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simplify expression under sqrt ...

itsme 769 Maple
simplify simplification sqrt
April 24 2019
3 3

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.

 


 

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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)
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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)
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expr1- desired_form:
simplify(%);

0

 (3)
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Download factor_under_sqrt.mw

Implicit=false in Eigenvectors() vs Eige...

itsme 769 Maple
linearalgebra eigenvalues
April 24 2019
1 1

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

 

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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)
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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)
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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)
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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)
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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)
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Download evals.mw

 

 

 

 

convert code from mathematica to maple...

itsme 769 Maple
mathematica frommma mmatranslator
April 19 2019
1 5

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!
 

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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)]]]"

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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)
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Download translate_from_mma.mw

same command, different output form...

itsme 769 Maple
assuming series subs
November 09 2018
1 1

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

 

 

how to get maple to automatically simpli...

itsme 769 Maple
simplification trig
November 07 2018
3 3

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!

 

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