MaplePrimes Questions

Hi, I am using the GroupTheory package and I wanted to created the following group in Maple:

I stumbled across this link https://www.maplesoft.com/products/maple/features/grouptheory.aspx and then tried to use the following commands to define this group in Maple:

1. First a defined a 12x12 matrix:

ct := <<e | p | q | r | s | t | u | v | w | x | y | z>, <p | q | e | y | u | w | z | r | x | t | v | s>, <q | e | p | v | z | x | s | y | t | w | r | u>, <r | z | t | s | e | y | v | x | p | u | q | w>, <s | w | y | e | r | q | x | u | z | v | t | p>, <t | r | z | x | w | u | e | q | y | p | s | v>, <u | x | v | p | y | e | t | z | s | r | w | q>, <v | u | x | z | q | r | y | w | e | s | p | t>, <w | y | s | t | x | z | p | e | v | q | u | r>, <x | v | u | w | t | s | q | p | r | e | z | y>, <y | s | w | u | p | v | r | t | q | z | e | x>, <z | t | r | q | v | p | w | s | u | y | x | e>>

 

2. Then I tried to define my  group using:

G := Group(ct)

 

However this doesn't work because I get the following error:

Error, (in GroupTheory:-Group) invalid input: arguments to GroupTheory:-Group, [Matrix(12, 12, {(1, 1) = e, (1, 2) = p, (1, 3) = q, (1, 4) = r, (1, 5) = s, (1, 6) = t, (1, 7) = u, (1, 8) = v, (1, 9) = w, (1, 10) = x, (1, 11) = y, (1, 12) = z, (2, 1) = p, (2, 2) = q, (2, 3) = e, (2, 4) = y, (2, 5) = u, (2, 6) = w, (2, 7) = z, (2, 8) = r, (2, 9) = x, (2, 10) = t, (2, 11) = v, (2, 12) = s, (3, 1) = q, (3, 2) = e, (3, 3) = p, (3, 4) = v, (3, 5) = z, (3, 6) = x, (3, 7) = s, (3, 8) = y, (3, 9) = t, (3, 10) = w, (3, 11) = r, (3, 12) = u, (4, 1) = r, (4, 2) = z, (4, 3) = t, (4, 4) = s, (4, 5) = e, (4, 6) = y, (4, 7) = v, (4, 8) = x, (4, 9) = p, (4, 10) = ...  (12, 8) = s, (12, 9) = u, (12, 10) = y, (12, 11) = x, (12, 12) = e})], do not match any of the accepted calling sequences

 

I don't know what's going wrong. It doesn't give a 2D Plot. Thanks in advance.

Temperature over 24hr period

 

y := 0.26e-1*x^3-1.03*x^2+10.2*x+34, 0 <= x and x <= 24

``

``

 

NULL


 

Download temperature24hr.mw

BE312-1920-CW2-Amended-Maple-Codemw-46469mw-46557_(1).mw

 

How do you run this code in Maple 2019 to Maple 18 because I can't see the output?

Thank you

I thought the easiest way to show the world map, a projected flat map into 3d was to use the builtin one and just transform it.  You can zoom into it and rotate it no problem but unforunately it's not as clean as I thought.  Is it possible to have cleaner shading manipulating the Builtin map to 3d?

with(plots):
with(plottools):
with(DataSets):
with(Builtin):
m := WorldMap():
m1 := Display(m)
                                

to3d := transform((x, y) -> [x, y, 0]):
m2 := to3d(m1)
                               

display(m2)

 

 

If a maple command or function are not available on the target language  of the code generation of maple, is it possible to set myself the expected output for such cases so that the Csharp(...)  recognizes the cases and generates the expect code?

for example 

h := proc(x::Array(1 .. 3, 1 .. 3), y::Array(1 .. 3, 1 .. 3)) local z; z := evalm(x &* y); return z[1, 1] + z[2, 2]; end proc;
CSharp(h);

The function names {`&*`, evalm} can not be recognized in the target language

but for the &* it shoud be easy to add a template with the desired C# output. 

Is it possible to add templates in existing languages but not new language definitions?


 

I am trying to solve a set of equations

Why are the results not the same as the following results?

