MaplePrimes Questions

Dear All

I have started exploring Lie Algebra package in Maple 18 and it wonderful experience for me. But as I am in learning stage so I feel little difficulty to understand even its basic enviroment.

I am trying to fing quotient algebra for Normalizer of certain element W1 in Lie algebra and I don't how to do it. I have expected answer for quotient of Normlizer but don't know to obtain it. Please see following details:

 

with(DifferentialGeometry):with(LieAlgebras):``

L1 := _DG([["LieAlgebra", Alg1, [6]], [[[1, 3, 1], -1], [[1, 6, 2], -1], [[2, 3, 2], -1], [[2, 4, 1], 1], [[2, 5, 2], 1], [[4, 5, 4], -1], [[4, 6, 3], -1], [[4, 6, 5], -2], [[5, 6, 6], -1]]])

_DG([["LieAlgebra", Alg1, [6]], [[[1, 3, 1], -1], [[1, 6, 2], -1], [[2, 3, 2], -1], [[2, 4, 1], 1], [[2, 5, 2], 1], [[4, 5, 4], -1], [[4, 6, 3], -1], [[4, 6, 5], -2], [[5, 6, 6], -1]]])

(1)

DGsetup(L1)

`Lie algebra: Alg1`

(2)
Alg1 > 

MultiplicationTable("LieTable")

"[[[,`| `,e1,e2,e3,e4,e5,e6],[,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`,-`---`],[e1,`| `,0,0,_DG([["vector",Alg1,[]],[[[1],-1]]]),0,0,_DG([["vector",Alg1,[]],[[[2],-1]]])],[e2,`| `,0,0,_DG([["vector",Alg1,[]],[[[2],-1]]]),_DG([["vector",Alg1,[]],[[[1],1]]]),_DG([["vector",Alg1,[]],[[[2],1]]]),0],[e3,`| `,_DG([["vector",Alg1,[]],[[[1],1]]]),_DG([["vector",Alg1,[]],[[[2],1]]]),0,0,0,0],[e4,`| `,0,_DG([["vector",Alg1,[]],[[[1],-1]]]),0,0,_DG([["vector",Alg1,[]],[[[4],-1]]]),_DG([["vector",Alg1,[]],[[[3],-1],[[5],-2]]])],[e5,`| `,0,_DG([["vector",Alg1,[]],[[[2],-1]]]),0,_DG([["vector",Alg1,[]],[[[4],1]]]),0,_DG([["vector",Alg1,[]],[[[6],-1]]])],[e6,`| `,_DG([["vector",Alg1,[]],[[[2],1]]]),0,0,_DG([["vector",Alg1,[]],[[[3],1],[[5],2]]]),_DG([["vector",Alg1,[]],[[[6],1]]]),0]]]"

(3)
Alg1 > 

W1 := [a*e3+e5]

[a*_DG([["vector", Alg1, []], [[[3], 1]]])+_DG([["vector", Alg1, []], [[[5], 1]]])]

(4)
Alg1 > 

Nor[W1] := SubalgebraNormalizer(W1)

[_DG([["vector", Alg1, []], [[[5], 1]]]), _DG([["vector", Alg1, []], [[[3], 1]]])]

(5)

How one can find Quotient alegebra "(Nor[W1])/(W1)....???`? ``The expected answer is {e3}.`"

I am trying verify 4th 2-dimensional subalgebra results given in research artcle by Coggeshall and Meyer-ter-Vehn (See pp. 3592 in article).

Download [670]_Normalizer_in_Abstract_Lie_Algebra.mw

Regards

I have tried to perform the examples given in the help section for DataSet retrival.  I cannot get Maple 2016 to access the internet available databases.  It does not return any outside of PC resources, like Maple 2015 did, on search items. Is there a setup item that I am missing or is there something amiss in Maple 2016.

