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Test for fatou.gp
#1
fatou.gp implements Kneser's super-logarithm or inverse of tetration for complex bases and complex heights.
Of course, We need some test to check behaviour of the program.

All results download(2019v1, 2019-09-11 GMT 15:00)
https://drive.google.com/drive/folders/1...sp=sharing

project for phase I:
P1-1. Show the behaviour for sexp and slog when all parameter is complex.
More results please click on the google drive link. Here are some pictures:
[Image: uc?export=view&id=1k5QpgRDh2TrK_Xbe_BFkUZm0Ab2TUmvh]
[Image: uc?export=view&id=1X67nwj7o3viRSP3VM-1Sz_J6t8UztLEq]
P1-2. Find the ill-behaviour and bug for fatou.gp.
https://math.eretrandre.org/tetrationfor...p?tid=1217
P1-3. Find the ill-behaviour and bug for superroot.gp.
More results please click on the google drive link.
Warning: I don't think I have a proper setup for superroot.gp
[Image: uc?export=view&id=1uZ3jQygRoa0HqSqBtP4RgErH5i7sRdtX]
project for phase II:
P2-1. Verify the new features in 2019v1 edition fatou.gp. 
[Image: uc?export=view&id=1TtxrteQ8eTb1WIubcg-tSiG4RI9-FEqj]
[Image: uc?export=view&id=1bplBlwPoCYAyX_6qs9z9gf-CUoTBQZXS]
It's more better in 2019v1 edition fatou.gp when circle closely around base zero. Add P2-3.

New ill-region base: close to 1, close the Shell-Thron region, Abs(base)>10E6.

P2-2. [b]Show the behaviour for pent, ipent, hex, ihex when all parameter is complex.[/b]
(working)
[b]P2-3. [b]Show the behaviour for [b]sexp and slog when circle closely around base zero.[/b][/b][/b]
(working)
[Image: uc?export=view&id=1BmC5Ql4urg_IM6YS1Du15yZyXyxqHpi4]
[Image: uc?export=view&id=1lMk7ZxIa9la9zWs0eUgP0Bv09xoVvfTj]
(working)

project for phase III: (planning)
[b]P3-1. [b]Show the behaviour for [b]sexp and slog when circle closely around base 1.[/b][/b][/b]
[b]P3-2. [b]Show the behaviour for [b]sexp and slog when base close the Shell-Thron region.[/b][/b][/b]

Wishlist:
W1. Holomorphic tetration to Base-0
It's looks mild when circle closely around base zero.
W2. Holomorphic tetration to Base-1
W3. Holomorphic tetration to Base-Infty
Upgrade from andydude work. 
W4. Holomorphic super-root (and hyper-5-root, hyper-6-root)
A trial version for super-root:
https://math.eretrandre.org/tetrationfor...44#pid8944
Reply
#2
More results with the ill-behaviour and bug for 2019v1 edition fatou.gp

P2-1-1. The initialization code for All test base.
Although all the initialization code is successful but not all can use sexp/slog.