Is there any other way to get the correct answer?


 

NULL

T[1] := 3*a__0*a__1^2*q = 0

3*a__0*a__1^2*q = 0

(1)

T[2] := 2*a__1*k^2*m^2+a__1^3*q = 0

2*a__1*k^2*m^2+a__1^3*q = 0

(2)

T[3] := -a__1*b__1*k^2*m^2+3*a__1^2*b__1^2*q+3*a__0^2*a__1*b__1-a__1*b__1*k^2+a__1*b__1*p = 0

-a__1*b__1*k^2*m^2+3*a__1^2*b__1^2*q+3*a__0^2*a__1*b__1-a__1*b__1*k^2+a__1*b__1*p = 0

(3)

T[4] := a__0^3*q+6*a__0*a__1*b__1*q+a__0*p = 0

a__0^3*q+6*a__0*a__1*b__1*q+a__0*p = 0

(4)

T[5] := b__1^3*q+2*b__1*k^2 = 0

b__1^3*q+2*b__1*k^2 = 0

(5)

vars := {a__0, a__1, b__1, k}

{a__0, a__1, b__1, k}

(6)

sys1 := {}; SolsT := {}; for i to 5 do sys1 := `union`(sys1, {T[i]}) end do; sys := sys1

{}

 

{}

 

{3*a__0*a__1^2*q = 0, b__1^3*q+2*b__1*k^2 = 0, 2*a__1*k^2*m^2+a__1^3*q = 0, a__0^3*q+6*a__0*a__1*b__1*q+a__0*p = 0, -a__1*b__1*k^2*m^2+3*a__1^2*b__1^2*q+3*a__0^2*a__1*b__1-a__1*b__1*k^2+a__1*b__1*p = 0}

(7)

``

for i to 5 do indets(T[i]) end do

{a__0, a__1, q}

 

{a__1, k, m, q}

 

{a__0, a__1, b__1, k, m, p, q}

 

{a__0, a__1, b__1, p, q}

 

{b__1, k, q}

(8)

Solll := [solve(sys, vars, explicit)]

[{a__0 = 0, a__1 = a__1, b__1 = 0, k = (1/2)*(-2*q)^(1/2)*a__1/m}, {a__0 = 0, a__1 = a__1, b__1 = 0, k = -(1/2)*(-2*q)^(1/2)*a__1/m}, {a__0 = (-q*p)^(1/2)/q, a__1 = 0, b__1 = b__1, k = (1/2)*(-2*q)^(1/2)*b__1}, {a__0 = -(-q*p)^(1/2)/q, a__1 = 0, b__1 = b__1, k = (1/2)*(-2*q)^(1/2)*b__1}, {a__0 = (-q*p)^(1/2)/q, a__1 = 0, b__1 = b__1, k = -(1/2)*(-2*q)^(1/2)*b__1}, {a__0 = -(-q*p)^(1/2)/q, a__1 = 0, b__1 = b__1, k = -(1/2)*(-2*q)^(1/2)*b__1}, {a__0 = (-q*p)^(1/2)/q, a__1 = 0, b__1 = 0, k = k}, {a__0 = -(-q*p)^(1/2)/q, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (1/2)*(-2*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(1/2)*(-2*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*q*(m^2-6*m+1)*p)^(1/2)*m/(q*(m^2-6*m+1)), b__1 = -(-2*q*(m^2-6*m+1)*p)^(1/2)/(q*(m^2-6*m+1)), k = ((m^2-6*m+1)*p)^(1/2)/(m^2-6*m+1)}, {a__0 = 0, a__1 = -(-2*q*(m^2-6*m+1)*p)^(1/2)*m/(q*(m^2-6*m+1)), b__1 = (-2*q*(m^2-6*m+1)*p)^(1/2)/(q*(m^2-6*m+1)), k = ((m^2-6*m+1)*p)^(1/2)/(m^2-6*m+1)}, {a__0 = 0, a__1 = (-2*q*(m^2-6*m+1)*p)^(1/2)*m/(q*(m^2-6*m+1)), b__1 = -(-2*q*(m^2-6*m+1)*p)^(1/2)/(q*(m^2-6*m+1)), k = -((m^2-6*m+1)*p)^(1/2)/(m^2-6*m+1)}, {a__0 = 0, a__1 = -(-2*q*(m^2-6*m+1)*p)^(1/2)*m/(q*(m^2-6*m+1)), b__1 = (-2*q*(m^2-6*m+1)*p)^(1/2)/(q*(m^2-6*m+1)), k = -((m^2-6*m+1)*p)^(1/2)/(m^2-6*m+1)}, {a__0 = 0, a__1 = (-2*q*(m^2+6*m+1)*p)^(1/2)*m/(q*(m^2+6*m+1)), b__1 = (-2*q*(m^2+6*m+1)*p)^(1/2)/(q*(m^2+6*m+1)), k = ((m^2+6*m+1)*p)^(1/2)/(m^2+6*m+1)}, {a__0 = 0, a__1 = -(-2*q*(m^2+6*m+1)*p)^(1/2)*m/(q*(m^2+6*m+1)), b__1 = -(-2*q*(m^2+6*m+1)*p)^(1/2)/(q*(m^2+6*m+1)), k = ((m^2+6*m+1)*p)^(1/2)/(m^2+6*m+1)}, {a__0 = 0, a__1 = (-2*q*(m^2+6*m+1)*p)^(1/2)*m/(q*(m^2+6*m+1)), b__1 = (-2*q*(m^2+6*m+1)*p)^(1/2)/(q*(m^2+6*m+1)), k = -((m^2+6*m+1)*p)^(1/2)/(m^2+6*m+1)}, {a__0 = 0, a__1 = -(-2*q*(m^2+6*m+1)*p)^(1/2)*m/(q*(m^2+6*m+1)), b__1 = -(-2*q*(m^2+6*m+1)*p)^(1/2)/(q*(m^2+6*m+1)), k = -((m^2+6*m+1)*p)^(1/2)/(m^2+6*m+1)}]

