## simplify command expresses results by unconvention...

Below is MAPLE code to simplify a series.  MAPLE expresses the result in terms of functions which many people are not familiar with.  Is there a way to express the answer in terms of more conventional functions expecially if N is a positive integer?

 (1)

## how to print matrix like command in text file with...

interface(prettyprint=0):
interface(screenwidth=500):
with(LinearAlgebra):

expect

Matrix([[a1,a2,3],[5,6,7],[9,10,12]])

but

it print datatype = anything,storage = rectangular,order = Fortran_order,shape  and (2,1) etc

Matrix(3,3,{(2, 1) = 1, (3, 1) = 1, (3, 2) = 1},datatype = anything,storage = rectangular,order = Fortran_order,shape = []),

## how to apply ricci flow?...

ode1a := diff(y1(tt), tt) = 1.342398800*10^5*y1(tt)+89591.20000*y2(tt)+44647.44000*y3(tt);
ode2a := diff(y2(tt), tt) = 89591.20000*y1(tt)+89803.24000*y2(tt)+44901.60000*y3(tt);
ode3a := diff(y3(tt), tt) = 44647.44000*y1(tt)+44901.60000*y2(tt)+44859.24000*y3(tt);

would like to find the origin eigenstate before it collapse to eigenvalues

how to apply ricci flow in this situation?

i find help file , and can not find some relationship between this application and inputs of ricci related function

which functions in maple can help to find origin of eigenstate

## How to put a geometric object in another geometric...

Assume I had a 2D line

how to put and draw this line into a new geometric world defined by patch?

## how to find a patch in maple?...

how to find back a patch in maple from Pi+GaussCurvature*Area(triangle) = Pi

restart:
with(LinearAlgebra):
EFG := proc(X)
local Xu, Xv, E, F, G;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
E := DotProduct(Xu, Xu, conjugate=false);
F := DotProduct(Xu, Xv, conjugate=false);
G := DotProduct(Xv, Xv, conjugate=false);
simplify([E,F,G]);
end proc;

UN := proc(X)
local Xu,Xv,Z,s;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Z := CrossProduct(Xu,Xv);
s := VectorNorm(Z, Euclidean, conjugate=false);
simplify(<Z[1]/s|Z[2]/s|Z[3]/s>,sqrt,trig,symbolic);
end:

lmn := proc(X)
local Xu,Xv,Xuu,Xuv,Xvv,U,l,m,n;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Xuu := <diff(Xu[1],u), diff(Xu[2],u), diff(Xu[3],u)>;
Xuv := <diff(Xu[1],v), diff(Xu[2],v), diff(Xu[3],v)>;
Xvv := <diff(Xv[1],v), diff(Xv[2],v), diff(Xv[3],v)>;
U := UN(X);
l := DotProduct(U, Xuu, conjugate=false);
m := DotProduct(U, Xuv, conjugate=false);
n := DotProduct(U, Xvv, conjugate=false);
simplify([l,m,n],sqrt,trig,symbolic);
end proc:

GK := proc(X)
local E,F,G,l,m,n,S,T;
S := EFG(X);
T := lmn(X);
E := S[1];
F := S[2];
G := S[3];
l := T[1];
m := T[2];
n := T[3];
simplify((l*n-m^2)/(E*G-F^2),sqrt,trig,symbolic);
end proc:

sph := <f(u,v)|g(u,v)|h(u,v)>;
cur := GK(sph);
X := sph;
Xu := <diff(X[1],u), diff(X[2],u), diff(X[3],u)>;
Xv := <diff(X[1],v), diff(X[2],v), diff(X[3],v)>;
Z := CrossProduct(Xu,Xv);
AreaTriangle := int(int(Z[1]^2+Z[2]^2+Z[3]^2,v=-Pi/2..Pi/2),u=0..2*Pi);
dsolve(Pi+cur*AreaTriangle = Pi, [f(u,v),g(u,v),h(u,v)]);

## how to dsolve for this equation?...

this equation is complicated

how to dsolve for this equation for function f ?

f(t,x,diff(x,t)) - f(t,x,p) - (diff(x,t)-p)*diff(f(t,x,p), p) = tan(t)

