dharr

Dr. David Harrington

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21 years, 41 days
University of Victoria
Professor or university staff
Victoria, British Columbia, Canada

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I am a retired professor of chemistry at the University of Victoria, BC, Canada. My research areas are electrochemistry and surface science. I have been a user of Maple since about 1990.

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These are answers submitted by dharr

restart;

interface(version);

`Standard Worksheet Interface, Maple 2022.2, Windows 10, October 23 2022 Build ID 1657361`

_EnvUseHeavisideAsUnitStep:=true;
expr:=(s+exp(-Pi*s)-exp(-2*Pi*s))/(s*(s^2+2*s+2));
inttrans:-invlaplace(expr,s,t);
Y:=convert(%,piecewise);
#remove all entries in piecwise which has undefined

_EnvUseHeavisideAsUnitStep := true

expr := (s+exp(-Pi*s)-exp(-2*Pi*s))/(s*(s^2+2*s+2))

exp(-t)*sin(t)+(1/2)*(-1+exp(-t+2*Pi)*(cos(t)+sin(t)))*Heaviside(t-2*Pi)+(1/2)*(1+exp(-t+Pi)*(cos(t)+sin(t)))*Heaviside(t-Pi)

piecewise(t < Pi, exp(-t)*sin(t), t < 2*Pi, exp(-t)*sin(t)+1/2+(1/2)*exp(-t+Pi)*(cos(t)+sin(t)), 2*Pi <= t, exp(-t)*sin(t)+(1/2)*exp(-t+2*Pi)*(cos(t)+sin(t))+(1/2)*exp(-t+Pi)*(cos(t)+sin(t)))

NULL

Download remove_undefined.mw

If I assign some values such as h_n:=[5,4], etc (for np=2) then it works.

points.mw

or a variation more suitable to a large number of points.

points2.mw

Your variable s__v_0 actually had an unseen multiplication in. I replaced it with just sv0. Some subscripts were made differently in different places, for example v[1] or v__1; I changed them all to the double-underline form. In your differential equation mu was strange (from a font perhaps instead of typing mu and using escape), and different from the mu in the parameters list. You had two alphas in the parameter list.

You now need to resolve the fact that yor equations have Q(t) but there is no differential equation for Q(t). You have some parameters in your parameter list that are not in your equations - I would have removed them but you give them values later. So next step is to resolve these inconsistencies.

Covid19_Simulation2.mw

Alias perhaps comes closest to "doing it automatically".

alias(g = 1+c__1/x+c__2/x^3+c__3/x^3)

g

f := (1-1/g)*A

(1-1/g)*A

df_dx := diff(f, x)

(-c__1/x^2-3*c__2/x^4-3*c__3/x^4)*A/g^2

NULL

Download alias.mw

I just removed all entries with bonds with H from the table, then made the matrix, rather than deleting rows and columns afterwards; I hope this is equivalent.

graph:=proc(t::table)
  local t2,n,A;
  t2:=remove['flatten'](x->x[1][-1]="H",t);          # remove all entries from table with string ending in "H"
  n:=max(ListTools:-Flatten([indices(t2)]));                   # find Matrix size
  A:=Matrix(n,n,t2,'shape'='symmetric');                       # table to Matrix
  LinearAlgebra:-Map(x->if x::list then x[2] else x end if,A); # keep only weights
  GraphTheory:-Graph(A);
end proc:

Download Graph.mw

 

I was working on this but see @Carl Love was first. Here's a slight variation.

restart;

s:={"a","b","c","d","e","f"}:

parts:=Iterator:-SetPartitionFixedSize([3,3]);

_m1926293387424

(1)

First 3 integers are the locations of the first 3, next 3 of the second 3

Print(parts,'showrank');

 1: 1 2 3 4 5 6
 2: 1 2 4 3 5 6
 3: 1 2 5 3 4 6
 4: 1 2 6 3 4 5
 5: 1 3 4 2 5 6
 6: 1 3 5 2 4 6
 7: 1 3 6 2 4 5
 8: 1 4 5 2 3 6
 9: 1 4 6 2 3 5
10: 1 5 6 2 3 4

 

for part in parts do
  {{seq(s[i],i in part[1..3])},{seq(s[i],i in part[4..6])}};
end do;

{{"a", "b", "c"}, {"d", "e", "f"}}

 

{{"a", "b", "d"}, {"c", "e", "f"}}

 

