Hello all of you,

I'm new here and I have a problem.

For homework I have to write a Maple package for the usage of dual quaternions. This is not a problem.

For example two functions of the package:

MyQuaternions := module()

  export Pretty, Ugly:
  local l1:
  option package:
 
  protect('i,j,k,epsilon'):
 
Pretty := proc(q::Vector)
  description "":
  return LinearAlgebra[Transpose](q)[1..4].Vector([1,i,j,k])+epsilon*(LinearAlgebra[Transpose](q)[5..8].Vector([1,i,j,k])):
end proc:

Ugly := proc(q)
  description "":
  local a;
  a := Vector(8);
  a[1]:=remove(has,remove(has,q,epsilon),{i,j,k});
  a[2]:=coeff(remove(has,q,epsilon),i,1);
  a[3]:=coeff(remove(has,q,epsilon),j,1);
  a[4]:=coeff(remove(has,q,epsilon),k,1);
  a[5]:=remove(has,coeff(q,epsilon),{i,j,k});
  a[6]:=coeff(coeff(q,epsilon),i,1);
  a[7]:=coeff(coeff(q,epsilon),j,1);
  a[8]:=coeff(coeff(q,epsilon),k,1);
  return a:
end proc:

end module:

savelib('MyQuaternions'):

Now I can load the module in a differnet maple worksheet "main.mw" by typing "with(MyQuaternions):"

The crucial thing now is the following: i,j,k,epsilon should be protected in "main.mw". I can do this by typing "protect('i,j,k,epsilon'):" Is there a way to tell maple to protect these variables automatically when the module is loaded? Or do I always have to type in the protect command by hand?

Thank you,

Josef

For application of object recognition with 3d sensor

plot3d(subs(c=1, a*b+a*c), a=-1..1, b=-1..1);
plot3d(subs(c=1, a+a*b*c), a=-1..1, b=-1..1);

after draw above two equations, they looked having similar structure

i find a book

Differential Geometry and its application John Oprea, page 98

having some measure to determine the shape, however they seems for

2 variables and need parametric form

how to use them to determine above two equations which have 3 variables

a*b+a*c  and  a+a*b*c

though not know the 3 variables version of below code, 

i think subs(c=1, a*b+a*c), subs(a=1, a*b+a*c), subs(b=1, a*b+a*c)

3 sets of equations after substitute third variables with 1, is it still possible to determine the shape?

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:
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:
shape := proc(X)
local Y,Z,a,b,c,d;
Y:=EFG(X);
Z:=lmn(X);
a:=simplify((Z[1]*Y[3]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
b:=simplify((Z[2]*Y[1]-Z[1]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
c:=simplify((Z[2]*Y[3]-Z[3]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
d:=simplify((Z[3]*Y[1]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
[S(x_u)=a*x_u+b*x_v,S(x_v)=c*x_u+d*x_v];
end:
shape_matrix := proc(X)
local Y,Z,a,b,c,d;
Y:=EFG(X);
Z:=lmn(X);
a:=simplify((Z[1]*Y[3]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
b:=simplify((Z[2]*Y[1]-Z[1]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
c:=simplify((Z[2]*Y[3]-Z[3]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
d:=simplify((Z[3]*Y[1]-Z[2]*Y[2])/(Y[1]*Y[3]-Y[2]^2));
Matrix([[a,c],[b,d]]);
end:

how to convert between (system of polynomials or module) and rational function which is a four dimensional space

1. is module in algebraic geometry or group cohomology to classify homology group?

2. is final result like this? for example,

a dictionary  or table store

homology group 1, key=invariant = 1 hole in topological space , value = module 1, module 2 module 3 etc

homology group 2, key=invariant = 2 holes in topological space , value =module 4, module 5, module 6 etc

homology group 3, key=invariant = 3 holes in topological space , value = module 7, module 8.. etc

 ... etc

3. i find betti number can count holes, however how to know the form for

all combination?

i mean if it is module, how to change the module to get the full combination

http://www.singular.uni-kl.de/Manual/html/sing_159.htm

i find betti number's input is just ideal, but it is not module

if ideal is enough, why need module?

how to permuate module? and what do it classify and result in module?

1. is module in algebraic geometry for classification of topological space which a poset is a frame

2. which invariant is for doing this classification of topological space in algebraic geometry or group cohomology?

3. if want to do full combination before classification, which kind of polynomials be a full combination

4. is poset just like function fst and snd function for meet and join in functional programming instead of using "and" and "or" logic? how a matrix group related with topological space which a poset is a frame?

5. is there any invariant function for classification of topological space in maple?

