non-sequencial manner everthing thing fully shuffled.

I tried but I am unable to find the right way.

Attached a code I tried

Code like below

toy_shuffle.mw

A basic question mostly I am not able find the ans...

Asked by: vs140580 495
do-loop pause
April 21 2023
0  1

Inside a big running for loop 

If a particular condition is satisfied I want loop to pause until i again press the enter key again 

As if the condition is satisfied I want to note down the output results printed on screen when that condition is satisfied.

previously C I used to use like getch() for it to wait

Kind help please.

I dont want  breakpoint it will simply call the debugger so only.

idk what this line should do...

Asked by: adr279 10
rtfm statistics fit
April 21 2023
2  3

H:= Fit(a*B+b*sinh(c*B), Bdata, Hdata, B)

can someone help me ? i have never used maple13 and i have to describe a code but i cant understand what this line does. can someone help me, please?! 
thank u in advance. 

How do I calculus the K constant in Einstein's equ...

Asked by: MichaelVio 40
tensor physics
April 21 2023
1  0

How can I solve Einstein’s equation and calculus of the value of the K constant in Einstein's equation and the value of the tensor stress energy that fits in this equation?

   

 

QTBend.docxSqBend.mw

Double collect function ...

Asked by: ControlLaw 40
collect incomplete-question
April 21 2023
1  4

Hello,
I m wondering if/how (i) can use the collect function twice:  collect(a, x, form, func ):  
collect(a, x, form, collect(x)), but it seems I can't use a func with opt. 
Can someone help please? 

Merci 

Working symbolically with general/unknown matrices...

Asked by: Diasaur 25
linear-algebra abstract incomplete-question
April 21 2023
5  9

Hello Y'all,

I've been on this problem for a few days now and can't seem to find a solution and hope you fine people here can help me.

Is there a way to symbolically work with matrices? In detail I'm trying to calculate blocks in a block matrix equation symbolically/analytically. The first problem I had was that of course matrices dont commutate, which is solvable by just using the LinearAlgebra package and typing in

A.B instead of A*B

For now the big problem that remains is that of course in addition to that the inversion of a matrix A is not just 1/A (or \frac{1}{A} in LaTeX) but simply A^(-1). There is the MatrixInverse function but that needs a declared matrix. And since I dont have explicit matrices I can't use Matrix or the like to declare that A is a matrix. Any help here would appreciated. I tried to work with assume, but that didn't work either and I am kind of out of options (that I find on the web) right now. In essence I just want Maple to write A^(-1) and only cancel that if an A is next to it... (albeit with not just A but of course A also being setup by addition and multiplication of matrices...).

A smaller, related interest would be a general identity matrix. One that basically just fulfills A.I=I.A=A and I^(-1)=I. At least to me that seems kind of similar but I can't just define a Mtrix as being a Matrix and not having elements...

Thank you in advance and have a nice weekend y'all! :)

differentiate output of pdsolve...

Asked by: mehdi jafari 774
differentiation pde numeric
April 21 2023
2  1

Hi. I want to differentiate output of pdsolve, CA(y,z) with respect to z. how can i get the result? thnx in advance.

> 

restart
> 

CA0 := 0:CAi := 0.0336:L := 3:`&Gamma;_1` := 0.05:mu := 0.000894:rho := 998:Dab := 0.196e-8:
Re_1 := 4*`&Gamma;_1`*rho/mu:g := 9.8:delta := evalf(3*mu*`&Gamma;_1`/(rho^2*g))^(1/3):
> 

Eq1 := mu*diff(uy(z), z, z) = -rho*g;

0.894e-3*(diff(diff(uy(z), z), z)) = -9780.4

 (1)
> 

Bcs := uy(delta) = 0., D[1](uy)(0) = 0.;

uy(0.2395046078e-3) = 0., (D(uy))(0) = 0.

 (2)
> 

sol:=dsolve({Bcs, Eq1}):UY:=rhs(sol);

-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000

 (3)
> 

uy_bar := rho*g*delta^2/(3*mu):
> 

Eq2 := UY*diff(CA(y, z), y) = Dab*diff(CA(y, z), z, z);

(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y)) = 0.196e-8*(diff(diff(CA(y, z), z), z))

 (4)
> 

IBC := {CA(0, z) = 0, CA(y, 0) = 0.0336, D[2](CA)(y, delta) = 0};

{CA(0, z) = 0, CA(y, 0) = 0.336e-1, (D[2](CA))(y, 0.2395046078e-3) = 0}

 (5)
> 

sol2:= pdsolve(Eq2, IBC, numeric)

_m1045849856

 (6)
> 

sol2:-value(output=listprocedure);

