Examples from "Minimization of Differential Equations and Algebraic Values of E-Functions" requires algvalues and a recent version of gfun, to be downloaded from https://perso.ens-lyon.fr/bruno.salvy/software/the-gfun-package/
restart;st:=time():
with(gfun,minimizediffeq):
if gfun:-version()<3.95 then error "this worksheet requires a recent version of gfun" fi;
infolevel[minimizediffeq]:=4: # reduce to display less information
read "algvalues.mpl";
minimizediffeq
Example 2.2.3
uu:=Sum(n!*(n+k)!/k!^4/(n-k)!^3,k=0..n);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSN1dUdGKC1JJFN1bUdGJTYkKiotSSpmYWN0b3JpYWxHRiY2I0kibkdGKCIiIi1GMzYjLCZGNUY2SSJrR0YoRjZGNi1GMzYjRjohIiUtRjM2IywmRjVGNkY6ISIiISIkL0Y6OyIiIUY1NyNGLg==
SumTools[Hypergeometric][Zeilberger](op(1,uu),n,k,Sn)[1];
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
degree(%,Sn);
IiIl
deq:=gfun:-rectodiffeq({add(coeff(%%,Sn,i)*u(n+i),i=0..%),seq(u(i)=value(eval(uu,n=i)),i=0..%-1)},u(n),y(z));
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
With this option use_ILP=2, the computation is that described in sections 2.2.3 & 2.3.6
minimizediffeq(deq,y(z),use_ILP=2);
minimizediffeq: entering with order 10 and degree 8
minimizediffeq: looking for a factor of order 9
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.008 sec.
minimizediffeq: ILP completed in 0.07 sec.
minimizediffeq: no feasible integer solution
minimizediffeq: proved no factor of order 9
minimizediffeq: looking for a factor of order 8
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.004 sec.
minimizediffeq: ILP completed in 0.221 sec.
minimizediffeq: no feasible integer solution
minimizediffeq: proved no factor of order 8
minimizediffeq: looking for a factor of order 7
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: ILP completed in 0.024 sec.
minimizediffeq: no feasible integer solution
minimizediffeq: proved no factor of order 7
minimizediffeq: looking for a factor of order 6
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.004 sec.
minimizediffeq: ILP improved bound from 5 to 4 in 0.038 sec.
minimizediffeq: # apparent singularities <= 4
minimizediffeq: bound on the degrees of the coefficients at order 6: [30, 29, 28, 26, 26, 26, 26]
minimizediffeq: computing 25 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 73 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found modular operator of order 6 and degree 8
minimizediffeq: modular gcrd of order 6 and degree 8
minimizediffeq: computing 75 rational coefficients
minimizediffeq: try guessing
minimizediffeq: checking equation of order 6
minimizediffeq: it is a right factor
minimizediffeq: found a right factor of order 6
minimizediffeq: looking for a factor of order 5
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: ILP improved bound from 3 to 2 in 0.01 sec.
minimizediffeq: # apparent singularities <= 2
minimizediffeq: bound on the degrees of the coefficients at order 5: [15, 14, 13, 13, 13, 13]
minimizediffeq: computing 97 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: looking for a factor of order 4
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 4 not larger
minimizediffeq: looking for a factor of order 3
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 3 not larger
minimizediffeq: looking for a factor of order 2
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 2 not larger
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.004 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 1 not larger
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
The same result is achieved without the option, with different intermediate computations:
minimizediffeq(deq,y(z));
minimizediffeq: entering with order 10 and degree 8
minimizediffeq: looking for a factor of order 9
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.006 sec.
minimizediffeq: # apparent singularities <= 3
minimizediffeq: bound on the degrees of the coefficients at order 9: [36, 35, 34, 33, 32, 31, 26, 26, 26, 26]
minimizediffeq: computing 14 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 40 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 118 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found modular operator of order 6 and degree 8
minimizediffeq: modular gcrd of order 6 and degree 8
minimizediffeq: computing 75 rational coefficients
minimizediffeq: try guessing
minimizediffeq: checking equation of order 6
minimizediffeq: it is a right factor
minimizediffeq: found a right factor of order 6
minimizediffeq: looking for a factor of order 5
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 5 not larger
minimizediffeq: looking for a factor of order 4
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 4 not larger
minimizediffeq: looking for a factor of order 3
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 3 not larger
minimizediffeq: looking for a factor of order 2
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 2 not larger
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 1 not larger
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
Note at the end of 2.3.6
minimizediffeq(deq,y(z),use_ILP=0);
minfact: entering with order 10 and degree 8
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_deg_coeffs: # apparent singularities <= 4
minfact: bound on the degrees of the coefficients at order 9: [45, 44, 43, 42, 41, 40, 35, 35, 35, 35]
minfact: computing 17 modular coefficients
minfact: try guessing mod p
minfact: computing 49 modular coefficients
minfact: try guessing mod p
minfact: computing 145 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 6 and degree 8
minfact: modular gcrd of order 6 and degree 8
minfact: computing 75 rational coefficients
minfact: try guessing
minfact: checking equation of order 6
minfact: it is a right factor
minfact: found a right factor of order 6
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_deg_coeffs: # apparent singularities <= 5
minfact: bound on the degrees of the coefficients at order 5: [30, 29, 28, 28, 28, 28]
minfact: computing 187 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
Simple test (section 4.1)
A:=z^2*Dz+3:
B:=(z-3)*Dz+4*z^5: # Here, 4 can be changed into any positive integer, and 5 too.