Code:
matrix_ir(-0.01,400,250,14/15,45/46)
matrix_ir(-0.008,500,400,0.95,0.98)
matrix_ir(-0.005,500,400,0.96,0.985)
matrix_ir(-0.004,500,400,0.97,0.995)
matrix_ir(-0.003,500,400,0.98,0.999)
matrix_ir(-0.002+I*1E-30,600,250)
matrix_ir(-0.001+I*1E-30,600,250)
matrix_ir(-0.0009,600,250)
matrix_ir(-0.0008,600,250)
matrix_ir(-0.0005,600,250)
matrix_ir(-0.0001,600,250)
matrix_ir(-1E-5,600,250,14/15,45/46)
matrix_ir(-1E-6,600,250,14/15,45/46)
matrix_ir(-1E-7,600,250,14/15,45/46)
matrix_ir(-1E-8,600,250,14/15,45/46)
matrix_ir(-1E-9,600,250,14/15,45/46)
matrix_ir(-1E-10,600,250,14/15,45/46)
matrix_ir(-1E-15,600,250,0.9999,0.9999)
matrix_ir(-1E-16+I*1E-46,600,250,0.99,0.99)
matrix_ir(-1E-17,600,250,0.99,0.99)
/* 1E-18 fail */
matrix_ir(1E-17*(-1)^(29/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(28/30),600,250,0.975,0.975)
matrix_ir(1E-17*(-1)^(27/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(26/30),600,250,0.969,0.969)
matrix_ir(1E-17*(-1)^(25/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(24/30),600,250,0.969,0.969)
matrix_ir(1E-17*(-1)^(23/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(22/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(21/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(20/30),600,250,0.974,0.974)
matrix_ir(1E-17*(-1)^(19/30),600,250,0.976,0.976)
matrix_ir(1E-17*(-1)^(18/30),600,250,0.995,0.995)
matrix_ir(1E-17*(-1)^(17/30)+I*1E-47,600,250,0.989,0.989)
matrix_ir(1E-17*(-1)^(16/30),600,250,0.995,0.995)
matrix_ir(1E-17*(-1)^(15/30),600,90,0.999,0.999)
matrix_ir(1E-17*(-1)^(14/30),600,250,0.968,0.968)
matrix_ir(1E-17*(-1)^(13/30),700,250,0.978,0.978)
matrix_ir(1E-17*(-1)^(12/30),600,250,0.975,0.975)
matrix_ir(1E-17*(-1)^(11/30),600,250,0.975,0.975)
matrix_ir(1E-17*(-1)^(10/30),600,250,0.975,0.975)
matrix_ir(1E-17*(-1)^(9/30)+I*1E-30,600,250,0.975,0.975)
matrix_ir(1E-17*(-1)^(8/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(7/30),600,250,0.975,0.975)
matrix_ir(1E-17*(-1)^(6/30),600,250,0.985,0.985)
matrix_ir(1E-17*(-1)^(5/30),600,250,0.99,0.99)
matrix_ir(1E-17*(-1)^(4/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(3/30),650,300,0.98,0.98)
matrix_ir(1E-17*(-1)^(2/30)+I*1E-47,550,90,0.97,0.97)
matrix_ir(1E-17*(-1)^(1/30)+I*1E-47,700,90,0.99,0.99)
matrix_ir(1E-17+I*1E-47,600,250,0.99,0.99)
matrix_ir(1E-16+I*1E-46,600,250,0.98,0.98)
matrix_ir(1E-15+I*1E-45,600,250,0.975,0.975)
matrix_ir(1E-10,600,250,14/15,45/46)
matrix_ir(1E-9+I*1E-39,600,250,14/15,45/46)
matrix_ir(1E-8+I*1E-38,600,250,14/15,45/46)
matrix_ir(1E-7+I*1E-37,600,250,14/15,45/46)
matrix_ir(1E-6+I*1E-36,600,250,14/15,45/46)
matrix_ir(1E-5+I*1E-35,600,250,13/14,45/46)
matrix_ir(0.0001,400,250)
matrix_ir(0.0005,400,250)
matrix_ir(0.001+I*1E-30,400,250)
matrix_ir(0.005,400,250)
matrix_ir(0.01+I*1E-30,400,250)
matrix_ir(0.04,400,250)
matrix_ir(0.05+I*1E-30,400,250)
matrix_ir(0.06+I*1E-30,400,90,14/15,45/46)
matrix_ir(0.07,600,600,0.99,0.999)
matrix_ir(0.08,600,600,14/15,45/46)
matrix_ir(0.1,600,600,14/15,45/46)
matrix_ir(0.12+I*1E-30,400,90,14/15,45/46)
matrix_ir(0.14,400,400,14/15,45/46)
matrix_ir(0.16,400,400,14/15,45/46)
matrix_ir(0.18,400,400,14/15,45/46)
matrix_ir(0.2+I*1E-30,400,250)