[y = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[1]) end proc, z = proc () option `Copyright (c) 2000 by Waterloo Maple Inc. All rights reserved.`; evalf(args[2]) end proc, CA(y, z) = proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (36893488148465195156) ] ) ] ) INFO := table( [( "leftwidth" ) = 1, ( "vectorhf" ) = true, ( "timeadaptive" ) = false, ( "extrabcs" ) = [0], ( "solmat_is" ) = 0, ( "spaceadaptive" ) = false, ( "pts", z ) = [0, 0.2395046078e-3], ( "linear" ) = true, ( "mixed" ) = false, ( "solvec3" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "theta" ) = 1/2, ( "solution" ) = Array(1..3, 1..21, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0}, datatype = float[8], order = C_order), ( "solmat_i2" ) = 0, ( "depdords" ) = [[[1, 2]]], ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, _s3, xi; _s1 := -(49/50000000000)/h^2; _s2 := -(2445100000/447)/k; _s3 := (49/111750000000000000000000)*(715596653038961964979*h^2+4470000000000*k)/(k*h^2); mat[4] := 1; mat[8*n-4] := (3/2)/h; mat[8*n-6] := (1/2)/h; mat[8*n-5] := -2/h; for xi from 2 to n-1 do mat[8*xi-4] := _s2*x[xi]^2+_s3; mat[8*xi-5] := _s1; mat[8*xi-3] := _s1 end do end proc, ( "totalwidth" ) = 8, ( "solmatrix" ) = Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order), ( "eqnords" ) = [[1, 2]], ( "multidep" ) = [false, false], ( "maxords" ) = [1, 2], ( "errorest" ) = false, ( "norigdepvars" ) = 1, ( "spacevar" ) = z, ( "eqndep" ) = [1], ( "spaceidx" ) = 2, ( "dependson" ) = [{1}], ( "bandwidth" ) = [2, 3], ( "spacestep" ) = 0.119752303900000e-4, ( "solvec5" ) = 0, ( "matrixhf" ) = true, ( "depords" ) = [[1, 2]], ( "erroraccum" ) = true, ( "depeqn" ) = [1], ( "stages" ) = 1, ( "startup_only" ) = false, ( "spacepts" ) = 21, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, xi; _s2 := (49/50000000000)/h^2; _s3 := -(2445100000/447)/k; _s4 := (35064235998909136283971/111750000000000000000000)/k; vec[1] := 0.336e-1; vec[n] := 0; for xi from 2 to n-1 do _s1 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := _s2*_s1+(_s3*x[xi]^2+_s4)*vp[xi] end do end proc, ( "t0" ) = 0, ( "allocspace" ) = 21, ( "initialized" ) = false, ( "method" ) = theta, ( "depvars" ) = [CA], ( "BCS", 1 ) = {[[1, 0, 0], b[1, 0, 0]-0.336e-1], [[1, 1, 0.2395046078e-3], b[1, 1, 0.2395046078e-3]]}, ( "timeidx" ) = 1, ( "solmat_v" ) = Vector(168, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0, (127) = .0, (128) = .0, (129) = .0, (130) = .0, (131) = .0, (132) = .0, (133) = .0, (134) = .0, (135) = .0, (136) = .0, (137) = .0, (138) = .0, (139) = .0, (140) = .0, (141) = .0, (142) = .0, (143) = .0, (144) = .0, (145) = .0, (146) = .0, (147) = .0, (148) = .0, (149) = .0, (150) = .0, (151) = .0, (152) = .0, (153) = .0, (154) = .0, (155) = .0, (156) = .0, (157) = .0, (158) = .0, (159) = .0, (160) = .0, (161) = .0, (162) = .0, (163) = .0, (164) = .0, (165) = .0, (166) = .0, (167) = .0, (168) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order))]), ( "depshift" ) = [1], ( "PDEs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y))-(49/25000000000)*(diff(diff(CA(y, z), z), z))], ( "periodic" ) = false, ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "adjusted" ) = false, ( "timevar" ) = y, ( "banded" ) = true, ( "explicit" ) = false, ( "solspace" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = 0.2395046078e-3}, datatype = float[8]), ( "ICS" ) = [0], ( "inputargs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y)) = 0.196e-8*(diff(diff(CA(y, z), z), z)), {CA(0, z) = 0, CA(y, 0) = 0.336e-1, (D[2](CA))(y, 0.2395046078e-3) = 0}], ( "solmat_i1" ) = 0, ( "fdepvars" ) = [CA(y, z)], ( "solvec2" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "minspcpoints" ) = 4, ( "IBC" ) = b, ( "indepvars" ) = [y, z], ( "intspace" ) = Matrix(21, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0}, datatype = float[8], order = C_order), ( "rightwidth" ) = 0, ( "timestep" ) = 0.119752303900000e-4, ( "solvec1" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "solvec4" ) = 0, ( "solmat_ne" ) = 0, ( "autonomous" ) = true ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := []; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2: ", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2: ", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "1st"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc]

 (7)
> 

U:= subs(sol2:-value(output=listprocedure), CA(y, z));