CC:=DEtools[mult](A,B,[Dz,z]):
deq:={DEtools[diffop2de](CC,[Dz,z],y(z)),y(0)=1};
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXFHRig8JCwoKiYsJiomIiM/IiIiKUkiekdGKCIiJ0Y0RjQqJiIjN0Y0KUY2IiImRjRGNEY0LUkieUdGKDYjRjZGNEY0KiYsKiomIiIlRjQpRjYiIihGNEY0KiQpRjYiIiNGNEY0KiYiIiRGNEY2RjRGNCIiKiEiIkY0LUklZGlmZkdGJjYkRjxGNkY0RjQqJiwmKiQpRjZGSUY0RjQqJkZJRjRGRkY0RktGNC1GTTYkRjwtSSIkR0YmNiRGNkZHRjRGNC8tRj02IyIiIUY0NyM8JCwoRjBGNEY/RjQqJkZQRjQtRk02JEZMRjZGNEY0Rlk=
minimizediffeq(deq,y(z));
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_deg_coeffs: # apparent singularities <= 967
minfact: bound on the degrees of the coefficients at order 1: [970, 974]
minfact: computing 10 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 1 and degree 5
minfact: modular gcrd of order 1 and degree 5
minfact: computing 19 rational coefficients
minfact: try guessing
minfact: checking equation of order 1
minfact: it is a right factor
minfact: found a right factor of order 1
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM8JCwmKigiIiUiIiItSSJ5R0YoNiNJInpHRihGMClGNCIiJkYwRjAqJiwmRjRGMCIiJCEiIkYwLUklZGlmZkdGJjYkRjFGNEYwRjAvLUYyNiMiIiFGMEYr
A family of Ap\303\251ry-like examples (section 4.5)
_MAXORDER:=infinity:
Z:=proc(a,b)
local n,k,j,i,Sn,rec,u,
unk:=binomial(n,k)^a*binomial(n+k,n)^b/n!,
S:=op(1,SumTools[Hypergeometric][Zeilberger](unk,n,k,Sn));
rec:={add(coeff(S,Sn,i)*u(n+i),i=0..degree(S,Sn)),
seq(u(i)=add(eval(unk,[n=i,k=j]),j=0..i),i=0..degree(S,Sn)-1)};
gfun:-rectodiffeq(rec,u(n),y(z),'homogeneous'=true)
end:
for i to 4 do for j to 4 do tt:=time(); print(i,j,minimizediffeq(Z(i,j),y(z)),time()-tt) od od:
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: proved no factor of order 1
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyYiIiJGLDwkLCgqJkkiekdGKEYsLUklZGlmZkdGJjYkLUkieUdGKDYjRjAtSSIkR0YmNiRGMCIiI0YsRiwqJiwmRixGLComIiInRixGMEYsISIiRiwtRjI2JEY0RjBGLEYsKiYsJkYwRiwiIiRGP0YsRjRGLEYsLy1GNTYjIiIhRiwkIiN1ISIkNyZGLEYsPCQsKEZCRixGO0YsKiYtRjI2JEZARjBGLEYwRixGLEZFRkk=
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_deg_coeffs: # apparent singularities <= 1
minfact: bound on the degrees of the coefficients at order 4: [8, 7, 6, 6, 6]
minfact: computing 17 modular coefficients
minfact: try guessing mod p
minfact: computing 47 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 4 and degree 3
minfact: modular gcrd of order 4 and degree 3
minfact: computing 30 rational coefficients
minfact: try guessing
minfact: checking equation of order 4
minfact: it is a right factor
minfact: found a right factor of order 4
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_deg_coeffs: # apparent singularities <= 4
minfact: bound on the degrees of the coefficients at order 9: [45, 44, 43, 42, 41, 40, 35, 35, 35, 35]
minfact: computing 17 modular coefficients
minfact: try guessing mod p
minfact: computing 49 modular coefficients
minfact: try guessing mod p
minfact: computing 145 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 6 and degree 8
minfact: modular gcrd of order 6 and degree 8
minfact: computing 75 rational coefficients
minfact: try guessing
minfact: checking equation of order 6
minfact: it is a right factor
minfact: found a right factor of order 6
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
minfact: looking for a factor of order 18
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.013 sec.
bound_deg_coeffs: # apparent singularities <= 6
minfact: bound on the degrees of the coefficients at order 18: [126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 100, 100, 100, 100, 100]
minfact: computing 29 modular coefficients
minfact: try guessing mod p
minfact: computing 85 modular coefficients
minfact: try guessing mod p
minfact: computing 253 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 9 and degree 16
minfact: modular gcrd of order 9 and degree 16
minfact: computing 185 rational coefficients
minfact: try guessing
minfact: checking equation of order 9
minfact: it is a right factor
minfact: found a right factor of order 9
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: ILP improved bound from 11 to 9 in 0.038 sec.
bound_deg_coeffs: # apparent singularities <= 9
minfact: bound on the degrees of the coefficients at order 8: [80, 79, 78, 77, 74, 74, 74, 74, 74]
minfact: computing 706 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.006 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: proved no factor of order 2
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: proved no factor of order 1
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyYiIiMiIiI8JCwqKiYsJkkiekdGKCEiIiIiJEYzRi0tSSJ5R0YoNiNGMkYtRi0qJiwoKiQpRjJGLEYtRjMqJiIjQUYtRjJGLUYzRi1GLUYtLUklZGlmZkdGJjYkRjVGMkYtRi0qJiwmKiYiIzZGLUY7Ri1GMyomRjRGLUYyRi1GLUYtLUY/NiRGNS1JIiRHRiY2JEYyRixGLUYtKiZGO0YtLUY/NiRGNS1GSTYkRjJGNEYtRi0vLUY2NiMiIiFGLSQiI2khIiQ3JkYsRi08JCwqRjBGLUY4Ri0qJkZCRi0tRj82JEY+RjJGLUYtKiZGO0YtLUY/NiRGZW5GMkYtRi1GUEZU
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: proved no factor of order 3
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: proved no factor of order 2
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: proved no factor of order 1
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
minfact: looking for a factor of order 13
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_deg_coeffs: # apparent singularities <= 5
minfact: bound on the degrees of the coefficients at order 13: [78, 77, 76, 75, 74, 73, 72, 71, 70, 69, 60, 60, 60, 60]
minfact: computing 39 modular coefficients
minfact: try guessing mod p
minfact: computing 115 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 9 and degree 9
minfact: modular gcrd of order 8 and degree 12
minfact: computing 131 rational coefficients
minfact: try guessing
minfact: checking equation of order 8
minfact: it is a right factor
minfact: found a right factor of order 8
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: ILP improved bound from 7 to 5 in 0.015 sec.
bound_deg_coeffs: # apparent singularities <= 5
minfact: bound on the degrees of the coefficients at order 7: [42, 41, 40, 39, 36, 36, 36, 36]
minfact: computing 326 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
minfact: looking for a factor of order 25
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.021 sec.
bound_deg_coeffs: # apparent singularities <= 6
minfact: bound on the degrees of the coefficients at order 25: [175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162, 161, 160, 159, 158, 157, 156, 155, 135, 135, 135, 135, 135]
minfact: computing 53 modular coefficients
minfact: try guessing mod p
minfact: computing 157 modular coefficients
minfact: try guessing mod p
minfact: computing 469 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 11 and degree 24
minfact: modular gcrd of order 11 and degree 24
minfact: computing 317 rational coefficients
minfact: try guessing
minfact: checking equation of order 11
minfact: it is a right factor
minfact: found a right factor of order 11
minfact: looking for a factor of order 10
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: ILP improved bound from 16 to 13 in 0.03 sec.
bound_deg_coeffs: # apparent singularities <= 13
minfact: bound on the degrees of the coefficients at order 10: [140, 139, 138, 137, 136, 135, 130, 130, 130, 130, 130]
minfact: computing 1501 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 9 not larger
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 8 not larger
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_deg_coeffs: # apparent singularities <= 4
minfact: bound on the degrees of the coefficients at order 9: [45, 44, 43, 42, 41, 40, 35, 35, 35, 35]
minfact: computing 17 modular coefficients
minfact: try guessing mod p
minfact: computing 49 modular coefficients
minfact: try guessing mod p
minfact: computing 145 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 6 and degree 8
minfact: modular gcrd of order 6 and degree 8
minfact: computing 75 rational coefficients
minfact: try guessing
minfact: checking equation of order 6
minfact: it is a right factor
minfact: found a right factor of order 6
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
minfact: looking for a factor of order 18
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.012 sec.
bound_deg_coeffs: # apparent singularities <= 6
minfact: bound on the degrees of the coefficients at order 18: [126, 125, 124, 123, 122, 121, 120, 119, 118, 117, 116, 115, 114, 113, 100, 100, 100, 100, 100]
minfact: computing 29 modular coefficients
minfact: try guessing mod p
minfact: computing 85 modular coefficients
minfact: try guessing mod p
minfact: computing 253 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 9 and degree 16
minfact: modular gcrd of order 9 and degree 16
minfact: computing 185 rational coefficients
minfact: try guessing
minfact: checking equation of order 9
minfact: it is a right factor
minfact: found a right factor of order 9
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: ILP improved bound from 11 to 9 in 0.038 sec.