matrix_ir(0.22+I*1E-30,400,250)
matrix_ir(0.24+I*1E-30,400,250)
matrix_ir(0.26,400,250)
matrix_ir(0.28,400,250)
matrix_ir(0.3+I*1E-30,400,250)
matrix_ir(0.32+I*1E-30,400,250)
matrix_ir(0.34+I*1E-30,400,250)
matrix_ir(0.36,400,250)
matrix_ir(0.38,400,250)
matrix_ir(0.4+I*1E-30,400,250)
matrix_ir(0.42+I*1E-30,400,250)
matrix_ir(0.44+I*1E-30,400,250)
matrix_ir(0.46,400,250)
matrix_ir(0.5+I*1E-30,400,250)
matrix_ir(0.52+I*1E-30,400,250)
matrix_ir(0.54,400,250)
matrix_ir(0.56,400,250)
matrix_ir(0.58+I*1E-30,400,250)
matrix_ir(0.6+I*1E-30,400,250)
matrix_ir(0.62,400,250)
matrix_ir(0.7,400,250)
matrix_ir(0.74+I*1E-30,400,250)
matrix_ir(0.76,400,250)
matrix_ir(0.78,400,250)
matrix_ir(0.8,400,250)
matrix_ir(0.82+I*1E-30,400,250)
matrix_ir(0.84,400,250)
matrix_ir(0.86,400,250)
matrix_ir(0.88+I*1E-30,400,250)
matrix_ir(0.9+I*1E-30,400,250)
matrix_ir(0.92,400,250)
matrix_ir(0.94+I*1E-30,400,250)
matrix_ir(0.96+I*1E-30,400,250)
matrix_ir(0.98,400,250)
matrix_ir(0.99+I*1E-30,400,250)
matrix_ir(0.999+I*1E-30,400,250)
matrix_ir(1+1E-3*(-1)^(1/30),400,250)
matrix_ir(1+1E-3*(-1)^(2/30),400,250)
matrix_ir(1+1E-3*(-1)^(3/30),400,250)
matrix_ir(1+1E-3*(-1)^(4/30),400,250)
matrix_ir(1+1E-3*(-1)^(5/30),400,250,13/14,44/45)
matrix_ir(1+1E-3*(-1)^(6/30),400,250,13/14,44/45)
matrix_ir(1+1E-3*(-1)^(7/30),400,250,13/14,44/45)
matrix_ir(1+1E-3*(-1)^(8/30),400,250,13/14,44/45)
matrix_ir(1+1E-3*(-1)^(9/30),400,250)
matrix_ir(1+1E-3*(-1)^(10/30),400,250)
matrix_ir(1+1E-3*(-1)^(11/30),400,250)
matrix_ir(1+1E-3*(-1)^(12/30),400,250)
matrix_ir(1+1E-3*(-1)^(13/30),400,250)
/* 14-29 fail */
matrix_ir(0.101+I*1E-30,400,250)
matrix_ir(0.11+I*1E-30,400)
matrix_ir(1.1,600,250)
matrix_r(1.04)
matrix_ir(etaB+1E-2,400,300)
matrix_r(etaB+1E-3)
matrix_r(etaB+1E-4)
matrix_r(etaB+1E-5)
matrix_r(etaB+1E-6)
matrix_r(etaB+1E-7)
matrix_r(etaB+1E-8)
matrix_r(etaB+1E-9)
matrix_r(etaB+1E-10)
matrix_r(etaB+1E-11)
matrix_r(etaB+1E-12)
matrix_r(etaB+1E-13)
matrix_r(etaB+1E-14)
matrix_r(etaB+1E-15)
matrix_r(etaB+1E-16)
matrix_r(etaB+1E-17)
matrix_r(etaB+1E-18)
matrix_r(etaB+1E-19)
matrix_r(etaB+(1E-19)*(-1)^(1/30))
matrix_r(etaB+(1E-19)*(-1)^(2/30))
matrix_r(etaB+(1E-19)*(-1)^(3/30))
matrix_r(etaB+(1E-19)*(-1)^(4/30))
matrix_r(etaB+(1E-19)*(-1)^(5/30))
matrix_r(etaB+(1E-19)*(-1)^(6/30))
matrix_r(etaB+(1E-19)*(-1)^(7/30))
matrix_r(etaB+(1E-19)*(-1)^(8/30))
matrix_r(etaB+(1E-19)*(-1)^(9/30))
matrix_r(etaB+(1E-19)*(-1)^(10/30))
/* 11-14 fail */
matrix_r(etaB+(1E-19)*(-1)^(15/30))
/* 16-20 fail */
matrix_r(etaB+(1E-19)*(-1)^(21/30))
matrix_r(etaB+(1E-19)*(-1)^(22/30))
matrix_r(etaB+(1E-19)*(-1)^(23/30))
matrix_r(etaB+(1E-19)*(-1)^(24/30))
matrix_r(etaB+(1E-19)*(-1)^(25/30))
matrix_r(etaB+(1E-19)*(-1)^(26/30))
matrix_r(etaB+(1E-19)*(-1)^(27/30))
matrix_r(etaB+(1E-19)*(-1)^(28/30))
matrix_r(etaB+(1E-19)*(-1)^(29/30))
matrix_r(etaB-1E-19)
matrix_r(etaB-1E-18)
matrix_r(etaB-1E-17)
matrix_r(etaB-1E-16)
matrix_r(etaB-1E-15)
matrix_r(etaB-1E-14)
matrix_r(etaB-1E-13)
matrix_r(etaB-1E-12)
matrix_r(etaB-1E-11)
matrix_r(etaB-1E-10)
matrix_r(etaB-1E-9)
matrix_r(etaB-1E-8)
matrix_r(etaB-1E-7)
matrix_r(etaB-1E-6)
matrix_r(etaB-1E-5)
matrix_r(etaB-1E-4)
matrix_r(etaB-1E-3)
matrix_ir(etaB-1E-2,400,300)