proc () local tv, xv, solnproc, stype, ndsol, vals; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; Digits := trunc(evalhf(Digits)); solnproc := proc (tv, xv) local INFO, errest, nd, dvars, dary, daryt, daryx, vals, msg, i, j; option `Copyright (c) 2001 by Waterloo Maple Inc. All rights reserved.`; table( [( "soln_procedures" ) = array( 1 .. 1, [( 1 ) = (36893488148465189476) ] ) ] ) INFO := table( [( "leftwidth" ) = 1, ( "vectorhf" ) = true, ( "timeadaptive" ) = false, ( "extrabcs" ) = [0], ( "solmat_is" ) = 0, ( "spaceadaptive" ) = false, ( "pts", z ) = [0, 0.2395046078e-3], ( "linear" ) = true, ( "mixed" ) = false, ( "solvec3" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "theta" ) = 1/2, ( "solution" ) = Array(1..3, 1..21, 1..1, {(1, 1, 1) = .0, (1, 2, 1) = .0, (1, 3, 1) = .0, (1, 4, 1) = .0, (1, 5, 1) = .0, (1, 6, 1) = .0, (1, 7, 1) = .0, (1, 8, 1) = .0, (1, 9, 1) = .0, (1, 10, 1) = .0, (1, 11, 1) = .0, (1, 12, 1) = .0, (1, 13, 1) = .0, (1, 14, 1) = .0, (1, 15, 1) = .0, (1, 16, 1) = .0, (1, 17, 1) = .0, (1, 18, 1) = .0, (1, 19, 1) = .0, (1, 20, 1) = .0, (1, 21, 1) = .0, (2, 1, 1) = .0, (2, 2, 1) = .0, (2, 3, 1) = .0, (2, 4, 1) = .0, (2, 5, 1) = .0, (2, 6, 1) = .0, (2, 7, 1) = .0, (2, 8, 1) = .0, (2, 9, 1) = .0, (2, 10, 1) = .0, (2, 11, 1) = .0, (2, 12, 1) = .0, (2, 13, 1) = .0, (2, 14, 1) = .0, (2, 15, 1) = .0, (2, 16, 1) = .0, (2, 17, 1) = .0, (2, 18, 1) = .0, (2, 19, 1) = .0, (2, 20, 1) = .0, (2, 21, 1) = .0, (3, 1, 1) = .0, (3, 2, 1) = .0, (3, 3, 1) = .0, (3, 4, 1) = .0, (3, 5, 1) = .0, (3, 6, 1) = .0, (3, 7, 1) = .0, (3, 8, 1) = .0, (3, 9, 1) = .0, (3, 10, 1) = .0, (3, 11, 1) = .0, (3, 12, 1) = .0, (3, 13, 1) = .0, (3, 14, 1) = .0, (3, 15, 1) = .0, (3, 16, 1) = .0, (3, 17, 1) = .0, (3, 18, 1) = .0, (3, 19, 1) = .0, (3, 20, 1) = .0, (3, 21, 1) = .0}, datatype = float[8], order = C_order), ( "solmat_i2" ) = 0, ( "depdords" ) = [[[1, 2]]], ( "matrixproc" ) = proc (v, vp, vpp, t, x, k, h, n, mat) local _s1, _s2, _s3, xi; _s1 := -(49/50000000000)/h^2; _s2 := -(2445100000/447)/k; _s3 := (49/111750000000000000000000)*(715596653038961964979*h^2+4470000000000*k)/(k*h^2); mat[4] := 1; mat[8*n-4] := (3/2)/h; mat[8*n-6] := (1/2)/h; mat[8*n-5] := -2/h; for xi from 2 to n-1 do mat[8*xi-4] := _s2*x[xi]^2+_s3; mat[8*xi-5] := _s1; mat[8*xi-3] := _s1 end do end proc, ( "totalwidth" ) = 8, ( "solmatrix" ) = Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order), ( "eqnords" ) = [[1, 2]], ( "multidep" ) = [false, false], ( "maxords" ) = [1, 2], ( "errorest" ) = false, ( "norigdepvars" ) = 1, ( "spacevar" ) = z, ( "eqndep" ) = [1], ( "spaceidx" ) = 2, ( "dependson" ) = [{1}], ( "bandwidth" ) = [2, 3], ( "spacestep" ) = 0.119752303900000e-4, ( "solvec5" ) = 0, ( "matrixhf" ) = true, ( "depords" ) = [[1, 2]], ( "erroraccum" ) = true, ( "depeqn" ) = [1], ( "stages" ) = 1, ( "startup_only" ) = false, ( "spacepts" ) = 21, ( "vectorproc" ) = proc (v, vp, vpp, t, x, k, h, n, vec) local _s1, _s2, _s3, _s4, xi; _s2 := (49/50000000000)/h^2; _s3 := -(2445100000/447)/k; _s4 := (35064235998909136283971/111750000000000000000000)/k; vec[1] := 0.336e-1; vec[n] := 0; for xi from 2 to n-1 do _s1 := vp[xi-1]-2*vp[xi]+vp[xi+1]; vec[xi] := _s2*_s1+(_s3*x[xi]^2+_s4)*vp[xi] end do end proc, ( "t0" ) = 0, ( "allocspace" ) = 21, ( "initialized" ) = false, ( "method" ) = theta, ( "depvars" ) = [CA], ( "BCS", 1 ) = {[[1, 0, 0], b[1, 0, 0]-0.336e-1], [[1, 1, 0.2395046078e-3], b[1, 1, 0.2395046078e-3]]}, ( "timeidx" ) = 