bound_deg_coeffs: # apparent singularities <= 9
minfact: bound on the degrees of the coefficients at order 8: [80, 79, 78, 77, 74, 74, 74, 74, 74]
minfact: computing 706 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.006 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.006 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
minfact: looking for a factor of order 27
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.042 sec.
bound_deg_coeffs: # apparent singularities <= 10
minfact: bound on the degrees of the coefficients at order 27: [297, 296, 295, 294, 293, 292, 291, 290, 289, 288, 287, 286, 285, 284, 283, 282, 281, 280, 279, 278, 277, 276, 255, 255, 255, 255, 255, 255]
minfact: computing 34 modular coefficients
minfact: try guessing mod p
minfact: computing 100 modular coefficients
minfact: try guessing mod p
minfact: computing 298 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 13 and degree 19
minfact: modular gcrd of order 12 and degree 29
minfact: computing 408 rational coefficients
minfact: try guessing
minfact: checking equation of order 12
minfact: it is a right factor
minfact: found a right factor of order 12
minfact: looking for a factor of order 11
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: ILP improved bound from 21 to 18 in 0.128 sec.
bound_deg_coeffs: # apparent singularities <= 18
minfact: bound on the degrees of the coefficients at order 11: [209, 208, 207, 206, 205, 204, 199, 199, 199, 199, 199, 199]
minfact: computing 2461 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 10
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 10 not larger
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.306 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 9 not larger
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 8 not larger
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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`_nF5F3F3F^\nFb\nFg\nF^]n
minfact: looking for a factor of order 50
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.122 sec.
bound_deg_coeffs: # apparent singularities <= 8
minfact: bound on the degrees of the coefficients at order 50: [450, 449, 448, 447, 446, 445, 444, 443, 442, 441, 440, 439, 438, 437, 436, 435, 434, 433, 432, 431, 430, 429, 428, 427, 426, 425, 424, 423, 422, 421, 420, 419, 418, 417, 416, 415, 414, 413, 412, 411, 410, 409, 408, 407, 364, 364, 364, 364, 364, 364, 364]
minfact: computing 90 modular coefficients
minfact: try guessing mod p
minfact: computing 268 modular coefficients
minfact: try guessing mod p
minfact: computing 802 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 17 and degree 29
minfact: modular gcrd of order 16 and degree 47
minfact: computing 838 rational coefficients
minfact: try guessing
minfact: checking equation of order 16
minfact: it is a right factor
minfact: found a right factor of order 16
minfact: looking for a factor of order 15
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.012 sec.
bound_apparent: ILP improved bound from 37 to 34 in 0.376 sec.
bound_deg_coeffs: # apparent singularities <= 34
minfact: bound on the degrees of the coefficients at order 15: [525, 524, 523, 522, 521, 520, 519, 518, 517, 509, 509, 509, 509, 509, 509, 509]
minfact: computing 8288 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 14
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 14 not larger
minfact: looking for a factor of order 13
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 13 not larger
minfact: looking for a factor of order 12
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 12 not larger
minfact: looking for a factor of order 11
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 11 not larger
minfact: looking for a factor of order 10
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 10 not larger
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 9 not larger
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 8 not larger
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.012 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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minfact: looking for a factor of order 15
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.009 sec.
bound_deg_coeffs: # apparent singularities <= 5
minfact: bound on the degrees of the coefficients at order 15: [90, 89, 88, 87, 86, 85, 84, 83, 82, 81, 80, 79, 68, 68, 68, 68]
minfact: computing 50 modular coefficients
minfact: try guessing mod p
minfact: computing 148 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 9 and degree 13
minfact: modular gcrd of order 9 and degree 13
minfact: computing 155 rational coefficients
minfact: try guessing
minfact: checking equation of order 9
minfact: it is a right factor
minfact: found a right factor of order 9
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: ILP improved bound from 9 to 6 in 0.046 sec.
bound_deg_coeffs: # apparent singularities <= 6
minfact: bound on the degrees of the coefficients at order 8: [56, 55, 54, 53, 52, 48, 48, 48, 48]
minfact: computing 484 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.004 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.005 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.009 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.006 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
minfact: looking for a factor of order 26
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.025 sec.
bound_deg_coeffs: # apparent singularities <= 6
minfact: bound on the degrees of the coefficients at order 26: [182, 181, 180, 179, 178, 177, 176, 175, 174, 173, 172, 171, 170, 169, 168, 167, 166, 165, 164, 163, 162, 161, 140, 140, 140, 140, 140]
minfact: computing 57 modular coefficients
minfact: try guessing mod p
minfact: computing 169 modular coefficients
minfact: try guessing mod p
minfact: computing 505 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 12 and degree 24
minfact: modular gcrd of order 12 and degree 24
minfact: computing 343 rational coefficients
minfact: try guessing
minfact: checking equation of order 12
minfact: it is a right factor
minfact: found a right factor of order 12
minfact: looking for a factor of order 11
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: ILP improved bound from 17 to 14 in 0.138 sec.
bound_deg_coeffs: # apparent singularities <= 14
minfact: bound on the degrees of the coefficients at order 11: [165, 164, 163, 162, 161, 160, 159, 153, 153, 153, 153, 153]
minfact: computing 1927 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 10
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: ILP completed in 0.01 sec.
bound_apparent: no feasible integer solution
minfact: bound on the degrees of the coefficients at order 10 not larger
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.009 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 9 not larger
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 8 not larger
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.009 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.009 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.008 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.007 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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minfact: looking for a factor of order 40
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.081 sec.
bound_deg_coeffs: # apparent singularities <= 7
minfact: bound on the degrees of the coefficients at order 40: [320, 319, 318, 317, 316, 315, 314, 313, 312, 311, 310, 309, 308, 307, 306, 305, 304, 303, 302, 301, 300, 299, 298, 297, 296, 295, 294, 293, 292, 291, 290, 289, 288, 287, 286, 252, 252, 252, 252, 252, 252]
minfact: computing 52 modular coefficients
minfact: try guessing mod p
minfact: computing 154 modular coefficients
minfact: try guessing mod p
minfact: computing 460 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 16 and degree 25
minfact: modular gcrd of order 15 and degree 38
minfact: computing 645 rational coefficients
minfact: try guessing
minfact: checking equation of order 15
minfact: it is a right factor
minfact: found a right factor of order 15
minfact: looking for a factor of order 14
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.012 sec.
bound_apparent: ILP improved bound from 28 to 25 in 0.247 sec.
bound_deg_coeffs: # apparent singularities <= 25
minfact: bound on the degrees of the coefficients at order 14: [364, 363, 362, 361, 360, 359, 358, 357, 356, 348, 348, 348, 348, 348, 348]
minfact: computing 5362 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 13
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.012 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 13 not larger
minfact: looking for a factor of order 12
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 12 not larger
minfact: looking for a factor of order 11
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 11 not larger
minfact: looking for a factor of order 10
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 10 not larger
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 9 not larger
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 8 not larger
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.011 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.01 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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minfact: looking for a factor of order 45
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.186 sec.
