Adam Ledger

Mr. Adam Ledger

360 Reputation

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9 years, 148 days
unemployed
hobo
Perth, Australia

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These are replies submitted by Adam Ledger

here is the result

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/GROUP_REDUCTION_METHOD_EXAMPLE_20.mw .

Download GROUP_REDUCTION_METHOD_EXAMPLE_20.mwGROUP_REDUCTION_METHOD_EXAMPLE_20.mwGROUP_REDUCTION_METHOD_EXAMPLE_20.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/GROUP_REDUCTION_METHOD_EXAMPLE_20.mw .

Download GROUP_REDUCTION_METHOD_EXAMPLE_20.mw

Maple Worksheet - Error

Failed to load the worksheet /maplenet/convert/GROUP_REDUCTION_METHOD_EXAMPLE_20.mw .

Download GROUP_REDUCTION_METHOD_EXAMPLE_20.mw

 what i was trying to achieve

@nm look if you are in the same situation as i am sure i understand why they piss you off but the help system is extremely good, it would be hypocritical for me to say otherwise when i have used it so much.

and it has a bug where it sometimes inserts an additional comma somehow when you copy and paste stuff to and from inert  text and command line.

but seriously if you cant see why what you posted doesnt work, i just dont know what i can do to help you to be honest. anyway, this will help:

help(unapply);

showstat(unapply);

as in, if you look at the group above, very easy to see it can be reducled to only 3 2x2 matrices which can be parameterized with scalars to produce the total group as shown, ie it is a reducible group and im asking if there is a patch of code already for this. maple has a broad scope of computation in terms of set theory operators that hand complex arguements, thats in a nut shell why it appealled to me.

Well i didnt know these where done by maple already also! but just at first glance, two things stand out.

1) the function is only required to be algebraic

2)  these two lines are the transform being performed when the CAS is able to determine the ceiling

       F := eval(fnc,var = t);
       1/GAMMA(-v)*int((var-t)^(-v-1)*F,t = 0 .. var);

3) the reasons for failure of the procedure have been listed by the author of the code as seen below are:

"Cannot decide sign of integer order of derivative"

"Unable to determine ceiling of"

 

So, those would be the first few things i would take a look at, the transform being performed on F indeed looks like a laplace integral or inverse of, but anyway, that would be my starting place, manipulation of the arguements and functions of those arguements that the maple procedure executes.

showstat(fracdiff);

the error term for which i was previously referring to being convergent

CONGRUENT_FUNCTIONS_OF_THE_FRACTIONAL_PART_OVER_Q_LEMMA_411ERROR_TERM_ALL_ZERO_IDS.mw

yea it will take a few hours sometimes for mine to be visible i guess maybe they r doing the maintenance? lol

yep thanks i forgot about that one actually old favorite i am trying to work around using the floor function as much as i did in the past tho, ive found everything still seems to get buggy when its used in an indexing function( ie in the oprands of a discrete sum or series) but ill see how it goes

is there a chance you can whip up something like chloroform so that after im done she doesnt want talky time and understands the importance of me studying? well, not exactly, but yea passed out will do.

if (1) and (2) are known to have exact solutions and are of the same order, however one linear and the other non-linear.

yep. it is imbarassing being back to front at times.

@Carl Love just looking at the first case i submitted to the maple applications centre, the lastexception had error message "lack of hypergeometric convergence" so, im guessing thats why i wasnt welcoming with ballons and cake.

 

Its still very well within the CAS error handling potential either way well at least im confident looking at it 3 or 4 months later with the other case for psi i showed, so i dont see whats the need for all the phantom of the opera dramatics.