1, ( "solmat_v" ) = Vector(168, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0, (22) = .0, (23) = .0, (24) = .0, (25) = .0, (26) = .0, (27) = .0, (28) = .0, (29) = .0, (30) = .0, (31) = .0, (32) = .0, (33) = .0, (34) = .0, (35) = .0, (36) = .0, (37) = .0, (38) = .0, (39) = .0, (40) = .0, (41) = .0, (42) = .0, (43) = .0, (44) = .0, (45) = .0, (46) = .0, (47) = .0, (48) = .0, (49) = .0, (50) = .0, (51) = .0, (52) = .0, (53) = .0, (54) = .0, (55) = .0, (56) = .0, (57) = .0, (58) = .0, (59) = .0, (60) = .0, (61) = .0, (62) = .0, (63) = .0, (64) = .0, (65) = .0, (66) = .0, (67) = .0, (68) = .0, (69) = .0, (70) = .0, (71) = .0, (72) = .0, (73) = .0, (74) = .0, (75) = .0, (76) = .0, (77) = .0, (78) = .0, (79) = .0, (80) = .0, (81) = .0, (82) = .0, (83) = .0, (84) = .0, (85) = .0, (86) = .0, (87) = .0, (88) = .0, (89) = .0, (90) = .0, (91) = .0, (92) = .0, (93) = .0, (94) = .0, (95) = .0, (96) = .0, (97) = .0, (98) = .0, (99) = .0, (100) = .0, (101) = .0, (102) = .0, (103) = .0, (104) = .0, (105) = .0, (106) = .0, (107) = .0, (108) = .0, (109) = .0, (110) = .0, (111) = .0, (112) = .0, (113) = .0, (114) = .0, (115) = .0, (116) = .0, (117) = .0, (118) = .0, (119) = .0, (120) = .0, (121) = .0, (122) = .0, (123) = .0, (124) = .0, (125) = .0, (126) = .0, (127) = .0, (128) = .0, (129) = .0, (130) = .0, (131) = .0, (132) = .0, (133) = .0, (134) = .0, (135) = .0, (136) = .0, (137) = .0, (138) = .0, (139) = .0, (140) = .0, (141) = .0, (142) = .0, (143) = .0, (144) = .0, (145) = .0, (146) = .0, (147) = .0, (148) = .0, (149) = .0, (150) = .0, (151) = .0, (152) = .0, (153) = .0, (154) = .0, (155) = .0, (156) = .0, (157) = .0, (158) = .0, (159) = .0, (160) = .0, (161) = .0, (162) = .0, (163) = .0, (164) = .0, (165) = .0, (166) = .0, (167) = .0, (168) = .0}, datatype = float[8], order = C_order, attributes = [source_rtable = (Matrix(21, 8, {(1, 1) = .0, (1, 2) = .0, (1, 3) = .0, (1, 4) = .0, (1, 5) = .0, (1, 6) = .0, (1, 7) = .0, (1, 8) = .0, (2, 1) = .0, (2, 2) = .0, (2, 3) = .0, (2, 4) = .0, (2, 5) = .0, (2, 6) = .0, (2, 7) = .0, (2, 8) = .0, (3, 1) = .0, (3, 2) = .0, (3, 3) = .0, (3, 4) = .0, (3, 5) = .0, (3, 6) = .0, (3, 7) = .0, (3, 8) = .0, (4, 1) = .0, (4, 2) = .0, (4, 3) = .0, (4, 4) = .0, (4, 5) = .0, (4, 6) = .0, (4, 7) = .0, (4, 8) = .0, (5, 1) = .0, (5, 2) = .0, (5, 3) = .0, (5, 4) = .0, (5, 5) = .0, (5, 6) = .0, (5, 7) = .0, (5, 8) = .0, (6, 1) = .0, (6, 2) = .0, (6, 3) = .0, (6, 4) = .0, (6, 5) = .0, (6, 6) = .0, (6, 7) = .0, (6, 8) = .0, (7, 1) = .0, (7, 2) = .0, (7, 3) = .0, (7, 4) = .0, (7, 5) = .0, (7, 6) = .0, (7, 7) = .0, (7, 8) = .0, (8, 1) = .0, (8, 2) = .0, (8, 3) = .0, (8, 4) = .0, (8, 5) = .0, (8, 6) = .0, (8, 7) = .0, (8, 8) = .0, (9, 1) = .0, (9, 2) = .0, (9, 3) = .0, (9, 4) = .0, (9, 5) = .0, (9, 6) = .0, (9, 7) = .0, (9, 8) = .0, (10, 1) = .0, (10, 2) = .0, (10, 3) = .0, (10, 4) = .0, (10, 5) = .0, (10, 6) = .0, (10, 7) = .0, (10, 8) = .0, (11, 1) = .0, (11, 2) = .0, (11, 3) = .0, (11, 4) = .0, (11, 5) = .0, (11, 6) = .0, (11, 7) = .0, (11, 8) = .0, (12, 1) = .0, (12, 2) = .0, (12, 3) = .0, (12, 4) = .0, (12, 5) = .0, (12, 6) = .0, (12, 7) = .0, (12, 8) = .0, (13, 1) = .0, (13, 2) = .0, (13, 3) = .0, (13, 4) = .0, (13, 5) = .0, (13, 6) = .0, (13, 7) = .0, (13, 8) = .0, (14, 1) = .0, (14, 2) = .0, (14, 3) = .0, (14, 4) = .0, (14, 5) = .0, (14, 6) = .0, (14, 7) = .0, (14, 8) = .0, (15, 1) = .0, (15, 2) = .0, (15, 3) = .0, (15, 4) = .0, (15, 5) = .0, (15, 6) = .0, (15, 7) = .0, (15, 8) = .0, (16, 1) = .0, (16, 2) = .0, (16, 3) = .0, (16, 4) = .0, (16, 5) = .0, (16, 6) = .0, (16, 7) = .0, (16, 8) = .0, (17, 1) = .0, (17, 2) = .0, (17, 3) = .0, (17, 4) = .0, (17, 5) = .0, (17, 6) = .0, (17, 7) = .0, (17, 8) = .0, (18, 1) = .0, (18, 2) = .0, (18, 3) = .0, (18, 4) = .0, (18, 5) = .0, (18, 6) = .0, (18, 7) = .0, (18, 8) = .0, (19, 1) = .0, (19, 2) = .0, (19, 3) = .0, (19, 4) = .0, (19, 5) = .0, (19, 6) = .0, (19, 7) = .0, (19, 8) = .0, (20, 1) = .0, (20, 2) = .0, (20, 3) = .0, (20, 4) = .0, (20, 5) = .0, (20, 6) = .0, (20, 7) = .0, (20, 8) = .0, (21, 1) = .0, (21, 2) = .0, (21, 3) = .0, (21, 4) = .0, (21, 5) = .0, (21, 6) = .0, (21, 7) = .0, (21, 8) = .0}, datatype = float[8], order = C_order))]), ( "depshift" ) = [1], ( "PDEs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y))-(49/25000000000)*(diff(diff(CA(y, z), z), z))], ( "periodic" ) = false, ( "soltimes" ) = Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]), ( "adjusted" ) = false, ( "timevar" ) = y, ( "banded" ) = true, ( "explicit" ) = false, ( "solspace" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = 0.2395046078e-3}, datatype = float[8]), ( "ICS" ) = [0], ( "inputargs" ) = [(-(2445100000/447)*z^2+35064235998909136283971/111750000000000000000000)*(diff(CA(y, z), y)) = 0.196e-8*(diff(diff(CA(y, z), z), z)), {CA(0, z) = 0, CA(y, 0) = 0.336e-1, (D[2](CA))(y, 0.2395046078e-3) = 0}], ( "solmat_i1" ) = 0, ( "fdepvars" ) = [CA(y, z)], ( "solvec2" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "minspcpoints" ) = 4, ( "IBC" ) = b, ( "indepvars" ) = [y, z], ( "intspace" ) = Matrix(21, 1, {(1, 1) = .0, (2, 1) = .0, (3, 1) = .0, (4, 1) = .0, (5, 1) = .0, (6, 1) = .0, (7, 1) = .0, (8, 1) = .0, (9, 1) = .0, (10, 1) = .0, (11, 1) = .0, (12, 1) = .0, (13, 1) = .0, (14, 1) = .0, (15, 1) = .0, (16, 1) = .0, (17, 1) = .0, (18, 1) = .0, (19, 1) = .0, (20, 1) = .0, (21, 1) = .0}, datatype = float[8], order = C_order), ( "rightwidth" ) = 0, ( "timestep" ) = 0.119752303900000e-4, ( "solvec1" ) = Vector(21, {(1) = .0, (2) = .0, (3) = .0, (4) = .0, (5) = .0, (6) = .0, (7) = .0, (8) = .0, (9) = .0, (10) = .0, (11) = .0, (12) = .0, (13) = .0, (14) = .0, (15) = .0, (16) = .0, (17) = .0, (18) = .0, (19) = .0, (20) = .0, (21) = .0}, datatype = float[8]), ( "solvec4" ) = 0, ( "solmat_ne" ) = 0, ( "autonomous" ) = true ] ); if xv = "left" then return INFO["solspace"][1] elif xv = "right" then return INFO["solspace"][INFO["spacepts"]] elif tv = "start" then return INFO["t0"] elif not (type(tv, 'numeric') and type(xv, 'numeric')) then error "non-numeric input" end if; if xv < INFO["solspace"][1] or INFO["solspace"][INFO["spacepts"]] < xv then error "requested %1 value must be in the range %2..%3", INFO["spacevar"], INFO["solspace"][1], INFO["solspace"][INFO["spacepts"]] end if; dary := Vector(3, {(1) = .0, (2) = .0, (3) = .0}, datatype = float[8]); daryt := 0; daryx := 0; dvars := []; errest := false; nd := nops(INFO["depvars"]); if dary[nd+1] <> tv then try `pdsolve/numeric/evolve_solution`(INFO, tv) catch: msg := StringTools:-FormatMessage(lastexception[2 .. -1]); if tv < INFO["t0"] then error cat("unable to compute solution for %1<%2: ", msg), INFO["timevar"], INFO["failtime"] else error cat("unable to compute solution for %1>%2: ", msg), INFO["timevar"], INFO["failtime"] end if end try end if; if dary[nd+1] <> tv or dary[nd+2] <> xv then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["solspace"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, dary); if errest then `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_t"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryt); `pdsolve/interp2dto0d`(3, INFO["soltimes"], INFO["spacepts"], INFO["err_x"], nops(INFO["depvars"]), INFO["solution"], true, tv, xv, daryx) end if end if; dary[nd+1] := tv; dary[nd+2] := xv; if dvars = [] then [seq(dary[i], i = 1 .. INFO["norigdepvars"])] else vals := NULL; for i to nops(dvars) do j := eval(dvars[i]); try if errest then vals := vals, evalhf(j(tv, xv, dary, daryt, daryx)) else vals := vals, evalhf(j(tv, xv, dary)) end if catch: userinfo(5, `pdsolve/numeric`, `evalhf failure`); try if errest then vals := vals, j(tv, xv, dary, daryt, daryx) else vals := vals, j(tv, xv, dary) end if catch: vals := vals, undefined end try end try end do; [vals] end if end proc; stype := "1st"; if nargs = 1 then if args[1] = "left" then return solnproc(0, "left") elif args[1] = "right" then return solnproc(0, "right") elif args[1] = "start" then return solnproc("start", 0) else error "too few arguments to solution procedure" end if elif nargs = 2 then if stype = "1st" then tv := evalf(args[1]); xv := evalf(args[2]) else tv := evalf(args[2]); xv := evalf(args[1]) end if; if not (type(tv, 'numeric') and type(xv, 'numeric')) then if procname <> unknown then return ('procname')(args[1 .. nargs]) else ndsol := pointto(solnproc("soln_procedures")[1]); return ('ndsol')(args[1 .. nargs]) end if end if else error "incorrect arguments to solution procedure" end if; vals := solnproc(tv, xv); vals[1] end proc