(9)

for i to nops(Solll) do SOlls[i] := simplify(Solll[i], 'symbolic') end do

{a__0 = 0, a__1 = a__1, b__1 = 0, k = ((1/2)*I)*2^(1/2)*q^(1/2)*a__1/m}

 

{a__0 = 0, a__1 = a__1, b__1 = 0, k = -((1/2)*I)*2^(1/2)*q^(1/2)*a__1/m}

 

{a__0 = I*p^(1/2)/q^(1/2), a__1 = 0, b__1 = b__1, k = ((1/2)*I)*2^(1/2)*q^(1/2)*b__1}

 

{a__0 = -I*p^(1/2)/q^(1/2), a__1 = 0, b__1 = b__1, k = ((1/2)*I)*2^(1/2)*q^(1/2)*b__1}

 

{a__0 = I*p^(1/2)/q^(1/2), a__1 = 0, b__1 = b__1, k = -((1/2)*I)*2^(1/2)*q^(1/2)*b__1}

 

{a__0 = -I*p^(1/2)/q^(1/2), a__1 = 0, b__1 = b__1, k = -((1/2)*I)*2^(1/2)*q^(1/2)*b__1}

 

{a__0 = I*p^(1/2)/q^(1/2), a__1 = 0, b__1 = 0, k = k}

 

{a__0 = -I*p^(1/2)/q^(1/2), a__1 = 0, b__1 = 0, k = k}

 

{a__0 = 0, a__1 = 0, b__1 = b__1, k = ((1/2)*I)*2^(1/2)*q^(1/2)*b__1}

 

{a__0 = 0, a__1 = 0, b__1 = b__1, k = -((1/2)*I)*2^(1/2)*q^(1/2)*b__1}

 

{a__0 = 0, a__1 = 0, b__1 = 0, k = k}

 

{a__0 = 0, a__1 = I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2-6*m+1)^(1/2)), b__1 = -I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2-6*m+1)^(1/2)), k = p^(1/2)/(m^2-6*m+1)^(1/2)}

 

{a__0 = 0, a__1 = -I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2-6*m+1)^(1/2)), b__1 = I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2-6*m+1)^(1/2)), k = p^(1/2)/(m^2-6*m+1)^(1/2)}

 