IS_problem_psi_function_lemma_4_and_asymptoptic_relation_of_interest.mw

`𝒜`[S](PI(z), z, n): approximation to n terms of accuracy to the infinite asymptopic series expansion of  PI(z)*centered*at*z = 0``

``

FunctionAdvisor(Psi, quiet):

`𝒜`[f] := proc (F, N) options operator, arrow; convert(asympt(F, z, N), 'polynom') end proc

proc (F, N) options operator, arrow; convert(asympt(F, z, N), 'polynom') end proc

(1)

`ℱ` := proc (Y) options operator, arrow; Y*exp(-2*Psi(Y)-Pi*cot(Pi*Y)) end proc

`𝒦` := proc (s) options operator, arrow; eval(`ℱ`(Y), Y = -(1/2)*s/Pi) end proc

is(diff((ln(2*`𝒦`(1/z)*Pi*z)+2*Psi(-1/(2*Pi*z))-Pi*cot(1/(2*z)))/(I*Pi)-1, z) = 0)

true

(2)

[seq(`𝒜`[f](Pi^(2*k-1)*z^(2*k-1)*(exp(Pi*z))^2*`𝒦`(1/z)/exp(2*gamma), k), k = 1 .. 10)]

[-1/2, -(1/2)*Pi^2*z^2, -(1/2)*Pi^4*z^4-(1/4)*Pi^2*Zeta(3)*z^2, -(1/2)*Pi^6*z^6-(1/4)*Pi^4*Zeta(3)*z^4, -(1/2)*Pi^8*z^8-(1/4)*Pi^6*Zeta(3)*z^6-(1/16)*Pi^4*(Zeta(5)+Zeta(3)^2)*z^4, -(1/2)*Pi^10*z^10-(1/4)*Pi^8*Zeta(3)*z^8-(1/16)*Pi^6*(Zeta(5)+Zeta(3)^2)*z^6, -(1/2)*Pi^12*z^12-(1/4)*Pi^10*Zeta(3)*z^10-(1/16)*Pi^8*(Zeta(5)+Zeta(3)^2)*z^8-(1/192)*Pi^6*(3*Zeta(7)+6*Zeta(3)*Zeta(5)+2*Zeta(3)^3)*z^6, -(1/2)*Pi^14*z^14-(1/4)*Pi^12*Zeta(3)*z^12-(1/16)*Pi^10*(Zeta(5)+Zeta(3)^2)*z^10-(1/192)*Pi^8*(3*Zeta(7)+6*Zeta(3)*Zeta(5)+2*Zeta(3)^3)*z^8, -(1/2)*Pi^16*z^16-(1/4)*Pi^14*Zeta(3)*z^14-(1/16)*Pi^12*(Zeta(5)+Zeta(3)^2)*z^12-(1/192)*Pi^10*(3*Zeta(7)+6*Zeta(3)*Zeta(5)+2*Zeta(3)^3)*z^10-(1/768)*Pi^8*(3*Zeta(9)+6*Zeta(3)*Zeta(7)+3*Zeta(5)^2+6*Zeta(5)*Zeta(3)^2+Zeta(3)^4)*z^8, -(1/2)*Pi^18*z^18-(1/4)*Pi^16*Zeta(3)*z^16-(1/16)*Pi^14*(Zeta(5)+Zeta(3)^2)*z^14-(1/192)*Pi^12*(3*Zeta(7)+6*Zeta(3)*Zeta(5)+2*Zeta(3)^3)*z^12-(1/768)*Pi^10*(3*Zeta(9)+6*Zeta(3)*Zeta(7)+3*Zeta(5)^2+6*Zeta(5)*Zeta(3)^2+Zeta(3)^4)*z^10]

(3)

 


Download IS_problem_psi_function_lemma_4_and_asymptoptic_relation_of_interest.mw

@Carl Love 

 

you might of already got here by now but this would be my take ive already uploaded you the first part may as well send theseIS_evalf_fix_case_three_error_DELTAS.mw

`𝒜`[S](PI(z), z, n): approximation to n terms of accuracy to the infinite asymptopic series expansion of  PI(z)*centered*at*z = 0``

``

FunctionAdvisor(Psi, quiet):

"`𝒜`[S]:=(convert( asympt( PI(z), n, N), 'polynom')"

 

`ℱ` := proc (Y) options operator, arrow; Y*exp(-2*Psi(Y)-Pi*cot(Pi*Y)) end proc:

`𝒦` := proc (s) options operator, arrow; eval(`ℱ`(Y), Y = -(1/2)*s/Pi) end proc:

`ℋ`[1] := proc (y) options operator, arrow; eval(`𝒦`(s), s = 1/2+I*y) end proc:

`ℋ`[2] := proc (y) options operator, arrow; eval(`𝒦`(s), s = 1/2-I*y) end proc:

