itsme

569 Reputation

13 Badges

12 years, 148 days

MaplePrimes Activity


These are questions asked by itsme

what's the easiest way to have maple simplify the expression below from 'expr1' to the form of 'desired_form'? mathematica automatically simplifies to that (subjectively of course!) much nicer looking form.

 


 

restart:

 

expr1:=-lambda-(1/2)*kappa__c-gamma__p-(1/2)*sqrt(-16*N*g^2+4*lambda^2-8*lambda*gamma__p+4*lambda*kappa__c+4*gamma__p^2-4*gamma__p*kappa__c+kappa__c^2);

-lambda-(1/2)*kappa__c-gamma__p-(1/2)*(-16*N*g^2+4*lambda^2-8*lambda*gamma__p+4*lambda*kappa__c+4*gamma__p^2-4*gamma__p*kappa__c+kappa__c^2)^(1/2)

(1)

desired_form:=1/2*(-2*gamma__p - kappa__c - 2 *lambda - sqrt(-16*N*g^2 + (-2 * gamma__p + kappa__c + 2 * lambda)^2));

-gamma__p-(1/2)*kappa__c-lambda-(1/2)*(-16*N*g^2+(-2*gamma__p+kappa__c+2*lambda)^2)^(1/2)

(2)

expr1- desired_form:
simplify(%);

0

(3)

 


 

Download factor_under_sqrt.mw

how can i get an 'implicit=false' form (no RootOf) of my eigenvalues from the Eigenvectors() command? Should one expect the behavior be the same in Eigenvectors() and Eigenvalues()?

thanks

 

restart:

 

 

M:=Matrix(3, 3, [[-2*lambda-kappa__c, -2*sqrt(2)*g, 0], [(1/2)*g*N*sqrt(2), -lambda-(1/2)*kappa__c-gamma__phi, -sqrt(2)*g], [0, g*N*sqrt(2), -2*gamma__phi]])

Matrix(3, 3, {(1, 1) = -2*lambda-`#msub(mi("κ",fontstyle = "normal"),mi("c"))`, (1, 2) = -2*sqrt(2)*g, (1, 3) = 0, (2, 1) = (1/2)*g*N*sqrt(2), (2, 2) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`, (2, 3) = -sqrt(2)*g, (3, 1) = 0, (3, 2) = g*N*sqrt(2), (3, 3) = -2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`})

(1)

LinearAlgebra:-Eigenvalues(M); #this is what i want but from Eigenvectors()

Vector(3, {(1) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`, (2) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+(1/2)*sqrt(-16*N*g^2+4*lambda^2+4*lambda*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-8*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`^2-4*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+4*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`^2), (3) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`-(1/2)*sqrt(-16*N*g^2+4*lambda^2+4*lambda*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-8*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`^2-4*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+4*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`^2)})

(2)

LinearAlgebra:-Eigenvalues(M, implicit=true); #RootOf notation; not what i want, but option works here

Vector(3, {(1) = -lambda-(1/2)*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`-`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`, (2) = RootOf(_Z^2+(2*lambda+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`)*_Z+4*N*g^2+4*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`, index = 1), (3) = RootOf(_Z^2+(2*lambda+`#msub(mi("κ",fontstyle = "normal"),mi("c"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`)*_Z+4*N*g^2+4*lambda*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`+2*`#msub(mi("γ",fontstyle = "normal"),mi("φ",fontstyle = "normal"))`*`#msub(mi("κ",fontstyle = "normal"),mi("c"))`, index = 2)})

(3)

evals, evecs:=LinearAlgebra:-Eigenvectors(M); #RootOf everywhere;

evals, evecs := Vector(3, {(1) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1), (2) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2), (3) = -lambda-(1/2)*`κ__c`-`γ__φ`}), Matrix(3, 3, {(1, 1) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`)^2, (1, 2) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`)^2, (1, 3) = 2/N, (2, 1) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`), (2, 2) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`), (2, 3) = -(1/4)*sqrt(2)*(2*lambda+`κ__c`-2*`γ__φ`)/(g*N), (3, 1) = 1, (3, 2) = 1, (3, 3) = 1})

(4)

 

 

evals, evecs:=LinearAlgebra:-Eigenvectors(M, implicit=false); #still RootOf everywhere;

evals, evecs := Vector(3, {(1) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1), (2) = RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2), (3) = -lambda-(1/2)*`κ__c`-`γ__φ`}), Matrix(3, 3, {(1, 1) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`)^2, (1, 2) = 8*g^2/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`)^2, (1, 3) = 2/N, (2, 1) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 1)+2*lambda+`κ__c`), (2, 2) = -2*sqrt(2)*g/(RootOf(_Z^2+(2*lambda+`κ__c`+2*`γ__φ`)*_Z+4*g^2*N+4*`γ__φ`*lambda+2*`γ__φ`*`κ__c`, index = 2)+2*lambda+`κ__c`), (2, 3) = -(1/4)*sqrt(2)*(2*lambda+`κ__c`-2*`γ__φ`)/(g*N), (3, 1) = 1, (3, 2) = 1, (3, 3) = 1})

(5)

 

 


 

Download evals.mw

 

 

 

 

Not sure if i'm missing something, but this does not seem to work how i would expect.

Trying to understand why the [1,1] element is simplifed to -3, as well as the [3,3] element to -2. 

Any ideas?

thanks!
 

restart:

MM:=Matrix(convert("{{1/2 (-2 \[Kappa] - 4 \[Lambda]), -2 Sqrt[2] g, 0}, {g/Sqrt[
  2], -\[CapitalGamma] - \[Kappa]/2 - \[Lambda], -Sqrt[2] g}, {0,
  Sqrt[2] g, -2 \[CapitalGamma]}}", FromMma));

"[[[-1/2 2(Kappa)-1/2 4(Lambda),-2 sqrt(2) g,0],[(g)/(sqrt(2)),-CapitalGamma-1/2 Kappa-Lambda,-sqrt(2) g],[0,sqrt(2) g,-2(CapitalGamma)]]]"

(1)

simplify(MM); #why is the first element simplified this way?

Matrix(3, 3, {(1, 1) = -3, (1, 2) = -2*sqrt(2)*g, (1, 3) = 0, (2, 1) = (1/2)*sqrt(2)*g, (2, 2) = -CapitalGamma-(1/2)*Kappa-Lambda, (2, 3) = -sqrt(2)*g, (3, 1) = 0, (3, 2) = sqrt(2)*g, (3, 3) = -2})

(2)

 


 

Download translate_from_mma.mw

i've come across a confusing behavior where the same command (a copy/paste of another command) is giving an output in a a different form.

Attaching a screen shot that shows this. Eq 6.8 is executed just after 6.7.

(i know the command is weird, i.e. subs(beta=beta, ..), etc.. this is part of some larger code base and i just put this in when trying to undertand what's going on).

I would hope for the same command to spit out the same output in this case. (nothing else gets assigned/called in betwen).

any idea what's going on?

 

i'm on maple 2018.2 on linux.

thanks

 

 

does anyone khow to force maple to automatically simplify expressions that look like this:

restart:

cc:=arctan(sin(phi)/cos(phi))-arccos(cos(phi))      
simplify(cc) assuming phi::real; #should be zero

i've played with convert/expand/simplify and in certain cases of course i can force maple to do this... (kind of manually).. but was hoping this could be more automatic.

thanks!

 

1 2 3 4 5 6 7 Last Page 1 of 10