bound_deg_coeffs: # apparent singularities <= 10
minfact: bound on the degrees of the coefficients at order 45: [495, 494, 493, 492, 491, 490, 489, 488, 487, 486, 485, 484, 483, 482, 481, 480, 479, 478, 477, 476, 475, 474, 473, 472, 471, 470, 469, 468, 467, 466, 465, 464, 463, 462, 461, 460, 459, 458, 457, 456, 417, 417, 417, 417, 417, 417]
minfact: computing 90 modular coefficients
minfact: try guessing mod p
minfact: computing 268 modular coefficients
minfact: try guessing mod p
minfact: computing 802 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 19 and degree 31
minfact: modular gcrd of order 18 and degree 47
minfact: computing 936 rational coefficients
minfact: try guessing
minfact: checking equation of order 18
minfact: it is a right factor
minfact: found a right factor of order 18
minfact: looking for a factor of order 17
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.015 sec.
bound_apparent: ILP improved bound from 34 to 31 in 2.485 sec.
bound_deg_coeffs: # apparent singularities <= 31
minfact: bound on the degrees of the coefficients at order 17: [544, 543, 542, 541, 540, 539, 538, 537, 536, 535, 534, 533, 522, 522, 522, 522, 522, 522]
minfact: computing 9634 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 16
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.015 sec.
bound_apparent: ILP completed in 1.366 sec.
bound_apparent: no feasible integer solution
minfact: bound on the degrees of the coefficients at order 16 not larger
minfact: looking for a factor of order 15
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.016 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 15 not larger
minfact: looking for a factor of order 14
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.014 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 14 not larger
minfact: looking for a factor of order 13
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.014 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 13 not larger
minfact: looking for a factor of order 12
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.014 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 12 not larger
minfact: looking for a factor of order 11
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.016 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 11 not larger
minfact: looking for a factor of order 10
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.015 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 10 not larger
minfact: looking for a factor of order 9
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.014 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 9 not larger
minfact: looking for a factor of order 8
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.015 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 8 not larger
minfact: looking for a factor of order 7
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.015 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 7 not larger
minfact: looking for a factor of order 6
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.014 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 6 not larger
minfact: looking for a factor of order 5
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.015 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 5 not larger
minfact: looking for a factor of order 4
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.014 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 4 not larger
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.017 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 3 not larger
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.015 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.013 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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A big equation
deq:={\134(-34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521*x^6 - 31296888332031952456617184580962723443077127991668239464969602946942230810585963626702535568823007378745062133640056293298633608280008107401854871264951476400302170944481850813500412570152179986374844134095348757756692020617606674185081012291589240770913099227088643835380778922386588575430119325*x^5 - 47157422350331417866445764884800746546368802749152352262137888046237459023870232786487518785528621247731687258088919542010565437781130450488974622658844859229940878270569997235539235306439965276400052819418981390574346121459602288764087812965757072085754017081040421332093302291592658797013051103*x^4 + 53356637847663350136612986210489123077151794805001254471029057457933306450776403050602517776650152710403028430629076181469657259946311976630285285353370938658938550157590978209207754438187149126069641289368246014948188605665519762787545738969949265180468592382059246815823432724717327744543893882*x^3)*diff(f(x), x, x, x, x) + (382757754368349052173101075031434096437090200300982843193329232471054532872729394018465280420221004494084266051137452063764944171383281535771124809674382101116517743350119698628474458134700138344980042444675163887305815628530862059379938002125609397057217852531129723273681845306506911808607731*x^6 + 341719046356597716356689344175285298710895281898040995845949482459627525290252890184807906790344939117553526064984060549238972759727383354429462835099084168180273660391780212065168483669174098223776189169908631961033425186190322081496763544584481592454183363947567931393869987005832454446709780021*x^5 + 500010354069082442083758836600315797893093222428676302796356381807745256544800370109925778587910825756759647629785024241197346456852063501152354531889640289810930819254623845260069176845423766295034550188091861827109276677628488224971694020109909111266037001975297152490637262265231615203848231990*x^4 - 655384393767832526354122400566018903076491458186152150180877031596288543876956296811747870338686728185121961263536584559614743671530744945090401651697355645698731241784206511552056447192533832501508709263311010036074265498038327703927407003992568420340616469427610417793661715462535245849052462478*x^3 + 114861863518040641883089515315076463428799593289294260688166308773006094876321714085702666191068694395011083126152762656349631792344797362956548526172797258826918616076728357731949551071353621635737854242558496317970058599853290605040188287292590071407238137695085984103805310048551166907086551540*x^2)*diff(f(x), x, x, x) + (34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521*x^6 + 59693624339691668835886834024345408331998604305375243264040581703520435231578499818840829983032790918302877855313339192868364797331155485837974233043828652954971108660553586228825487655785578014537883533082272038836055282883002216174864447146715466452438320134098432307158853312313314200475585150*x^5 + 