E := 2*ln(sqrt(256/125)*(limit(abs(`ℋ`[1](s)*`ℋ`[2](s))^2, s = 1))^(1/2)*(1/(sqrt(5)*Pi^2))^(-1))/((25*(1/110))*sqrt(506+22*sqrt(23)))+1 = 0:

is(E)

FAIL

(1)

H[0] := limit(abs(`ℋ`[1](s)*`ℋ`[2](s))^2, s = 1):

H[1] := allvalues(RootOf(2*ln((16/5)*sqrt(h)*Pi^2)/((25*(1/110))*sqrt(506+22*sqrt(23)))+1)):

ERRORDELTA1 := proc (n) options operator, arrow; evalf[n](H[0])-evalf[n](H[1]) end proc:

ERRORDELTA2 := proc (N) options operator, arrow; CurveFitting[RationalInterpolation](map(convert, [seq([n, (1/177)*ERRORDELTA(n+11)*10^(n+11)], n = 1 .. 10)], 'rational'), N) end proc

proc (N) options operator, arrow; CurveFitting[RationalInterpolation](map(convert, [seq([n, (1/177)*ERRORDELTA(n+11)*10^(n+11)], n = 1 .. 10)], 'rational'), N) end proc

(2)

[seq([k, ERRORDELTA2(k)], k = 1 .. 10)]

[[1, 1/1000], [2, 1/100], [3, 1/10], [4, 1], [5, 10], [6, 100], [7, 1000], [8, 10000], [9, 100000], [10, 1000000]]

(3)

``


Download IS_evalf_fix_case_three_error_DELTAS.mw

@Carl Love see it works both ways for the evalf, some cases like case 3 im sharing with you today, thats extremly precise computation i dont mean to be rude or critical when im say a problem with this and that no i wouldnt use the software if i wasnt impressed with its functionality of course.

@Carl Love this is case three on the same part of my studies on the psi function, and i would remark the closeness of this approximation should be of reasonable interest to you

``

``

FunctionAdvisor(Psi, quiet):

``

 

`ℱ` := proc (Y) options operator, arrow; Y*exp(-2*Psi(Y)-Pi*cot(Pi*Y)) end proc

proc (Y) options operator, arrow; Y*exp(-2*Psi(Y)-Pi*cot(Pi*Y)) end proc

(1)

`𝒦` := proc (s) options operator, arrow; eval(`ℱ`(Y), Y = -(1/2)*s/Pi) end proc

proc (s) options operator, arrow; eval(`ℱ`(Y), Y = -(1/2)*s/Pi) end proc

(2)

`ℋ`[1] := proc (y) options operator, arrow; eval(`𝒦`(s), s = 1/2+I*y) end proc

proc (y) options operator, arrow; eval(`𝒦`(s), s = 1/2+I*y) end proc

(3)

`ℋ`[2] := proc (y) options operator, arrow; eval(`𝒦`(s), s = 1/2-I*y) end proc

proc (y) options operator, arrow; eval(`𝒦`(s), s = 1/2-I*y) end proc

(4)

E := 2*ln(sqrt(256/125)*(limit(abs(`ℋ`[1](s)*`ℋ`[2](s))^2, s = 1))^(1/2)*(1/(sqrt(5)*Pi^2))^(-1))/((25*(1/110))*sqrt(506+22*sqrt(23)))+1 = 0:

is(E)

FAIL

(5)

simplify(sqrt(256/125)*H[1]^(1/2)*(1/(sqrt(5)*Pi^2))^(-1))

(16/5)*H[1]^(1/2)*Pi^2

(6)

H[0] := limit(abs(`ℋ`[1](s)*`ℋ`[2](s))^2, s = 1):

H[1] := allvalues(RootOf(2*ln((16/5)*sqrt(h)*Pi^2)/((25*(1/110))*sqrt(506+22*sqrt(23)))+1)):

evalf[100](H[0]), evalf[100](H[1])

0.3633265308701580349381170477570478491823611496659343613675006167796108877920534986053500377774416407e-5, 0.3633265132104698217425574219913442503492158503857492441267673903331440002490789044931789020378047661e-5

(7)

``


Download IS_case_three.mw

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