## how to solve this system?...

updated:
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));

restart:
with(Groebner):
p1 := vector([a*cos(q1), a*sin(q1)]);
p2 := evalm(p1 + b*vector([cos(q1+q2), sin(q1+q2)]));
P := evalm(p2 + c*vector([cos(q1+q2+q3), sin(q1+q2+q3)]));
Pe := map(expand, P);
A := {cos(q1) = c1, sin(q1) =s1, cos(q2)=c2, sin(q2)=s2, cos(q3)=c3, sin(q3)=s3};
P := subs(A, op(Pe));
F1 := [x - P[1], y - P[2], s1^2+c1^2-1, s2^2+c2^2-1, s3^2+c3^2-1 ];
F2 := subs({a=1, b=1, c=1}, F1);

g2 := Basis(F2, plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[1], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[2], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[3], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[4], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[5], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[6], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[7], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[8], plex(c3, s3, c2, s2, c1, s1));
LeadingTerm(g2[9], plex(c3, s3, c2, s2, c1, s1));

1, c1
2       2    2   2
16 y  + 16 x , s1  s2
2
8 x, c1 s2
2      2    2
2 y  + 2 x , s1  c2
2 x, c1 c2
3            2
2 x  - 2 x + 2 y  x, s2 c2
2
1, c2
2 x, s3
2, c3
originally i think
g2[1], g2[7], g2[9] have single variables c1, c2, c3 respectively
can be used to solve system

but without x and y, these equations can not be used
if choose leading term has x and y , but there is no single variable s1 or c1.

originally expect solve as follows
g2spec := subs({x=1, y=1/2}, [g2[3],g2[5],g2[6]]);
S1 := [solve([g2spec[1]])];
q1a := evalf(arccos(S1[1]));
q1b := evalf(arccos(S1[2]));
S2 := [solve(subs(s1=S1[1], g2spec[2])), solve(subs(s1=S1[2], g2spec[2])) ];
q2a := evalf(arccos(S2[1]));
q2b := evalf(arccos(S2[2]));
S3 := [solve(subs(s1=S2[1], g2spec[2])), solve(subs(s1=S2[2], g2spec[2])) ];
q2a := evalf(arccos(S3[1]));
q2b := evalf(arccos(S3[2]));

## Error, (in limit/dosubs) invalid input: `limit/dos...

f := -ln(-1-ln(exp(x)))+ln(-ln(exp(x)))-Ei(1, -1-ln(exp(x)))+Ei(1, -ln(exp(x)))
solve(limit(diff((subs(x=q, f)-f),h), h=0) = f, q);
limit(diff((subs(x=x*h, f)-f),h), h=0);
Error, (in limit/dosubs) invalid input: `limit/dosubs` uses a 3rd argument, newx, which is missing

guess an operator called Lee, Lee(f, x) = f

solve(limit(diff((subs(x=q, f)-f),h), h=0) = f, q);

suspect q = x*h or q=x*f

limit(diff((subs(x=x*h, f)-f),h), h=0);
Error, (in limit/dosubs) invalid input: `limit/dosubs` uses a 3rd argument, newx, which is missing

limit(diff((subs(x=f*h, f)-f),h), h=0);
Error, (in depends/internal) invalid input: `depends/internal` uses a 2nd argument, x, which is missing

## how to find back the input if slope is this?...

sph := <R*cos(u)*cos(v)|R*sin(u)*cos(v)|R*sin(v)>;
GK(sph); #Gauss Curvature
MK(sph); #Mean Curvature

how to find sph if slope is tan(u) ?

## how to find back the term in summation?...

Lee := (-1+Int(exp(LambertW(1/(-1+t))*(-1+t)), t=1..x))/(Int(exp(LambertW(1/(-1+t))*(-1+t)), t=1..x));
sum(unknown, n=1..infinity) = Lee

how to find unknown?

## How to draw this graph?...

A system of algebraic equation

in terms of x, y, z

how draw 3 different circles to show the range of possible values for x, y and z respectively?

it may not be a circle

It may be 3 bounded area graph to show the range of x , y , z respectively

updated

like the graph in many examples in

algebraic and geometric ideas in the theory of discrete optimization

bound area have color

## is it possible to change ODE to PDE?...

is it possible to change ODE to PDE?

the ODE has diff(a(t),t) and diff(b(t),t)

how to convert to diff(t, a), diff(t, b) ?