I am working on fopurier analysis and below is what I have. The method I used worked fine when I had a piecewise continuous function, but now the bottom int function below is not calculating the integral.

restart;
with(plots);

f := 2*sin(Pi-Pi*exp(-t))

A[0] := (1/3)*(Int(f, t = 0 .. 3))

A[0] := (1/3)*(int(f, t = 0 .. 3))   I think this one is evaluating it correctly. The bold and italicized below is the answer from this calulation

A[0] := (2/3)*Si(Pi)-(2/3)*Si(exp(-3)*Pi)

a[n] := (2/3)*(Int(f*cos(2*Pi*n*t*(1/3)), t = 0 .. 3))  this prints the integral like I want it to.

a[n] := (2/3)*(int(f*cos(2*Pi*n*t*(1/3)), t = 0 .. 3))  this just reporints the integral, I want it to evaluate it. Am I doing something wrong? Even with the assume(n, integer); it still just prints the integral.

Is there any help that y'all can provide? My professor is not ver proficent in the Math softwares out there.

Hello,

how to write a^tilde , a^check on maple

thank,

Gerard.

How about this equation

restart:
solve(x^2 - 2*(m+1)*x+m^2 - 2*m + m^2=0,{x},parametric=full);
allvalues(%);?

Greetings to all!

Recently I encouter the following issue:

Maple (version 17) coudn't recognize that 20.0 equals with 20 and with 20.00. Believe me, this is very annoying!

Do I miss something? Is there any command that do the trick?

Thank you!

Giorgos K.

Hi,

   I have a set of linear equations in terms of Ax+B=0, where A and B are matrices.

  I used linsolve or LinearSolve to solve the equations.

   Is there any simple way to run linsolve/LinearSolve parallelly? suppose I already have matrices A and B.

Thank you very much

#page 320 and 322 of book Singular introduction to commutative algebra

it return too many recursion 

hilbertseries([a+a*c, a+a*b, a+b+c]);

eq1 := a+a*c;

eq2 := a+a*b;

eq3 := a+b+c;

eq1a := Homogenize(eq1, h);

eq2a := Homogenize(eq2, h);

eq3a := Homogenize(eq3, h);

T3:=lexdeg([a,b,c,h]);

GB := Basis([eq1a,eq2a,eq3a], T3); #a

#MonomialHilbertPoincare(LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3));

with(PolynomialIdeals):

MonomialHilbertPoincare := proc (I3)

#I3:=[LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3)];

T2:=lexdeg([h,c,b,a]);

varj := [h,c,b,a];

I2 := InterReduce(I3, T2);

s := nops(I2);

if I2[1] = 0 then return 1 end if:

if I2[1] = 1 then return 0 end if:

if degree(I2[s]) = 1 then return (1-varj[1])^s end if:

lt := LeadingTerm(I2[s],T2);

leadexp := [degree(lt[2],h),degree(lt[2],c),degree(lt[2],b),degree(lt[2],a)];

j := 1;

for z from 1 to nops(leadexp) do

                if leadexp[j] = 0 then

                                j := j + 1;

                end if:

od:

finallist := [];

for z from 1 to nops(GB) do

                finallist := [op(finallist), GB[z]+varj[j]];

od:

quotientlist := Generators(Quotient(GB, varj[j]));

finallist2 := [];

for z from 1 to nops(quotientlist) do

                finallist2 := [op(finallist2), op(z,quotientlist)];

od:

return MonomialHilbertPoincare(finallist) + varj[1]*MonomialHilbertPoincare(finallist2);

end proc;

F:=[LeadingMonomial(GB[1],T3), LeadingMonomial(GB[2],T3), LeadingMonomial(GB[3],T3)];

MonomialHilbertPoincare(F);

but if restart the program，the menu of Plot Builder is appear，in same function（x^2+y^2+(1/1000000000)*z-25 = 0），why thing like this happen？

when run the order like this, the menu of Plot builder disapper

Thank you in advance for your help

Hi,

I was wondering how I could assign small angel assumptions so that I could simplify an equation of motion to solve for theta double dot. Thank you for your help.

Download small_angle_assumption.mw

Download small_angle_assumption.mw

with(Groebner):
eq1 := a+b*c;
eq2 := a*b*c+a;
eq1a := Homogenize(eq1, h);
eq2a := Homogenize(eq2, h);
eliminate([eq1a,eq2a], h);

after eliminate not equal to eq1 and eq2

Hello,

How can I pde with maple?please explain completely,and other question :How can I solve pde with plot in maple because some questions dont have exact answer?