604580025606282495021935364842323309090472176220098849221868955788742971951254171151125064446009975115220148954185608236380662020876459529515025080524906405640168294597792579347761946574495559053669169880635053376730750368439802506482211117142070995023692371377825299995400562393025677886448202661*x^4 + 893324988138761166884059465434510884466235264584752323499283227231360485126441179354294841949862827328690605340117858850934065192640384203041208079302718500012952603931788576213922958247474833388783719771313269880566973607486549930284223370390583099361425354618744035545856910443389272967068595309*x^3 - 511057000660030775229520707459888222861245477976028382297590076222345838563849297675160557677692144587607533286177989056202537348315519716028854261058251775382906011116811791568863819733509618212988793084636601264589378841375867697332305717775911069589511017976452088712818823102064122104668097415*x^2 - 242337425770174925853474302370150963562270962987131017116820705718248086329575291299519696969945596629400063358461550027117334482375039654063492560368688548767568203503315687105436645605997775479552491455375217210519898862760845575542438266791671702763440103117393762662641829826237104468723178082*x)*diff(f(x), x, x) + (2616317614729824130131159138037647180487142410364362422024027999004478086715024144196069063148182231277445453429492759239408739383866423633808226053504687150525950496311077737632140867615281651500729040130145313178788097990356945822651215714295621370780221705412810745004705112293930230623097596*x^5 + 24556392592795658333855383869018985234041919367949405495611574102728577727220202628203452660350475737981049057313104549473384101213673210479271074948863068873423173427861820554361129627011115674366456663228754892007488703825062021465628889931992494528492689633808022864437533993144312637865419664*x^4 - 866212183880713733589509692490083202630777397703431070911348098139948718789882806640378358339855803637747567959790524956008096287337264332740831664025282529449935272438935054897448907218817670357450299468950152148895989152537013870242290502808315518188666184018303672085618055693783463419068010024*x^3 - 969707287739315678844601988277151335984210970608475860930612156702065233594234274751595702783655956725704736151038922216475995098270000943774980270037132190524551433601434300587190014554841542701896802774948524963996876216983756807928919592506516698404534849273303179230994273595507386274699410373*x^2 + 1826628252497110428538283488342129239911759251878122779150064310956247384006723752692348041420613859511777255372218845741776632038367651471493728148643508641431419107190855869082841877353480560265252551242736886116066005982285302555495750936782794593329522167481875476607848821224494079698511505983*x - 151921325720276108799975415737369151956959380735712011666978978516660437377560301167309922692182069157004059026992618250998654507386762520194877900594057434467774134711226533314089221119582123994610352204282733756770884428474308208897540407557156254495104824215210249975311853575035471815632917870)*diff(f(x), x) + (-2616317614729824130131159138037647180487142410364362422024027999004478086715024144196069063148182231277445453429492759239408739383866423633808226053504687150525950496311077737632140867615281651500729040130145313178788097990356945822651215714295621370780221705412810745004705112293930230623097596*x^4 - 14091122133876361813330747316868396512093349726491955807515462106710665380360106051419176407757746812871267243595133512515749143678207515944038170734844320271319371442617509603832566156549989068363540502708173639292336311863634238175024027074810009045371802812156779884418713543968591715373029280*x^3 + 1123935345925078987895835650537906736073321265015684921080276886840709557114724851117581151635283437806097148415127065021201914020776412170882194366851243426104683407468822853530538795179508994466969649945326484517355364805146173757051760058262086972839150416243909291695901073725501884712700702994*x^2 + 397802355362263768456190702398921433278060896549138410963215870403881661980472622975887174554242405785343328432561545748556664079340638183923249664119559179527998963295827800372725675502608816482996575511259963239378706734849624072250675226043206284959963339939307435703984113113881746171356937635*x + 379803314300690271999938539343422879892398451839280029167447446291651093443900752918274806730455172892510147567481545627496636268466906300487194751485143586169435336778066333285223052798955309986525880510706834391927211071185770522243851018892890636237762060538025624938279633937588679539082294675)*f(x), f(0) = 1, D(f)(0) = 5/2, (D@@2)(f)(0) = 15, (D@@3)(f)(0) = 219/2}:
minimizediffeq(deq,f(x));
minfact: looking for a factor of order 3
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_deg_coeffs: # apparent singularities <= 202
minfact: bound on the degrees of the coefficients at order 3: [618, 617, 616, 616]
minfact: computing 12 modular coefficients
minfact: try guessing mod p
minfact: computing 34 modular coefficients
minfact: try guessing mod p
minfact: computing 100 modular coefficients
minfact: try guessing mod p
minfact: found modular operator of order 3 and degree 8
minfact: modular gcrd of order 3 and degree 8
minfact: computing 45 rational coefficients
minfact: try guessing
minfact: checking equation of order 3
minfact: it is a right factor
minfact: found a right factor of order 3
minfact: checking for apparent singularity: x^3+31296888332031952456617184580962723443077127991668239464969602946942230810585963626702535568823007378745062133640056293298633608280008107401854871264951476400302170944481850813500412570152179986374844134095348757756692020617606674185081012291589240770913099227088643835380778922386588575430119325/34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521*x^2+47157422350331417866445764884800746546368802749152352262137888046237459023870232786487518785528621247731687258088919542010565437781130450488974622658844859229940878270569997235539235306439965276400052819418981390574346121459602288764087812965757072085754017081040421332093302291592658797013051103/34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521*x-53356637847663350136612986210489123077151794805001254471029057457933306450776403050602517776650152710403028430629076181469657259946311976630285285353370938658938550157590978209207754438187149126069641289368246014948188605665519762787545738969949265180468592382059246815823432724717327744543893882/34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521