{a__0 = 0, a__1 = I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2-6*m+1)^(1/2)), b__1 = -I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2-6*m+1)^(1/2)), k = -p^(1/2)/(m^2-6*m+1)^(1/2)}

 

{a__0 = 0, a__1 = -I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2-6*m+1)^(1/2)), b__1 = I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2-6*m+1)^(1/2)), k = -p^(1/2)/(m^2-6*m+1)^(1/2)}

 

{a__0 = 0, a__1 = I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2+6*m+1)^(1/2)), b__1 = I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2+6*m+1)^(1/2)), k = p^(1/2)/(m^2+6*m+1)^(1/2)}

 

{a__0 = 0, a__1 = -I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2+6*m+1)^(1/2)), b__1 = -I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2+6*m+1)^(1/2)), k = p^(1/2)/(m^2+6*m+1)^(1/2)}

 

{a__0 = 0, a__1 = I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2+6*m+1)^(1/2)), b__1 = I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2+6*m+1)^(1/2)), k = -p^(1/2)/(m^2+6*m+1)^(1/2)}

 

{a__0 = 0, a__1 = -I*2^(1/2)*p^(1/2)*m/(q^(1/2)*(m^2+6*m+1)^(1/2)), b__1 = -I*2^(1/2)*p^(1/2)/(q^(1/2)*(m^2+6*m+1)^(1/2)), k = -p^(1/2)/(m^2+6*m+1)^(1/2)}

(10)

 

Solsys := [allvalues([solve(sys, vars)])]

[[{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = (-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = (-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = (-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = (p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = (p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}], [{a__0 = 0, a__1 = a__1, b__1 = 0, k = -(-(1/2)*q)^(1/2)*a__1/m}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = -(-p/q)^(1/2), a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = 0, b__1 = b__1, k = -(-(1/2)*q)^(1/2)*b__1}, {a__0 = 0, a__1 = 0, b__1 = 0, k = k}, {a__0 = 0, a__1 = -(-2*p/(m^2*q-6*m*q+q))^(1/2)*m, b__1 = (-2*p/(m^2*q-6*m*q+q))^(1/2), k = -(p/(m^2-6*m+1))^(1/2)}, {a__0 = 0, a__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2)*m, b__1 = -(-2*p/(m^2*q+6*m*q+q))^(1/2), k = -(p/(m^2+6*m+1))^(1/2)}]]

(11)

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Hi all, assume data::list, I want check data is not empty, which one is faster ?

 

 

Greetings,

I need to numerically solve a set of about 95 simultaneous algebraic transcendental equations, with each having about 25 terms that are expressions of three independent variables and other parameters of the problem (some 2500 total terms).  I've had much difficulty solving this set on Engineering Equations Solver (EES, from fchart software), and I'm now suspecting bugs in that program.

I'm not able to find a spec sheet or user's manual that explains Maple's capabilities.  I haven't found a place to read about such things as, "maximum number of algebraic equations," or "maximum number of characters in an equation", or other kinds of guides that would give me a direct indication on the software's capabilities.

Is there a stand-alone desk top version than can crunch numbers without resource to the cloud?

Can anyone please direct me to a complete manual for the user explaining such details?  

Thanks,

Tom

I had expected that applying the power rule for exponents would lead to an answer of zero. Maple refuses to give the desired answer, but using a procedure it works as expected.

Did I miss something?
 

``

restart

kernelopts(version)

`Maple 2019.2, X86 64 WINDOWS, Nov 26 2019, Build ID 1435526`

(1)

interface(version)

`Standard Worksheet Interface, Maple 2019.2, Windows 10, November 26 2019 Build ID 1435526`

(2)

simplify(exp(k*(ln(t)+ln(a)))-(exp(ln(t)+ln(a)))^k, symbolic)

exp(k*(ln(t)+ln(a)))-t^k*a^k

(3)

W := proc (m, n) local r; r := simplify(exp(m*n)-(exp(m))^n, symbolic); return r end proc

W(n, k)

0

(4)

subs(n = ln(t)+ln(a), W(n, k))

0

(5)

V := proc (m, n) local r; r := simplify((exp(m))^n, symbolic); return r end proc

V(n, k)

exp(k*n)

(6)

V(ln(t)+ln(a), k)

t^k*a^k

(7)

``


 

Download mapleprimes.mw

Hi, 

Here is an example where evalf ( Int(....) ) fails to compute an in integral.
The function to integrate is very smooth and, except method=_Gquad, all the others seem to fail (even method=_MonteCarlo fails, which is probably the most surprising thing!)