{{"a", "b", "e"}, {"c", "d", "f"}}

 

{{"a", "b", "f"}, {"c", "d", "e"}}

 

{{"a", "c", "d"}, {"b", "e", "f"}}

 

{{"a", "c", "e"}, {"b", "d", "f"}}

 

{{"a", "c", "f"}, {"b", "d", "e"}}

 

{{"a", "d", "e"}, {"b", "c", "f"}}

 

{{"a", "d", "f"}, {"b", "c", "e"}}

 

{{"a", "e", "f"}, {"b", "c", "d"}}

(2)

NULL

NULL

Download partitions.mw

Some of the lambda's in vvalue were not formed with the double underline (use lprint vvalue to see this). After fixing this, simplify(...,size) executes in a reasonable time.
 

restart

with(LinearAlgebra)

assume(x::real); assume(t::real); assume(`&alpha;__1`::real); assume(`&alpha;__2`::real); assume(nu::real)

A2s := Matrix([[H__11*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__13*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`))+1, H__12*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__14*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__11*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__13*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__12*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__14*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))], [H__12*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__14*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), 1+H__11*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__13*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__12*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__14*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__11*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__13*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))], [H__13*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__33*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__14*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__34*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), 1+H__13*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__33*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__14*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__34*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))], [H__14*exp(I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__34*exp(I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__13*exp(-I*v__11)/(`&lambda;__1`-conjugate(`&lambda;__1`))+H__33*exp(-I*v__21)/(`&lambda;__1`-conjugate(`&lambda;__2`)), H__14*exp(I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__34*exp(I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`)), H__13*exp(-I*v__12)/(`&lambda;__2`-conjugate(`&lambda;__1`))+H__33*exp(-I*v__22)/(`&lambda;__2`-conjugate(`&lambda;__2`))+1]])

vvalue := {v__11 = (conjugate(`&lambda;__1`)-`&lambda;__1`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__1`)^3-`&lambda;__1`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__1`)^2-`&lambda;__1`^2)-8*nu*(conjugate(`&lambda;__1`)^4-`&lambda;__1`^4))*t, v__12 = (conjugate(`&lambda;__1`)-`&lambda;__2`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__1`)^3-`&lambda;__2`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__1`)^2-`&lambda;__2`^2)-8*nu*(conjugate(`&lambda;__1`)^4-`&lambda;__2`^4))*t, v__21 = (conjugate(`&lambda;__2`)-`&lambda;__1`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__2`)^3-`&lambda;__1`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__2`)^2-`&lambda;__1`^2)-8*nu*(conjugate(`&lambda;__2`)^4-`&lambda;__1`^4))*t, v__22 = (conjugate(`&lambda;__2`)-`&lambda;__2`)*x+(4*`&alpha;__1`*(conjugate(`&lambda;__2`)^3-`&lambda;__2`^3)+2*`&alpha;__2`*(conjugate(`&lambda;__2`)^2-`&lambda;__2`^2)-8*nu*(conjugate(`&lambda;__2`)^4-`&lambda;__2`^4))*t}

A2s2 := Determinant(A2s); dets22 := simplify(A2s2, size); length(%)

8445

dets22f := subs(vvalue, dets22)

dets22f2 := simplify(dets22f, size)