## how to buildsym in this case?...

with(DEtools, buildsym, equinv, symtest):
ans := dsolve([eq2,eq3,eq4], Lie);
Error, (in dsolve) too many arguments; some or all of the following are wrong: [{a(t), b(t), c(t)}, Lie]

ans := dsolve([eq2+eq3+eq4 = exp(t)], Lie);
Error, (in PDEtools/sdsolve) too many arguments; some or all of the following are wrong: [{a(t), b(t), c(t)}, Lie]

ans := dsolve([eq2,eq3,eq4]);
sym2 := buildsym(ans);
Error, (in buildsym) invalid input: `ODEtools/buildsym` expects its 1st argument, sol, to be of type {algebraic, algebraic = algebraic}, but received [{c(t) = ...}, {b(t) = ...}, {a(t) = ...)}]

PDEtools[declare](a(t), b(t), c(t), prime = t):
symgen(eq2+eq3+eq4=0);
a(t) will now be displayed as a
b(t) will now be displayed as b
c(t) will now be displayed as c
derivatives with respect to t of functions of one variable will now be
displayed with 'symgen(....)'

update
if it can not do for 3 function a(t),b(t),c(t) system of differential equations
then

i change to use
eq2 := subs(b(t)=a(t),subs(c(t)=a(t),eq2));
eq3 := subs(b(t)=a(t),subs(c(t)=a(t),eq3));
eq4 := subs(b(t)=a(t),subs(c(t)=a(t),eq4));

with(DEtools, buildsym, equinv, symtest):
ans := dsolve(eq2 = 0, Lie);
buildsym(ans[1], a(t));
buildsym(ans[2], a(t));
buildsym(ans[3], a(t));

there are 3 answers, can i use one of it to recover the equation eq2 or  eq3 or eq4?

ans := dsolve(eq3=0, Lie);
buildsym(ans[1], a(t));
sym2 := buildsym(ans[2], a(t));
buildsym(ans[3], a(t));

sym := [_xi=rhs(sym2[2]),_eta=rhs(sym2[1])];
ODE := equinv(sym, a(t));
eq3 - ODE;
sym := [_xi=rhs(sym2[1]),_eta=rhs(sym2[2])];
ODE := equinv(sym, a(t));
eq3 - ODE;
but ODE is not equal to original eq3
ans := dsolve(eq4=0, Lie);
buildsym(ans[1], a(t));
buildsym(ans[2], a(t));

ans := dsolve(eq2+eq3+eq4=0, Lie);
sym := buildsym(ans[1], a(t));
ODE := equinv(sym, a(t));
eq2+eq3+eq4 - ODE;
sym := buildsym(ans[2], a(t));
ODE := equinv(sym, a(t));
eq2+eq3+eq4 - ODE;
sym := buildsym(ans[3], a(t));
ODE := equinv(sym, a(t));
simplify(eq2+eq3+eq4 - - ODE);

can not recover the original result

## how to calculate probability of matrix in this cas...

i count the number among group
but when the list a large such as over 1000 records, the count will be over 30,000
use which denominator to find probability?
is there any functions in maple for this case?

with(LinearAlgebra):
correlationlist1 := [[1,2,3],[1,3,5]....]:
PAB := Matrix(50):
for ii from 1 to nops(correlationlist) do
for jj from 1 to nops(correlationlist[ii]) do
for kk from 1 to nops(correlationlist) do
for qq from 1 to nops(correlationlist[kk]) do
if ii <> kk then
#print("scan=",correlationlist2[kk],"kk=",kk,"qq=",qq,"row=",correlationlist[ii][jj],"column=",correlationlist[kk][qq]):
PAB[correlationlist[ii][jj],correlationlist[kk][qq]] := PAB[correlationlist[ii][jj],correlationlist[kk][qq]] + 1: # group to group relations
end if:
od:
od:
od:
od:

## How to use statistics correlate function with a li...

If there is a list

[[1,2],[2,2],[3,3]...

how to use correlate function?

assume [1,2] and [2,1] count as 2

when find correlation between 1and 2