matrix_ir(1E-5*(-1)^(29/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(28/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(27/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(26/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(25/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(24/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(23/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(22/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(21/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(20/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(19/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(18/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(17/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(16/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(15/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(14/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(13/30),700,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(12/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(11/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(10/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(9/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(8/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(7/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(6/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(5/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(4/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(3/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(2/30),600,250,13/14,44/45)
matrix_ir(1E-5*(-1)^(1/30),600,250,13/14,44/45)

matrix_ir(1E6,,,19/20)
matrix_ir(1E7,,,19/20)
matrix_ir(1E8+I*1E-30,,,19/20)
matrix_ir(1E9+I*1E-30,,,19/20)
matrix_ir(1E10+I*1E-30,,,19/20)
matrix_ir(1E11+I*1E-30,,,19/20)

P2-1-2. Why have the line in 0<b<1 ?
[Image: uc?export=view&id=1J5PlukYJg3VvjRZhn0S9kylWveGhy-Y9]
ε=I*1E-30.
P2-1-3. Too small good-region in 1<b<eta.
[Image: uc?export=view&id=19mKMuNoJi8MR-cRQ_SmuCzPOm4_eQSJy]
P2-1-4. Can't circle closely around base 1 and eta.

P2-1-5. crash for big base.

Code:
matrix_ir(1E9,,,19/20);sexp(1)
Reply
#3
Thanks Ember; cool plots.  Do you have any suggested enhancements that help with any of these boundary conditions?  I don't have any additional enhancements to improve convergence near the singularities at 0, 1, exp(1/e)

Alternatively, give me one base that might interest you the most if it worked, and what settings you used, and I can see what the problem is for that base.
- Sheldon
Reply
#4
(09/13/2019, 07:18 PM)sheldonison Wrote: Thanks Ember; cool plots.  Do you have any suggested enhancements that help with any of these boundary conditions?  I don't have any additional enhancements to improve convergence near the singularities at 0, 1, exp(1/e)

Alternatively, give me one base that might interest you the most if it worked, and what settings you used, and I can see what the problem is for that base.

Please watch P2-1-2. Why have the line in 0<b<1? Is this normal? And why good-region in 1<b<eta is quite smaller than 0<b<1?

A big problem (program crash) will happen in 
Code:
matrix_ir(1E9,,,19/20);sexp(1)



I am researching this base:
Code:
matrix_ir(1+1E-5*I,400,250,0.999,0.999)
matrix_ir(1+1E-5,400,250,0.99,0.99)






You can see displacement in these carzy base: 
Code:
matrix_ir(-1E-8,600,250,14/15,45/46)
matrix_ir(-1E-9,600,250,14/15,45/46)
matrix_ir(-1E-10,600,250,14/15,45/46)
matrix_ir(-1E-15,600,250,0.9999,0.9999)
matrix_ir(-1E-16+I*1E-46,600,250,0.99,0.99)
matrix_ir(-1E-17,600,250,0.99,0.99)
matrix_ir(1E-17+I*1E-47,600,250,0.99,0.99)
matrix_ir(1E-16+I*1E-46,600,250,0.98,0.98)
matrix_ir(1E-15+I*1E-45,600,250,0.975,0.975)
matrix_ir(1E-10,600,250,14/15,45/46)
matrix_ir(1E-9+I*1E-39,600,250,14/15,45/46)
matrix_ir(1E-8+I*1E-38,600,250,14/15,45/46)
matrix_ir(1E-7+I*1E-37,600,250,14/15,45/46)
matrix_ir(1E-6+I*1E-36,600,250,14/15,45/46)
And mabey you can fix this:
Code:
matrix_ir(1E-17*(-1)^(28/30),600,250,0.975,0.975)
matrix_ir(1E-17*(-1)^(27/30),600,250,0.97,0.97)
matrix_ir(1E-17*(-1)^(24/30),600,250,0.969,0.969)
Reply


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