Maple 12 Questions and Posts

simplify command expresses results by unconvention...

Asked by: tsunamiBTP 292

December 12 2017

0 1

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?

Cn := ((-I)*(1/2))*(2*(I*Pi*n*tau-(2*I)*Pi*n)*cos(Pi*n*tau/T)-T*(2*I)*sin(Pi*n*tau/T)+(4*I)*Pi*n)/(Pi^2*n^2); S4 := a[0]+sum(Cn*sin(2*Pi*n*x/T), n = 1 .. k); a[0] := 0; T := 4; tau := 2; Cn; S5 := unapply(S4, k, x); T := simplify(S5(N, x))

(1)

Download simplify.mw

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

Asked by: ComputerUser 535

December 09 2017

0 2

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?...

Asked by: ComputerUser 535

September 12 2017

0 0

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...

Asked by: ComputerUser 535

August 28 2017

0 1

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?...

Asked by: ComputerUser 535

August 23 2017

0 5

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?...

Asked by: ComputerUser 535

August 13 2017

0 5

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?...

Asked by: ComputerUser 535

August 12 2017

0 0

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...

Asked by: ComputerUser 535

July 27 2017

0 8

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?...

Asked by: ComputerUser 535

July 13 2017

0 2

read example

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?...

Asked by: ComputerUser 535

June 17 2017

0 3

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?...

Asked by: ComputerUser 535

June 15 2017

0 0

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?...

Asked by: ComputerUser 535

June 10 2017

0 0

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?...

Asked by: ComputerUser 535

June 08 2017

0 1

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...

Asked by: ComputerUser 535

May 11 2017

0 0

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...

Asked by: ComputerUser 535

May 11 2017

0 0

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

and how about

if [1,2] and [2,1] are different

first position as key

means 1 relate with 2 count as 1 case for 1 only

[2,1] count as 1 case for 2 only

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