minfact: apparent singularity: x^3+31296888332031952456617184580962723443077127991668239464969602946942230810585963626702535568823007378745062133640056293298633608280008107401854871264951476400302170944481850813500412570152179986374844134095348757756692020617606674185081012291589240770913099227088643835380778922386588575430119325/34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521*x^2+47157422350331417866445764884800746546368802749152352262137888046237459023870232786487518785528621247731687258088919542010565437781130450488974622658844859229940878270569997235539235306439965276400052819418981390574346121459602288764087812965757072085754017081040421332093302291592658797013051103/34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521*x-53356637847663350136612986210489123077151794805001254471029057457933306450776403050602517776650152710403028430629076181469657259946311976630285285353370938658938550157590978209207754438187149126069641289368246014948188605665519762787545738969949265180468592382059246815823432724717327744543893882/34796159488031732015736461366494008767008200027362076653939021133732230261157217638042298220020091317644024186467041096705904015580298321433738619061307463737865249395465427148043132557700012576816367494970469444300528693502805641761812545647782672459747077502829974843061985936955173800782521
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 2 not larger
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.003 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
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
Algebraic values
Eq. (7.5) from Adamczewski-Rivoal 2018
deq7_5:=diff(y(z),z$3)+(1-2*z-2*z^2)/z/(1+z)*diff(y(z),z,z)-(1+4*z+z^2)/z^2/(1+z)*diff(y(z),z);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdkZXE3XzVHRigsKC1JJWRpZmZHRiY2JC1JInlHRig2I0kiekdGKC1JIiRHRiY2JEY1IiIkIiIiKiosKComIiIjRjopRjVGPkY6ISIiKiZGPkY6RjVGOkZARjpGOkY6RjVGQCwmRjpGOkY1RjpGQC1GMDYkRjItRjc2JEY1Rj5GOkY6KiosKCokRj9GOkY6KiYiIiVGOkY1RjpGOkY6RjpGOkY/RkBGQkZALUYwNiRGMkY1RjpGQDcjLCgtRjA2JC1GMDYkRkxGNUY1RjoqKkY8RjpGNUZARkJGQEZSRjpGOkZHRkA=
sol:=series(add(n^2*binomial(2*n,n)/(n+1)^2*(z/2)^(n+1)/n!,n=0..Order),z);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRzb2xHRigrLUkiekdGKCMiIiIiIikiIiMjRjEiIiciIiQjIiM6IiRHIiIiJSMiIigiJD8iIiImLUkiT0dGJTYjRjFGNTcjRi4=
series(eval(deq7_5,y(z)=sol),z);
KyVJInpHNiItSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiMiIiIiIiQ=
deq7_5:={deq7_5,y(0)=0,(D@@2)(y)(0)=1/4};
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSdkZXE3XzVHRig8JSwoLUklZGlmZkdGJjYkLUkieUdGKDYjSSJ6R0YoLUkiJEdGJjYkRjYiIiQiIiIqKiwoKiYiIiNGOylGNkY/RjshIiIqJkY/RjtGNkY7RkFGO0Y7RjtGNkZBLCZGO0Y7RjZGO0ZBLUYxNiRGMy1GODYkRjZGP0Y7RjsqKiwoKiRGQEY7RjsqJiIiJUY7RjZGO0Y7RjtGO0Y7RkBGQUZDRkEtRjE2JEYzRjZGO0ZBLy1GNDYjIiIhRlIvLS0tSSNAQEdGJTYkSSJER0YlRj82I0Y0RlEjRjtGTDcjPCUsKC1GMTYkLUYxNiRGTUY2RjZGOyoqRj1GO0Y2RkFGQ0ZBRltvRjtGO0ZIRkFGT0ZT
algvalues(deq7_5,y(z));
minimizediffeq: checking for apparent singularity: 1+z
minimizediffeq: apparent singularity: 1+z
minimizediffeq: looking for a factor of order 2
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: # apparent singularities <= 2
minimizediffeq: bound on the degrees of the coefficients at order 2: [6, 5, 4]
minimizediffeq: computing 9 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 25 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: no feasible solution
minimizediffeq: bound on the degrees of the coefficients at order 1 not larger
minimizediffeq: found a rational integrating factor
PCMvLUkieUc2IjYjIiIiIyIiIiIiIw==
dsolve(deq7_5,y(z));
Ly1JInlHNiI2I0kiekdGJSwmIyIiIiIiI0YqKipGKUYqLUkkZXhwRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YlRiZGKiwmRidGKkYqISIiRiotSShCZXNzZWxJR0YvNiQiIiFGJ0YqRio=
eval(op(2,%),z=1);
IyIiIiIiIw==
Special cases of Prop. 4.1
deq:=gfun:-holexprtodiffeq(hypergeom([d+1],[a+d+1],-z),y(z));
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXFHRig8JCwoKiYsJkkiZEdGKCIiIkYzRjNGMy1JInlHRig2I0kiekdGKEYzRjMqJiwqRjdGM0kiYUdGKEYzRjJGM0YzRjNGMy1JJWRpZmZHRiY2JEY0RjdGM0YzKiZGN0YzLUY8NiRGNC1JIiRHRiY2JEY3IiIjRjNGMy8tRjU2IyIiIUYzNyM8JCwoRjBGM0Y4RjMqJkY3RjMtRjw2JEY7RjdGM0YzRkU=
The implementation does not deal with parameters, but can handle special cases:
algvalues(eval(deq,[d=5,a=-32/5]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 7
minimizediffeq: bound on the degrees of the coefficients at order 1: [8, 8]
minimizediffeq: computing 9 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 24 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyIjNyIiJiMiJTQ4IiREJy8tRiU2Iy1JJ1Jvb3RPZkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCwqJkYtIiIiKUkjX1pHRjMiIiVGOUY5KiYiJismPUY5KUY7IiIkRjkhIiIqJiInKzs8RjkpRjsiIiNGOUY5KiYiJ2cmUSZGOUY7RjlGQSInT0pLRjksJComIyInZT9AIiREIkY5LCoqJiIkXSNGOSlGMUZARjlGOSomIiVEVEY5KUYxRkVGOUZBKiYiJklvIkY5RjFGOUY5IiYpNDVGQUZBRkE=
algvalues(eval(deq,[d=5,a=-64/5]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 13
minimizediffeq: bound on the degrees of the coefficients at order 1: [14, 14]
minimizediffeq: computing 13 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 36 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyIjJSkiIiYjIiVQJSkiJEQnLy1GJTYjLUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsLComRi0iIiIpSSNfWkdGMyIiJUY5RjkqJiImKyZIRjkpRjsiIiRGOSEiIiomIicrJVslRjkpRjsiIiNGOUY5KiYiKCEzaUVGOUY7RjlGQSIoT05CJkY5LCQqJiMiKE1eOCIiJEQiRjksKComIiNERjkpRjFGRUY5RjkqJiIkIVJGOUYxRjlGQSIlJ1EiRjlGQUZB
algvalues(eval(deq,[d=4,a=-128/3]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.003 sec.
minimizediffeq: # apparent singularities <= 43
minimizediffeq: bound on the degrees of the coefficients at order 1: [44, 44]
minimizediffeq: computing 12 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 34 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 96 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyIkUyIiIiQjISZ0KyQiI0YvLUYlNiMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywqKiZGLSIiIilJI19aR0YzRipGOUY5KiYiJVtMRjkpRjsiIiNGOSEiIiomIidnPDhGOUY7RjlGOSIoKyNmO0ZALCQqJiMiKV14aV8iIipGOSwoKiZGSEY5KUYxRj9GOUY5KiYiJUk9RjlGMUY5RkAiJl09JkY5RkBGQA==
algvalues(eval(deq,[d=3,a=-27/7]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 4
minimizediffeq: bound on the degrees of the coefficients at order 1: [5, 5]
minimizediffeq: computing 7 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 18 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyIiJyIiKCMhI2wiI1wvLUYlNiMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywoKiZGLSIiIilJI19aR0YzIiIjRjlGOSomIiREJkY5RjtGOSEiIiIlcTZGOSwkKiYjIiQvIkYtRjksJiomRipGOUYxRjlGOSIjRUY/Rj9GPw==
algvalues(eval(deq,[d=3,a=-2197/725]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 4
minimizediffeq: bound on the degrees of the coefficients at order 1: [5, 5]
minimizediffeq: computing 7 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 18 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyIkNyQiJEQoIyEmKio0IyInRGNfLy1GJTYjLUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsKComRi0iIiIpSSNfWkdGMyIiI0Y5RjkqJiIodkFiJUY5RjtGOSEiIiIoL0h1KEY5LCQqJiMiJyNmXSQiJ0ReNUY5LCYqJkYqRjlGMUY5RjkiJSMqPkY/Rj9GPw==
algvalues(eval(deq,[d=4,a=-32/5]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 7
minimizediffeq: bound on the degrees of the coefficients at order 1: [8, 8]