 (8)
> 

U(1e-5,1e-6)

HFloat(0.02593255728999584)

 (9)
> 

CA_DZ:=diff(eval(CA(y,z), sol2:-value(output=listprocedure)),z);

Error, non-algebraic expressions cannot be differentiated

  
> 

 

Download Hw-02-01_problem.mw

`evala/Minpoly` and PolynomialTools:-MinimalPolyno...

Asked by: sursumCorda 1244
polynomial minpoly
April 21 2023
1  4

Here are three algebraic numbers: (In fact, they are solutions to some equation. See the attachment below.)

bSol := {RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 0.2246 .. 0.2266) - 1133, index = real[2]), RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 1.671 .. 1.68) - 1133, index = real[2]), RootOf(1216*_Z^4 + (264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 408*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 1580*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 6832*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 3508*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 9944*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 9948*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 10752*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 5204)*_Z^3 + (891*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 1652*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 4748*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 24076*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 5354*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 35356*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 29668*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 196*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 3971)*_Z^2 + (506*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 + 980*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 - 2264*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 - 12420*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 + 3676*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 + 11596*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 + 33800*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 - 7772*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) + 1210)*_Z - 473*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^8 - 720*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^7 + 2560*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^6 + 10960*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^5 - 8034*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^4 - 13840*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^3 - 9304*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657)^2 + 1104*RootOf(11*_Z^9 + 17*_Z^8 - 64*_Z^7 - 280*_Z^6 + 142*_Z^5 + 370*_Z^4 + 376*_Z^3 - 96*_Z^2 + 47*_Z - 11, 2.648 .. 2.657) - 1133, index = real[2])}:

One may check that 11_X9－47_X8＋96_X7－376_X6－370_X5－142_X4＋280_X3＋64_X2－17_X－11 is an “annihilating” polynomial of each of them (using another computer algebra system); accordingly, the degree of the minimal polynomial cannot be greater than 9. However, Maple's output indicates that the minimal polynomial is of degree 36! 

> 

restart;
> 

alias(`~`[`=`](alpha__ || (1 .. 3), ` $`, RootOf(11*_Z^9+17*_Z^8-64*_Z^7-280*_Z^6+142*_Z^5+370*_Z^4+376*_Z^3-96*_Z^2+47*_Z-11, .2246 .. .2266), RootOf(11*_Z^9+17*_Z^8-64*_Z^7-280*_Z^6+142*_Z^5+370*_Z^4+376*_Z^3-96*_Z^2+47*_Z-11, 1.671 .. 1.68), RootOf(11*_Z^9+17*_Z^8-64*_Z^7-280*_Z^6+142*_Z^5+370*_Z^4+376*_Z^3-96*_Z^2+47*_Z-11, 2.648 .. 2.657)))
> 

({PDETools:-Solve})({`~`[`>=`](a, b, ` $`, 0), a^5*b+4*a^4*b^2+4*a^3*b^3-7*a^4*b-6*a^2*b^3-7*a*b^4+b^5-6*a^3*b+12*a^2*b^2+4*b^4+4*a^3-6*a*b^2+4*b^3+4*a^2-7*a*b+a = 0, a <> b})
bSol := `~`[subs](%, b)
> 

evalf[2*Digits](`~`[eval](11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11, `~`[`=`](_X, bSol)))

{RootOf(1216*_Z^4+(264*alpha__1^8+408*alpha__1^7-1580*alpha__1^6-6832*alpha__1^5+3508*alpha__1^4+9944*alpha__1^3+9948*alpha__1^2-10752*alpha__1+5204)*_Z^3+(891*alpha__1^8+1652*alpha__1^7-4748*alpha__1^6-24076*alpha__1^5+5354*alpha__1^4+35356*alpha__1^3+29668*alpha__1^2-196*alpha__1+3971)*_Z^2+(506*alpha__1^8+980*alpha__1^7-2264*alpha__1^6-12420*alpha__1^5+3676*alpha__1^4+11596*alpha__1^3+33800*alpha__1^2-7772*alpha__1+1210)*_Z-473*alpha__1^8-720*alpha__1^7+2560*alpha__1^6+10960*alpha__1^5-8034*alpha__1^4-13840*alpha__1^3-9304*alpha__1^2+1104*alpha__1-1133, index = real[2]), RootOf(1216*_Z^4+(264*alpha__2^8+408*alpha__2^7-1580*alpha__2^6-6832*alpha__2^5+3508*alpha__2^4+9944*alpha__2^3+9948*alpha__2^2-10752*alpha__2+5204)*_Z^3+(891*alpha__2^8+1652*alpha__2^7-4748*alpha__2^6-24076*alpha__2^5+5354*alpha__2^4+35356*alpha__2^3+29668*alpha__2^2-196*alpha__2+3971)*_Z^2+(506*alpha__2^8+980*alpha__2^7-2264*alpha__2^6-12420*alpha__2^5+3676*alpha__2^4+11596*alpha__2^3+33800*alpha__2^2-7772*alpha__2+1210)*_Z-473*alpha__2^8-720*alpha__2^7+2560*alpha__2^6+10960*alpha__2^5-8034*alpha__2^4-13840*alpha__2^3-9304*alpha__2^2+1104*alpha__2-1133, index = real[2]), RootOf(1216*_Z^4+(264*alpha__3^8+408*alpha__3^7-1580*alpha__3^6-6832*alpha__3^5+3508*alpha__3^4+9944*alpha__3^3+9948*alpha__3^2-10752*alpha__3+5204)*_Z^3+(891*alpha__3^8+1652*alpha__3^7-4748*alpha__3^6-24076*alpha__3^5+5354*alpha__3^4+35356*alpha__3^3+29668*alpha__3^2-196*alpha__3+3971)*_Z^2+(506*alpha__3^8+980*alpha__3^7-2264*alpha__3^6-12420*alpha__3^5+3676*alpha__3^4+11596*alpha__3^3+33800*alpha__3^2-7772*alpha__3+1210)*_Z-473*alpha__3^8-720*alpha__3^7+2560*alpha__3^6+10960*alpha__3^5-8034*alpha__3^4-13840*alpha__3^3-9304*alpha__3^2+1104*alpha__3-1133, index = real[2])}