Is it a weakness of evalf+Int or a misusse of my own ?

restart:

interface(version)

`Standard Worksheet Interface, Maple 2015.2, Mac OS X, December 21 2015 Build ID 1097895`

(1)

plot3d(cos(x*y), x=-1..3, y=-1..-0.2)

 

int(cos(x*y), [x=-1..3, y=-1..-1/5]);
evalf[15](%);

Si(3)+Si(1)-Si(3/5)-Si(1/5)

 

2.00705070023234

(2)

CodeTools:-Usage( evalf[10](Int(cos(x*y), [x=-1..3, y=-1..-0.2], method=_Gquad)) );

memory used=1.24KiB, alloc change=0 bytes, cpu time=0ns, real time=0ns, gc time=0ns

 

2.007050700

(3)

CodeTools:-Usage( evalf[10](Int(cos(x*y), [x=-1..3, y=-1..-0.2], method=_CubaVegas)) );

memory used=22.14KiB, alloc change=0 bytes, cpu time=16.99s, real time=17.01s, gc time=0ns

 

Int(Int(cos(x*y), x = -1. .. 3.), y = -1. .. -.2)

(4)

CodeTools:-Usage( evalf[10](Int(cos(x*y), [x=-1..3, y=-1..-0.2], method=_MonteCarlo)) );

memory used=12.79KiB, alloc change=0 bytes, cpu time=1000.00us, real time=0ns, gc time=0ns

 

Int(Int(cos(x*y), x = -1. .. 3.), y = -1. .. -.2)

(5)

N := 10^6:
X := Statistics:-Sample(Uniform(-1, 3), N):
Y := Statistics:-Sample(Uniform(-1, -0.2), N):
Z := cos~(X*~Y):
add(Z) / N * (4*0.8);

HFloat(2.0076470771803545)

(6)

 


 

Download evalf_Int.mw

 

I'm using variable names that have subscripts, not as a table index but literal i.e. R__1 as a unique variable name.  It seems whenever I make assumptions on variables that have subscripts, when I use them the variables that have subscripts are printed twice:

 

Can anyone explain why this happens and how to get around it?

 

Thanks in advance.

 

My problem in package error, does anyone had a solution ping this!

Dear Friends

I want to know that how can I plot a 2D curve in 3D? 

I need to plot the curve for example z=y^2, in a 3D space and exactly in the plane x=0. The ranges are -1<y<1, -1<x<1, 0<z<1

(I want to copy and paste this curve in another 3D figure.) 

Thanks a lot

alternatingseries.mw
I have a double about this alternating series.
According to maple this series converges:

evalf(sum((-1)^(n+1)*(ln(n)/n+1),n=1..infinity))
                          0.3401310963

However limit ln(n)/n + 1 does not equal to zero, it equals 1. Therefore the series should diverge.

Also while I am on the subject of series and limits, why is limit (-1)^n  as n goes to infinity a range between -1-I and 1 + I.

limit((-1)^(n), n=infinity)
                        -1 - I .. 1 + I

 

 

Hello, I am having a bit of difficulty simplifying some calculations in Maple 2019. In short, in order to verify that the tensors that I am trying to use are indeed inverses of each other, I am simply trying to multiply component wise, for example the tensor component e[2,~2] with the tensor component f[~2,2], since they are essentially inverses of each other, i.e. the matrix defining f is actually the inverse of the matrix e, i.e. f=e^(-1), should give back 1 as an answer. Nonetheless, when I attempt to take this simple multiplication Maple does not reduce it, but rather just gives multiplies the terms with no simplification. Is there anything I can do so that Maple may simplify its calculations? I have already tried the "eval" calling sequence but that didn't do the trick, and I fear that when escalating the calculations I will get a bunch of long expressions rather than concise solutions. Thank you for your help in advance,
 

Christoffel_symbols_of_de_Sitter_metric_research.mw

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