minimizediffeq: computing 9 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 24 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjLUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YmNiMsKComIiNEIiIiKUkjX1pHRioiIiNGMUYxKiYiJD8lRjFGM0YxISIiIiVDN0YxLCQqJiMiJCg9RjBGMSwmKiYiIiZGMUYoRjFGMSIjPEY3RjdGMS8tRiU2Iy1GKTYjLChGL0YxKiYiJD8jRjFGM0YxRjciJGsjRjEsJComIyIleDhGMEYxLCYqJkY/RjFGREYxRjEiIiRGMUY3Rjc=
`union`(allvalues(%));
PCYvLUkieUc2IjYjLCYjIiNBIiImIiIiKiYjIiIjRitGLCkiI2IjRixGL0YsISIiLCQqJiMiJXg4IiNERiwsJkY4RiwqJkYvRixGMEYsRjNGM0YzLy1GJTYjLCZGKUYsRi1GLCwkKiZGNkYsLCZGOEYsRjpGLEYzRjMvLUYlNiMsJiMiI1VGK0YsKiYjIiInRitGLCkiIzpGMkYsRjMsJComIyIkKD1GOEYsLCZGOEYsKiZGSkYsRktGLEYzRjNGLC8tRiU2IywmRkZGLEZIRiwsJComRk9GLCwmRjhGLEZSRixGM0Ys
map(evala@Expand,%);
PCYvLUkieUc2IjYjLCYjIiNBIiImIiIiKiYjIiIjRitGLCkiI2IjRixGL0YsISIiLCYjIiM8RitGMyomIyIjTSIkRCJGLEYwRixGMy8tRiU2IywmRilGLEYtRiwsJkY1RjNGN0YsLy1GJTYjLCYjIiNVRitGLComIyIiJ0YrRiwpIiM6RjJGLEYzLCYjIiM2RitGLComIyIjbUY6RixGSUYsRiwvLUYlNiMsJkZERixGRkYsLCZGTEYsRk5GMw==
algvalues(eval(deq,[d=4,a=-8/3]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 4
minimizediffeq: bound on the degrees of the coefficients at order 1: [5, 5]
minimizediffeq: computing 7 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 18 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyIiIyIiJCMiIiYiI0YvLUYlNiMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywqKiZGLSIiIilJI19aR0YzRipGOUY5KiYiJHEjRjkpRjtGKUY5ISIiKiYiJFMmRjlGO0Y5RjkiI1NGOSwkKiYjRikiIipGOSwoKiZGRkY5KUYxRilGOUY5KiYiI0lGOUYxRjlGP0YpRj9GP0Y5
algvalues(eval(deq,[d=4,a=-1/3]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 4
minimizediffeq: bound on the degrees of the coefficients at order 1: [5, 5]
minimizediffeq: computing 7 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 18 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyEiIyIiJCMiI2IiI0YvLUYlNiMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywoKiZGLSIiIilJI19aR0YzRipGOUY5KiYiI2FGOSlGOyIiI0Y5ISIiIiNTRkAsJComIyIkNSIiIipGOSwoKiYiIz1GOSlGMUY/RjlGOSomIiM6RjlGMUY5RjkiIz9GOUZARjk=
algvalues(eval(deq,[d=4,a=-27/25]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 4
minimizediffeq: bound on the degrees of the coefficients at order 1: [5, 5]
minimizediffeq: computing 7 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 18 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyIjNyIjRCMiJXo7IiVESi8tRiU2Iy1JJ1Jvb3RPZkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkdGJjYjLCoqJiImRGMiIiIiKUkjX1pHRjMiIiRGOkY6KiYiJisrJ0Y6KUY8IiIjRjohIiIqJiImKzIjRjpGPEY6RkIiJW9cRkIsJComIyIlO24iJEQiRjosKComIiV2PUY6KUYxRkFGOkY6KiYiJHYmRjpGMUY6RjoiIyMqRjpGQkZC
algvalues(eval(deq,[d=4,a=-24/25]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 4
minimizediffeq: bound on the degrees of the coefficients at order 1: [5, 5]
minimizediffeq: computing 7 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 18 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCQvLUkieUc2IjYjIyEiJyIjRCMiJSo+JSIlREovLUYlNiMtSSdSb290T2ZHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRiY2IywqKiYiJkRjIiIiIilJI19aR0YzIiIkRjpGOiomIiZdUCdGOilGPCIiI0Y6ISIiKiYiJis8IkY6RjxGOkY6IiUvYEZCLCQqJiMiJSlSKSIkRCJGOiwoKiYiJXZWRjopRjFGQUY6RjoqJiIkXSdGOkYxRjpGQiIkVSVGOkZCRjo=
Special cases of Prop. 4.3
f:=exp(-c*z)*hypergeom([a],[b],z);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJmR0YoKiYtSSRleHBHRiU2IywkKiZJImNHRigiIiJJInpHRihGNSEiIkY1LUkqaHlwZXJnZW9tR0YlNiU3I0kiYUdGKDcjSSJiR0YoRjZGNTcjRi4=
deq:=gfun:-holexprtodiffeq(f,y(z));
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXFHRig8JCwoKiYsKiomKUkiY0dGKCIiIyIiIkkiekdGKEY2RjYqJkkiYkdGKEY2RjRGNkY2KiZGNEY2RjdGNiEiIkkiYUdGKEY7RjYtSSJ5R0YoNiNGN0Y2RjYqJiwoKihGNUY2RjRGNkY3RjZGNkY5RjZGN0Y7RjYtSSVkaWZmR0YmNiRGPUY3RjZGNiomRjdGNi1GRDYkRj0tSSIkR0YmNiRGN0Y1RjZGNi8tRj42IyIiIUY2NyM8JCwoRjBGNkZARjYqJkY3RjYtRkQ2JEZDRjdGNkY2Rkw=
deq:=gfun:-poltodiffeq(diff(y(z),z,z),[deq],[y(z)],y(z));
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
algvalues(eval(eval(deq,b=a*(2*c-1)/c^2),[c=1/3,a=1/2]),y(z));
minimizediffeq: checking for apparent singularity: z+9/2
minimizediffeq: apparent singularity: z+9/2
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 2
minimizediffeq: bound on the degrees of the coefficients at order 1: [3, 3]
minimizediffeq: computing 6 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 14 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found modular operator of order 1 and degree 2
minimizediffeq: modular gcrd of order 1 and degree 2
minimizediffeq: computing 13 rational coefficients
minimizediffeq: try guessing
minimizediffeq: checking equation of order 1
minimizediffeq: it is a right factor
minimizediffeq: found a right factor of order 1
minimizediffeq: no rational integrating factor
PCQvLUkieUc2IjYjIyEiKiIiIyIiIS8tRiU2IyMhIiJGKkYr
algvalues(eval(deq,[c=1,b=4/3,a=1/3]),y(z));
minimizediffeq: looking for a factor of order 1
minimizediffeq: solving LP problem
minimizediffeq: Relaxed LP completed in 0.002 sec.
minimizediffeq: # apparent singularities <= 2
minimizediffeq: bound on the degrees of the coefficients at order 1: [3, 3]
minimizediffeq: computing 6 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: computing 14 modular coefficients
minimizediffeq: try guessing mod p
minimizediffeq: found a rational integrating factor
PCMvLUkieUc2IjYjLUknUm9vdE9mRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiNiMsKComIiIqIiIiKUkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiMiIiIiIiIqJiIiJyIiIkkjX1pHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiIiIiIiIiIiIiUiIiIsJComIiIkIiIiLCYqJiIiJCIiIi1JJ1Jvb3RPZkc2JCUqcHJvdGVjdGVkR0koX3N5c2xpYkc2IjYjLCgqJiIiKiIiIilJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIjIiIiIiIiKiYiIiciIiJJI19aRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiIiIiIiIiIiIlIiIiIiIiIiIiIiIlIiIiISIiIiIi
`union`(allvalues(%));
PCQvLUkieUc2IjYjLCYjIiIiIiIkISIiKiYsJComRilGKl4jRipGKkYqRiopRisjRioiIiNGKkYsLCQqJkYrRiosJkYrRioqJiwkRjBGKkYqRjFGKkYsRixGKi8tRiU2IywmRilGLComRi9GKkYxRipGKiwkKiZGK0YqLCZGK0YqKiZGMEYqRjFGKkYqRixGKg==
Special cases of Prop. 4.4
a,b,c:=2/5, 3/5, 32/5:
deq:=gfun:-holexprtodiffeq(hypergeom([a,b],[c],z),y(z));
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXFHRig8JCwoKiYiIiciIiItSSJ5R0YoNiNJInpHRihGMkYyKiYsJiomIiNdRjJGNkYyRjIiJGciISIiRjItSSVkaWZmR0YmNiRGM0Y2RjJGMiomLCYqJiIjREYyKUY2IiIjRjJGMiomRkNGMkY2RjJGPEYyLUY+NiRGMy1JIiRHRiY2JEY2RkVGMkYyLy1GNDYjIiIhRjI3IzwkLChGMEYyRjdGMiomRkFGMi1GPjYkRj1GNkYyRjJGTA==
algvalues(deq,y(z));
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_deg_coeffs: # apparent singularities <= 5
minfact: bound on the degrees of the coefficients at order 1: [7, 6]
minfact: computing 8 modular coefficients
minfact: try guessing mod p
minfact: computing 21 modular coefficients
minfact: try guessing mod p
mininhom: no rational integrating factor
Error, (in Beukersatalpha) not an apparent singularity, 1 |algvalues.mpl:146|
This is not an E-function, which explains why the code, which is supposed to work only for E-functions, does not work there.
unassign('a','b','c');
A linear combination
f:=a+b*(z-1)+(z-1)^5*sum(binomial(2*n,n)*(z/2)^n/n!,n=0..infinity);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJmR0YoLChJImFHRigiIiIqJkkiYkdGKEYwLCZJInpHRihGMEYwISIiRjBGMCooKUYzIiImRjAtSShCZXNzZWxJR0YlNiQiIiFGNEYwLUkkZXhwR0YlNiNGNEYwRjA3I0Yu
gfun:-holexprtodiffeq(f,y(z));
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
deq:=eval(%,[a=1/3,b=1/7]);
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
deq:=gfun:-diffeqtohomdiffeq(%,y(z));
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXFHRig8JiwqKiYsLComIiVwUiIiIilJInpHRigiIiVGNEY0KiYiJiUqXCJGNClGNiIiJEY0RjQqJiImdUMiRjQpRjYiIiNGNEY0KiYiJTlcRjRGNkY0RjQiJVw5RjRGNC1JInlHRig2I0Y2RjRGNComLC4qJkYzRjQpRjYiIiZGNCEiIiomIiYnRz9GNEY1RjRGSyomIiZtQyRGNEY6RjRGSyomIiZZOiNGNEY+RjRGSyomIiUsISlGNEY2RjRGSyIlSz5GS0Y0LUklZGlmZkdGJjYkRkNGNkY0RjQqJiwwKiYiJCMpKUY0KUY2IiInRjRGNComIiVIX0Y0RklGNEY0KiYiJU9tRjRGNUY0RjQqJiIlZjtGNEY6RjRGSyomIiVNdUY0Rj5GNEZLKiYiJWNHRjRGNkY0RksiJCl6RktGNC1GVjYkRkMtSSIkR0YmNiRGNkY/RjRGNComLC4qJiIkVCVGNEZmbkY0RksqJiIkSSdGNEZJRjRGSyomIiREJkY0RjVGNEY0KiYiJTBBRjRGOkY0RjQqJiIlZzdGNEY+RjRGSyomIiQqUkY0RjZGNEZLRjQtRlY2JEZDLUZmbzYkRjZGO0Y0RjQvLUZENiMiIiEjISM8IiNALy0tSSJER0YlNiNGREZccSMiI0giIigvLS0tSSNAQEdGJTYkRmRxRj9GZXFGXHEjISNCRj83IzwmLCpGMEY0RkZGNComRllGNC1GVjYkRlVGNkY0RjQqJkZpb0Y0LUZWNiRGZXJGNkY0RjRGanBGYXFGaXE=
algvalues(deq,y(z));
minfact: checking for apparent singularity: z-1
minfact: apparent singularity: z-1
minfact: checking for apparent singularity: z^3+24/7*z^2+14/3*z+19/21
minfact: apparent singularity: z^3+24/7*z^2+14/3*z+19/21
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_deg_coeffs: # apparent singularities <= 10
minfact: bound on the degrees of the coefficients at order 2: [22, 21, 20]
minfact: computing 9 modular coefficients
minfact: try guessing mod p
minfact: computing 25 modular coefficients
minfact: try guessing mod p
minfact: computing 73 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
mininhom: found a rational integrating factor
PCMvLUkieUc2IjYjIiIiIyIiIiIiJA==
algvalues(deq,y(z),false);
minfact: checking for apparent singularity: z-1
minfact: apparent singularity: z-1
minfact: checking for apparent singularity: z^3+24/7*z^2+14/3*z+19/21
minfact: apparent singularity: z^3+24/7*z^2+14/3*z+19/21
minfact: looking for a factor of order 2
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_deg_coeffs: # apparent singularities <= 10
minfact: bound on the degrees of the coefficients at order 2: [22, 21, 20]
minfact: computing 9 modular coefficients
minfact: try guessing mod p
minfact: computing 25 modular coefficients
minfact: try guessing mod p
minfact: computing 73 modular coefficients
minfact: try guessing mod p
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_apparent: no feasible solution
minfact: bound on the degrees of the coefficients at order 1 not larger
mininhom: found a rational integrating factor
PCQvLCYjIiIiIiIkISIiLUkieUc2IjYjRiZGJiIiIS8sJiNGJiIiKEYoLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHRis2I0YqRixGJkYt
Eq (7.8) from Adamczewski-Rivoal 2018
At this stage, our code works only over Q(z).
f:=eval(z^a*exp(a*z)+z^b*exp(b*z),[a=1,b=3]);
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSJmR0YoLCYqJkkiekdGKCIiIi1JJGV4cEdGJTYjRjBGMUYxKiYpRjAiIiRGMS1GMzYjLCQqJkY3RjFGMEYxRjFGMUYxNyNGLg==
deq:=gfun:-holexprtodiffeq(f,y(z));
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXFHRig8JSwoKiYsKiomIiIkIiIiKUkiekdGKEYzRjRGNComIiIqRjQpRjYiIiNGNEY0KiZGOEY0RjZGNEY0RjNGNEY0LUkieUdGKDYjRjZGNEY0KiYsKComIiIlRjRGNUY0ISIiKiYiIilGNEY5RjRGQyomRjNGNEY2RjRGQ0Y0LUklZGlmZkdGJjYkRjxGNkY0RjQqJiwmKiRGNUY0RjQqJEY5RjRGNEY0LUZINiRGPC1JIiRHRiY2JEY2RjpGNEY0Ly0tSSJER0YlNiNGPTYjIiIhRjQvLS0tSSNAQEdGJTYkRlZGM0ZXRlhGODcjPCUsKEYwRjRGP0Y0KiZGS0Y0LUZINiRGR0Y2RjRGNEZTRlo=
series(f,z,4);
KytJInpHNiIiIiJGJUYlIiIjIyIiJEYmRigtSSJPRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliR0YkNiNGJSIiJQ==
Workaround weakness in holexprtodiffeq
deq:=deq union {(D@@3)(y)(0)=coeff(%,z,3)*3!};
LV9JLFR5cGVzZXR0aW5nRzYkJSpwcm90ZWN0ZWRHSShfc3lzbGliRzYiSSxtcHJpbnRzbGFzaEdGKDYkNyM+SSRkZXFHRig8JSwoKiYsKiomIiIkIiIiKUkiekdGKEYzRjRGNComIiIqRjQpRjYiIiNGNEY0KiZGOEY0RjZGNEY0RjNGNEY0LUkieUdGKDYjRjZGNEY0KiYsKComIiIlRjRGNUY0ISIiKiYiIilGNEY5RjRGQyomRjNGNEY2RjRGQ0Y0LUklZGlmZkdGJjYkRjxGNkY0RjQqJiwmKiRGNUY0RjQqJEY5RjRGNEY0LUZINiRGPC1JIiRHRiY2JEY2RjpGNEY0Ly0tSSJER0YlNiNGPTYjIiIhRjQvLS0tSSNAQEdGJTYkRlZGM0ZXRlhGODcjPCUsKEYwRjRGP0Y0KiZGS0Y0LUZINiRGR0Y2RjRGNEZTRlo=
algvalues(deq,y(z),false);
minfact: checking for apparent singularity: z
minfact: apparent singularity: z
minfact: checking for apparent singularity: z+1
minfact: apparent singularity: z+1
minfact: looking for a factor of order 1
bound_apparent: solving LP problem
bound_apparent: Relaxed LP completed in 0.002 sec.
bound_deg_coeffs: # apparent singularities <= 3
minfact: bound on the degrees of the coefficients at order 1: [3, 3]
minfact: computing 6 modular coefficients
minfact: try guessing mod p
minfact: computing 14 modular coefficients
minfact: try guessing mod p
mininhom: no rational integrating factor
PCMvLS1JIkRHNiQlKnByb3RlY3RlZEdJKF9zeXNsaWJHNiI2I0kieUc2IjYjISIiIiIh
time()-st;