This is the Error that I am getting: "Error, (in DataSets:-Search) invalid input: find_count expects its 1st argument, lst, to be of type list(nonnegint), but received [FAIL["total_count"], 0]. "

I was able to run this example in Maple 2105.  The example is the "Average Global Temperature"

 

Thanks

Bill Tolrud

I need to do this with a sequence of a large number of elements but here is my question with a sequence of fewer elements.

a:={10,11,-13,9,20,74,10}:

I want to check each element of the sequence if it is negative. And if any element is negative I want to replace with 0 (or do something else). I tried the following code but it didn't work. 

for k from 1 to 7 do
  if (a[k]<0) then subs(a[k]=0, a) end if:
end do;

Please help me to figure it out. 

@ecterrab 


hello dear,

was working with tensor package using debever formalism in maple v release 5 and got this problem, 
Error, (in factor) expecting a polynomial over an algebraic number field. would u tell me how to deal with this error in maple v release 5. aprl12.mws
thanks,
suresh

Hi,

can you please help me with the usage of applyrule? I have the following problem that I cannot isolate. I have a rule that I want to apply, but instead of applying the rule to the expression, the rule seems to be applied to itself. In an isolated worksheet everything is fine:

restart;

rule:=abs(''a''::algebraic)^2=''a''^2;

abs('a'::algebraic)^2 = 'a'^2

(1)

 

myexp:=abs(548.477146186283171377723+radius_motor*q_mot_vec_2(t)-l_wire_0[2])^2

abs(548.477146186283171377723+radius_motor*q_mot_vec_2(t)-l_wire_0[2])^2

(2)

applyrule(rule,myexp);

(548.477146186283171377723+radius_motor*q_mot_vec_2(t)-l_wire_0[2])^2

(3)

rule

abs(a::algebraic)^2 = a^2

(4)

 


Download applyrule.mw

What happens when I try to use this rule in my script is this:

restart;

#read "some_long_script.mpl":

rule:=abs(''a''::algebraic)^2=''a''^2;

abs('a'::algebraic)^2 = 'a'^2

(1)

applyrule(rule,abs(x)^2)

abs(x)^2

(2)

rule

a::algebraic^2 = a^2

(3)

 

>
 

I want to clarify, that the script that is read before applying those rules does not apply a similar rule. Also the variables rule and x were free. Can you please help me to locate the problem?

Thanks!

Honigmelone

Hello everyone!

I want to generate an lower triangular matrix. Please see the attachment and help me. I am waiting your quick response. 

Help.mw

The result I am looking for is Re[Sqrt[x + I*y]] = 1/2 Sqrt[2 (SQrt[x^2+y^2]+x)]. How can I get it?

Hey,

at some point in my maple calculations I have to read some symbolic constants because otherwise the expressions become to big. All my constants are in a range 1e-3 to 1e6 or something. No matter how exact I calculate my result always has some Numbers in the range of <1e-20 (how small they actually are varies with Digits) together with numbers 1e-3..1e6. I presume those 1e-20 are just zeros. Can I somehow tell maple to forget/drop very small numbers and assume them all to be zero?

Thanks!

Honigmelone

Hey all,

I want to symbolically differentiate a function and recalculate the result later. Here is what I have tried so far:


restart;

myexp:=dfdb+sthlong

dfdb+sthlong

(1)

b:=<b1(t),b2(t)>;

b := Vector(2, {(1) = b1(t), (2) = b2(t)})

(2)

dfdb:=Physics[diff]~(f(b),b)

dfdb := Vector(2, {(1) = (D(f))(Vector(2, {(1) = b1(t), (2) = b2(t)})), (2) = (D(f))(Vector(2, {(1) = b1(t), (2) = b2(t)}))})

(3)

f:=b->b(1)^2+b(2)

proc (b) options operator, arrow; b(1)^2+b(2) end proc

(4)

eval(myexp);  #actual result

 

 

sthlong+(Vector(2, {(1) = (D(f))(Vector(2, {(1) = b1(t), (2) = b2(t)})), (2) = (D(f))(Vector(2, {(1) = b1(t), (2) = b2(t)}))}))

(5)

dfdb:=Physics[diff]~(f(b),b):

eval(myexp); #expected result

sthlong+(Vector(2, {(1) = 2*b1(t), (2) = 1}))

(6)

 


Download physics_diff.mw

I wonder if this is even possible, or if I missunderstand something. Can you please help me?