  

{-0.7765721e-11, -0.40e-16, -0.2e-17}

 (1)
> 

`~`[`@`(evala, Minpoly)](bSol, _X)

{-17799961-(10941904462/121)*_X+(61823634144236824/14641)*_X^9-(31748793508955524/14641)*_X^8-(101389427707536/14641)*_X^7+(2187899683524768/14641)*_X^6+(660533278629392/14641)*_X^5-(35195970681077/1331)*_X^4+(4540912173250/1331)*_X^3-(226104907168/1331)*_X^2+_X^36+(562/11)*_X^35+(1306112/1331)*_X^34-(18882494/14641)*_X^33-(1885893201/14641)*_X^32-(8021957456/14641)*_X^31+(128807680096/14641)*_X^30+(601684442192/14641)*_X^29+(136952065956/14641)*_X^28-(7313279407608/14641)*_X^27-(20755313257248/14641)*_X^26-(72279502775080/14641)*_X^25-(235147325265588/14641)*_X^24+(407012808852624/14641)*_X^23-(2003920103008/1331)*_X^22-(2647129453154576/14641)*_X^21-(5329535956015778/14641)*_X^20-(11189597881735324/14641)*_X^19+(18014890583299168/14641)*_X^18-(25692630236542548/14641)*_X^17+(57603516516708946/14641)*_X^16-(875402744452912/121)*_X^15+(36990665431348512/14641)*_X^14+(67887070781490608/14641)*_X^13+(643327218250876/1331)*_X^12-(81888059180050616/14641)*_X^11+(306280599794336/14641)*_X^10}

 (2)
> 

`~`[PolynomialTools[MinimalPolynomial]](bSol, _X)

{14641*_X^36+748022*_X^35+14367232*_X^34-18882494*_X^33-1885893201*_X^32-8021957456*_X^31+128807680096*_X^30+601684442192*_X^29+136952065956*_X^28-7313279407608*_X^27-20755313257248*_X^26-72279502775080*_X^25-235147325265588*_X^24+407012808852624*_X^23-22043121133088*_X^22-2647129453154576*_X^21-5329535956015778*_X^20-11189597881735324*_X^19+18014890583299168*_X^18-25692630236542548*_X^17+57603516516708946*_X^16-105923732078802352*_X^15+36990665431348512*_X^14+67887070781490608*_X^13+7076599400759636*_X^12-81888059180050616*_X^11+306280599794336*_X^10+61823634144236824*_X^9-31748793508955524*_X^8-101389427707536*_X^7+2187899683524768*_X^6+660533278629392*_X^5-387155677491847*_X^4+49950033905750*_X^3-2487153978848*_X^2-1323970439902*_X-260609229001}

 (3)
> 

factor({{-260609229001-1323970439902*_X+407012808852624*_X^23-22043121133088*_X^22-2647129453154576*_X^21-5329535956015778*_X^20-11189597881735324*_X^19+18014890583299168*_X^18-25692630236542548*_X^17+57603516516708946*_X^16-105923732078802352*_X^15+36990665431348512*_X^14+67887070781490608*_X^13+7076599400759636*_X^12-81888059180050616*_X^11+306280599794336*_X^10+61823634144236824*_X^9-31748793508955524*_X^8-101389427707536*_X^7+2187899683524768*_X^6+660533278629392*_X^5-387155677491847*_X^4+49950033905750*_X^3-2487153978848*_X^2+14641*_X^36+748022*_X^35+14367232*_X^34-18882494*_X^33-1885893201*_X^32-8021957456*_X^31+128807680096*_X^30+601684442192*_X^29+136952065956*_X^28-7313279407608*_X^27-20755313257248*_X^26-72279502775080*_X^25-235147325265588*_X^24}[], {-17799961-(10941904462/121)*_X+(407012808852624/14641)*_X^23-(2003920103008/1331)*_X^22-(2647129453154576/14641)*_X^21-(5329535956015778/14641)*_X^20-(11189597881735324/14641)*_X^19+(18014890583299168/14641)*_X^18-(25692630236542548/14641)*_X^17+(57603516516708946/14641)*_X^16-(875402744452912/121)*_X^15+(36990665431348512/14641)*_X^14+(67887070781490608/14641)*_X^13+(643327218250876/1331)*_X^12-(81888059180050616/14641)*_X^11+(306280599794336/14641)*_X^10+(61823634144236824/14641)*_X^9-(31748793508955524/14641)*_X^8-(101389427707536/14641)*_X^7+(2187899683524768/14641)*_X^6+(660533278629392/14641)*_X^5-(35195970681077/1331)*_X^4+(4540912173250/1331)*_X^3-(226104907168/1331)*_X^2+_X^36+(562/11)*_X^35+(1306112/1331)*_X^34-(18882494/14641)*_X^33-(1885893201/14641)*_X^32-(8021957456/14641)*_X^31+(128807680096/14641)*_X^30+(601684442192/14641)*_X^29+(136952065956/14641)*_X^28-(7313279407608/14641)*_X^27-(20755313257248/14641)*_X^26-(72279502775080/14641)*_X^25-(235147325265588/14641)*_X^24}[]})