((lambda__2-conjugate(lambda__2))*(lambda__1-conjugate(lambda__1))*((-(-(-H__13^2+2*H__13*H__14-H__14^2+(H__33-H__34)*(H__11-H__12))*(-H__13^2-2*H__13*H__14-H__14^2+(H__33+H__34)*(H__11+H__12))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(lambda__1-conjugate(lambda__2))*(-H__13^3+(H__11*H__33+H__12*H__34+H__14^2)*H__13-H__14*(H__11*H__34+H__12*H__33)))*(lambda__2-conjugate(lambda__2))*(lambda__1-conjugate(lambda__1))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__2+x*conjugate(lambda__1)))-(lambda__2-conjugate(lambda__1))*((lambda__2-conjugate(lambda__2))*(lambda__1-conjugate(lambda__1))*(-H__13^3+(H__11*H__33+H__12*H__34+H__14^2)*H__13-H__14*(H__11*H__34+H__12*H__33))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(lambda__1-conjugate(lambda__2))*(((-H__13^2+2*H__13*H__14-H__14^2+(H__33-H__34)*(H__11-H__12))*(-H__13^2-2*H__13*H__14-H__14^2+(H__33+H__34)*(H__11+H__12))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(H__11^2*H__33-H__11*H__13^2-H__11*H__14^2-H__12^2*H__33+2*H__12*H__13*H__14)*(lambda__2-conjugate(lambda__2)))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(lambda__1-conjugate(lambda__1))*((-H__33*H__13^2+2*H__14*H__34*H__13-H__33*H__14^2+H__11*(H__33^2-H__34^2))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__33-H__13^2)))))*exp(-I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+((lambda__2-conjugate(lambda__2))*((H__13^3+(-H__11*H__33-H__12*H__34-H__14^2)*H__13+H__14*(H__11*H__34+H__12*H__33))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(H__13-H__14)*(H__13+H__14)*(lambda__1-conjugate(lambda__2)))*(lambda__1-conjugate(lambda__1))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__2+x*conjugate(lambda__1)))+(-(H__12*H__34-H__13^2)*(lambda__2-conjugate(lambda__2))*(lambda__1-conjugate(lambda__1))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(lambda__1-conjugate(lambda__2))*(((-H__13^3+(H__11*H__33+H__12*H__34+H__14^2)*H__13-H__14*(H__11*H__34+H__12*H__33))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__13-H__12*H__14))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+((H__13*H__33-H__14*H__34)*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+H__13*(lambda__2-conjugate(lambda__2)))*(lambda__1-conjugate(lambda__1))))*(lambda__2-conjugate(lambda__1)))*(lambda__1-conjugate(lambda__2)))*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__2+x*conjugate(lambda__1)))+((lambda__2-conjugate(lambda__2))*(lambda__1-conjugate(lambda__1))*(-(lambda__2-conjugate(lambda__2))*((-H__13^3+(H__11*H__33+H__12*H__34+H__14^2)*H__13-H__14*(H__11*H__34+H__12*H__33))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(H__12*H__34-H__13^2)*(lambda__1-conjugate(lambda__2)))*(lambda__1-conjugate(lambda__1))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__2+x*conjugate(lambda__1)))+(lambda__2-conjugate(lambda__1))*((H__13-H__14)*(H__13+H__14)*(lambda__2-conjugate(lambda__2))*(lambda__1-conjugate(lambda__1))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(lambda__1-conjugate(lambda__2))*(((-H__13^3+(H__11*H__33+H__12*H__34+H__14^2)*H__13-H__14*(H__11*H__34+H__12*H__33))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__13-H__12*H__14))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+((H__13*H__33-H__14*H__34)*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+H__13*(lambda__2-conjugate(lambda__2)))*(lambda__1-conjugate(lambda__1)))))*exp(-I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+((lambda__2-conjugate(lambda__2))*(((-(-H__13^2+2*H__13*H__14-H__14^2+(H__33-H__34)*(H__11-H__12))*(-H__13^2-2*H__13*H__14-H__14^2+(H__33+H__34)*(H__11+H__12))*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))-(H__11^2*H__33-H__11*H__13^2-H__11*H__14^2-H__12^2*H__33+2*H__12*H__13*H__14)*(lambda__2-conjugate(lambda__2)))*exp(-I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))-(lambda__1-conjugate(lambda__1))*((-H__33*H__13^2+2*H__14*H__34*H__13-H__33*H__14^2+H__11*(H__33^2-H__34^2))*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__33-H__13^2)))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(((-H__13^3+(H__11*H__33+H__12*H__34+H__14^2)*H__13-H__14*(H__11*H__34+H__12*H__33))*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__13-H__12*H__14))*exp(-I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(lambda__1-conjugate(lambda__1))*((H__13*H__33-H__14*H__34)*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+H__13*(lambda__2-conjugate(lambda__2))))*(lambda__1-conjugate(lambda__2)))*(lambda__1-conjugate(lambda__1))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__2+x*conjugate(lambda__1)))+(lambda__2-conjugate(lambda__1))*((lambda__2-conjugate(lambda__2))*(((-H__13^3+(H__11*H__33+H__12*H__34+H__14^2)*H__13-H__14*(H__11*H__34+H__12*H__33))*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__13-H__12*H__14))*exp(-I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(lambda__1-conjugate(lambda__1))*((H__13*H__33-H__14*H__34)*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+H__13*(lambda__2-conjugate(lambda__2))))*(lambda__1-conjugate(lambda__1))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__1+x*conjugate(lambda__2)))+(((((-H__13^2+2*H__13*H__14-H__14^2+(H__33-H__34)*(H__11-H__12))*(-H__13^2-2*H__13*H__14-H__14^2+(H__33+H__34)*(H__11+H__12))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(H__11^2*H__33-H__11*H__13^2-H__11*H__14^2-H__12^2*H__33+2*H__12*H__13*H__14)*(lambda__2-conjugate(lambda__2)))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(lambda__1-conjugate(lambda__1))*((-H__33*H__13^2+2*H__14*H__34*H__13-H__33*H__14^2+H__11*(H__33^2-H__34^2))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__33-H__13^2)))*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(((H__11^2*H__33-H__11*H__13^2-H__11*H__14^2-H__12^2*H__33+2*H__12*H__13*H__14)*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(H__11-H__12)*(H__11+H__12)*(lambda__2-conjugate(lambda__2)))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(lambda__1-conjugate(lambda__1))*((H__11*H__33-H__14^2)*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+H__11*(lambda__2-conjugate(lambda__2)))))*exp(-I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(lambda__1-conjugate(lambda__1))*((((-H__33*H__13^2+2*H__14*H__34*H__13-H__33*H__14^2+H__11*(H__33^2-H__34^2))*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(H__11*H__33-H__14^2))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(lambda__1-conjugate(lambda__1))*((H__33^2-H__34^2)*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+H__33*(lambda__2-conjugate(lambda__2))))*exp(-I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+(lambda__2-conjugate(lambda__2))*(((H__11*H__33-H__13^2)*exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))+H__11*(lambda__2-conjugate(lambda__2)))*exp(I*(8*t*nu*lambda__1^4-8*t*nu*conjugate(lambda__1)^4-4*t*alpha__1*lambda__1^3+4*t*alpha__1*conjugate(lambda__1)^3-2*t*alpha__2*lambda__1^2+2*t*alpha__2*conjugate(lambda__1)^2-x*lambda__1+x*conjugate(lambda__1)))+(exp(I*(8*t*nu*lambda__2^4-8*t*nu*conjugate(lambda__2)^4-4*t*alpha__1*lambda__2^3+4*t*alpha__1*conjugate(lambda__2)^3-2*t*alpha__2*lambda__2^2+2*t*alpha__2*conjugate(lambda__2)^2-x*lambda__2+x*conjugate(lambda__2)))*H__33+lambda__2-conjugate(lambda__2))*(lambda__1-conjugate(lambda__1)))))*(lambda__1-conjugate(lambda__2))))*(lambda__1-conjugate(lambda__2)))*(lambda__2-conjugate(lambda__1)))/((lambda__1-conjugate(lambda__1))^2*(lambda__1-conjugate(lambda__2))^2*(lambda__2-conjugate(lambda__1))^2*(lambda__2-conjugate(lambda__2))^2)