 

Thanks

 

Honigmelone

In Maple 17, I had

evalf(5^1.25, 30);
7.476743906

evalf(5^(5/4), 30);
7.47674390610610270955949497070

evalf(evalf(5^1.25, 30)-evalf(5^(5/4), 30), 30);
-1.0610270955949497070 *10^(-10)

I would expect the two results to be the same. 

I am using Maple 17 and windows 7 operating system. 

Is there a reason that  evalf(5^1.25, 30) will not compute 30 decimal places?

 

 

How to generate a random normal distribution of points around the point [3,15] for example?

Hello everyone

I have a problem with the code below in maple:

> restart;
> f := signum(a*cos(t+b)+sin(t+c));
> res := int(f, t = 0 .. 2*Pi);
                       2 Pi signum(a cos(b) + sin(c))
> a := 0.01; b := 0; c := 0;
> res; int(f, t = 0 .. 2*Pi);
                                    2 Pi
                                     0.

As you can see, results are not consistent with one another...

If I set a := 0.01; b := 1.35; c := 4.4; It is even worse, the computation of int(f, t = 0 .. 2*Pi) lasts more than 10 minutes (when I interrupt computation)

I tested it in Maple 12 and Maple 2015 and I get exactly the same results. I also replaced signum with csgn and I get the same problem.

I really need your help!!

Dear All

I intend to convert Lie algebra into abstract Lie algebra with the aid of Maple packages DifferentialGeometry and Lie algebras. I want to do this for classification of Lie algebra for group inavriant solution, can anybody help me out.....?

Regards

woud like to find H(x)

just for one of definition H(x) + H(y) = H(x+y), but it seems require to duplicate one more set of differential system

Error, (in dsolve) found differentiated functions with same name but depending on different arguments in the given DE system: [{a(x), a(y)}, {b(x), b(y)}]

eq2a := a(x)*(diff(c(x), x))+b(x);
eq3a := a(x)*(diff(b(x), x))+c(x)*(diff(b(x), x));
eq4a := a(x)*(diff(c(x), x))+a(x)*(diff(b(x), x))+b(x);
eq2b := a(y)*(diff(c(y), y))+b(y);
eq3b := a(y)*(diff(b(y), y))+c(y)*(diff(b(y), y));
eq4b := a(y)*(diff(c(y), y))+a(y)*(diff(b(y), y))+b(y);
inis := diff(a(x),x)=H(a(x)), diff(b(x),x)=H(b(x)), diff(c(x),x)=H(c(x)), a(1) = b(1), b(1) = c(1), a(0) = b(0), b(0) = c(0);
inis := diff(a(x),x)=H(a(x)), diff(b(x),x)=H(b(x)), diff(c(x),x)=H(c(x));
inio := diff(a(y),y)=H(a(y)), diff(b(y),y)=H(b(y)), diff(c(y),y)=H(c(y)),H(a(x)) + H(b(x)) = H(a(x)+b(x));
sol := dsolve([eq2a=1, eq3a=exp(a), eq4a=0, eq2b=1, eq3b=exp(b), eq4b=0, inis, inio], [a(x), b(x), c(x), a(y), b(y), c(y), H(a(x)), H(b(x)), H(a(y)), H(b(y))]);

I have a function c(k), I want to graph it where the x-axis has the units k/K (where K is a constant, about 0.0027). I was wondering how that is possible to do because for the life of me I can't figure out how to get maple to allow for relative units like that. Here's my code:

 

K:=0.0027

c := sqrt(9.8*K/k+0.7197e-1*k/K*(1/1000))

cmin:=(0.7197e-1*(4*9.8)*(1/1000))^(1/4);

C:=c/cmin

plot(C, k = 0 .. 4, 0 .. 4)

 

 

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