{(11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11)*(83746429305*_X-163433814*_X^23-1409885474*_X^22+7323055726*_X^21+92878340298*_X^20+291711433585*_X^19-28358008525*_X^18-1146850616945*_X^17+2003142623069*_X^16+7054039060380*_X^15+10860482240404*_X^14+4410674835220*_X^13-23715924119108*_X^12+39935154074341*_X^11-76564178781009*_X^10+246946329497683*_X^9-303627746551159*_X^8+41661161235738*_X^7+181533634595246*_X^6-146573328877410*_X^5+44279227597786*_X^4-3813039868649*_X^3+234521505317*_X^2+1331*_X^27+73689*_X^26+1609349*_X^25+4562111*_X^24+23691748091), (1/14641)*(11*_X^9-47*_X^8+96*_X^7-376*_X^6-370*_X^5-142*_X^4+280*_X^3+64*_X^2-17*_X-11)*(83746429305*_X-163433814*_X^23-1409885474*_X^22+7323055726*_X^21+92878340298*_X^20+291711433585*_X^19-28358008525*_X^18-1146850616945*_X^17+2003142623069*_X^16+7054039060380*_X^15+10860482240404*_X^14+4410674835220*_X^13-23715924119108*_X^12+39935154074341*_X^11-76564178781009*_X^10+246946329497683*_X^9-303627746551159*_X^8+41661161235738*_X^7+181533634595246*_X^6-146573328877410*_X^5+44279227597786*_X^4-3813039868649*_X^3+234521505317*_X^2+1331*_X^27+73689*_X^26+1609349*_X^25+4562111*_X^24+23691748091)}

 (4)
> 

``


 

Download minpoly.mw

Isn't the results incorrect? 

Normalize the matrix of columns of independent va...

Asked by: vs140580 495
linearalgebra do-loop statistics
April 21 2023
0  6

I have a n cross n matrix M I need help to write a function f say which takes the Matrix M as input function and Normalize each column of independent data.

Here normalization is  subtract by mean and divide by Standard deviation kind help if possible

If anyone has  idea of other different types of normalization please help it will help me a lot 

Kind help your ideas will all be acknowledge Please help

Installation issue of Maple on Intel Evo laptop...

Asked by: adamsmithad 5
installation
April 20 2023
1  0

Hello everyone,

I am facing an issue while installing Maple on my Intel Evo laptop. The installation process starts but then it fails and I get an error message. I have tried to install it multiple times but the issue persists. I have also checked for any updates or patches but there are none available.I am not sure what could be causing this issue. Has anyone else faced a similar problem? If so, could you please share your experience and any solutions that worked for you? I would appreciate any help or suggestions on how to resolve this issue.

Thank you in advance for your time and assistance.

Can a colored shape in the xy plane be projected o...

Asked by: Earl 985
sphere projection plotting
April 20 2023
2  3

Is there any simple way that the colored shape created in the xy plane by the uploaded code can be projected in the z direction onto the surface of the unit sphere centred at the origin?

Projection.mw

Can maplesim facilitate rigid-flexible coupling an...

Asked by: Maxie 25
multiple connected
April 20 2023
1  10

I am now using maplesim to do research on railway vehicles. When I replace the rails with flexible beams in maplesim, I try to connect the rails and two sleepers with moving pairs, and I find that there are over-constraint problems. How to replace the rails with flexible bodies? Are the rails connected with multiple sleepers?

I hope you can give me some advice, thank you very much.

Generally speaking, will eliminating the need for ...

Asked by: sursumCorda 1244
April 20 2023
0  5

Let us begin with the official descriptions of loops. The Maple® documentation claims that: 

Note that the examples above don't necessarily illustrate the best way to perform these operations. Often a functional form like seq, map, add, or mul is far more efficient.

Mma's tech tutorial also claims that: 

If you have a big program full of If, Do, Return, etc., you're probably not doing things right. 
Often, however, you can make more elegant and efficient programs using the functional programming constructs ….

Also, MatLab's Techniques to Improve Performance and Measure and Improve GPU Performance claims that: 

You can achieve better performance by rewriting loops to make use of higher-dimensional operations. The performance of a wide variety of element-wise functions can be improved … instead of looping over the matrices.

Well, I'm confused. Why did the official help page say like this? Actually, I find that lots of users in this forum still (and usually) use traditional for-loops instead of something which fits in with the alleged functional programming ideas. Did I misconstrue those statements? 
(For instance, as for the functional operations, it's unfortunate that Maple's built-in map cannot operate on arbitrary expression trees of any depth; so I have to use the loops to apply some procedure indirectly, which is not so convenient. In my opinion, owing to such limitation, people have to, and then gradually tend to, use the loops.) 

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