NULL

Download sol1det.mw

 

Hard to tell without an uploaded worksheet (use green up-arrow), but it looks like NN and MM weren't given values.

To evaluate y at a particular x value use eval (for evaluate). For example,

y:=0.1*x+0.3*x^2;
eval(y,x=2);

gives 1.4

To do a lot of them, set up y as a function (technically a procedure), and put the x values you want in a list:

y:=x->0.1*x+0.3*x^2;
xvals:=[seq(i,i=0..2,0.5)];
y~(xvals)

gives [0., 0.125, 0.400, 0.825, 1.400]

plottools:-exportplot can export .svg (should also do .tiff but I got an error message). The .svg file looks correct in CorelDraw.

restart;

with(plots):with(plottools):

A := [[[6, 13], [6, 7], [5, 7], [5, 5], [7, 5], [7, 4], [4, 4], [4, 13]], [[13, 13], [13, 20], [20, 20], [20, 23], [22, 23], [22, 22], [23, 22], [23, 16], [16, 16], [16, 9], [9, 9], [9, 6], [7, 6], [7, 7], [6, 7], [6, 13]], [[13, 23], [20, 23], [20, 20], [13, 20]], [[13, 24], [20, 24], [20, 23], [13, 23]], [[22, 24], [22, 23], [20, 23], [20, 24]], [[24, 24], [24, 22], [23, 22], [23, 23], [22, 23], [22, 24]], [[22, 22], [22, 23], [23, 23], [23, 22]], [[22, 25], [25, 25], [25, 16], [23, 16], [23, 22], [24, 22], [24, 24], [22, 24]], [[25, 6], [16, 6], [16, 9], [23, 9], [23, 16], [25, 16]], [[9, 6], [9, 9], [16, 9], [16, 6]], [[6, 6], [6, 7], [7, 7], [7, 6]], [[6, 20], [13, 20], [13, 13], [6, 13]], [[20, 28], [28, 28], [28, 16], [25, 16], [25, 25], [22, 25], [22, 24], [20, 24]], [[16, 5], [9, 5], [9, 6], [16, 6]], [[7, 5], [7, 6], [9, 6], [9, 5]], [[5, 5], [5, 7], [6, 7], [6, 6], [7, 6], [7, 5]], [[4, 23], [13, 23], [13, 20], [6, 20], [6, 13], [4, 13]], [[23, 9], [16, 9], [16, 16], [23, 16]], [[9, 1], [1, 1], [1, 13], [4, 13], [4, 4], [7, 4], [7, 5], [9, 5]]]:
arte := seq(polygonplot([A[i]], color = ColorTools:-Color([rand()/10^12, rand()/10^12, rand()/10^12]), axes = none, style = polygon, view = [1 .. max(A[]), 1 .. max(A[][])]), i = 1 .. nops(A)):
plt:=display(arte):

currentdir();

"C:\Users\dharr\Desktop"

exportplot(cat(currentdir(),"/myplot.svg"),plt);

13112

NULL

Download exportplot.mw

From the ?dsolve,numeric help page "All IVP methods can be used for complex-valued IVPs with a real-valued independent variable". Not sure what it would mean for a complex independent variable - some sort of path through the complex plane would be needed.

@dharr CayleyTableGroup is another way. (CustomGroup could also be used.) - works for add and multiply

restart

with(GroupTheory)

Addition mod 7

Madd := Matrix(7, 7, proc (i, j) options operator, arrow; `mod`(i+j-2, 7)+1 end proc)

Matrix(%id = 36893490821750137428)

Gadd := CayleyTableGroup(Madd)

_m2674416000448

lblsadd := proc (i) options operator, arrow; i-1 end proc

proc (i) options operator, arrow; i-1 end proc

DrawCayleyTable(Gadd, labels = lblsadd)

Multiplication mod 7

Mmult := Matrix(6, 6, proc (i, j) options operator, arrow; `mod`(i*j, 7) end proc)

Matrix(%id = 36893490821805543780)

Gmult := CayleyTableGroup(Mmult)

_m2674386086240

CayleyTable(Gmult)

Array(%id = 36893490821805550876)

But strangely the ordering is different here:

DrawCayleyTable(Gmult)

``

Download mod7.mw

I'm assuming you really want a group, rather than just doing arithmetic mod n. The addition case is just the CyclicGroup:

with(GroupTheory)

G := CyclicGroup(7)

_m1835422256320

lbl:=proc(el) local i;
  i:=convert(el,'list');
  if nops(i)=0 then 0 else i[1]-1 end if;
end proc:
     

DrawCayleyTable(G, labels = lbl)

 

 

Download mod7.mw

Following @Mariusz Iwaniuk but can't get the last step.

Download summation.mw

I clicked on a pMML link (5.13.E1), which downloaded a file. I opened it in a text editor, selected all the text and copied it. In a Maple 2D input region, I pasted and it asked me if I wanted to convert MathML to 2D input, and I said yes. It looks a little strange in the input region (not as bad as here), but seems to be functionally OK.

restart

q := (int(GAMMA(s+a)*GAMMA(b-s)*z^(-s), s = c-i*infinity .. c+i*infinity))/(2*Pi*i) = GAMMA(a+b)*z^a/(1+z)^(a+b)

(1/2)*(int(GAMMA(s+a)*GAMMA(b-s)*z^(-s), s = c-i*infinity .. c+i*infinity))/(Pi*i) = GAMMA(a+b)*z^a/(1+z)^(a+b)

lprint(q)

1/2/Pi/i*int(GAMMA(s+a)*GAMMA(b-s)*z^(-s),s = c-i*infinity .. c+i*infinity) =
GAMMA(a+b)*z^a/((1+z)^(a+b))

NULL

Download PMML.mw

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