Periodic_1_6's profile - activity

Why does sagemath 9.2 give me an error ?

TypeError: unable to make sense of Maxima expression

import time
Start_Time = time.time()
var('N p x y c M H W V')

eq0 = N-187 == 0

eq1 = (sqrt((16*c^4*N+24*c^4+c^2*M+c^2-2*c^2*sqrt(24*c^2+M))/(c^4))-8)/16 - x == 0
eq2 = (sqrt((16*c^4*N+24*c^4+c^2*H+c^2+2*c^2*sqrt(24*c^2+H))/(c^4))-8)/16 - x ==0
eq3 = (4*x+2)^2-(2*y-1)^2 - N == 0
eq4 = M*(8*y^2-8*y-1) - (8*W^2-8*W-1) == 0
eq5 = H*(8*y^2-8*y-1) - (8*V^2-8*V-1) == 0
eq6 = (W-V) - (2*y-1) ==0
eq7 = 4*x+1-2*(y-1)-p == 0

eq8 = 1 - c == 0

solutions = solve([eq0,eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8],N,p,x,y,c,M,H,W,V)
sol = solutions 
Execution_Time = time.time() - Start_Time
print (Execution_Time)
print(sol)

@Emmanuel Charpentier thank you

But Is version 10.0 ?

Could you please post the solutions?

Why does sagemath 9.2 give me an error ? Why does sagemath 9.2 give me an error ? TypeError: unable to make sense of Ma

@slelievre I did not understand! can't it be done with sagemath?

@Max Alekseyev is there a way in sagemath to reduce mod 9 coefficients? Also

How to reduce in sagemath a 40th degree equation to a 5th degree equation with a 6th degree equation? All three equation

What mathematical procedure does sagemath use to solve these types of systems? Is there a better process? UPDATE: I tri

thank you !

sorry! thank you

In SageMath 9.2 :"TypeError: unable to make sense of Maxima expression" .What does it mean ? is there anyone who would h

@John Palmieri there were errors, now it is corrected excuse me

@John Palmier there were errors, now it is corrected excuse me

Can the coefficients of these two pairs of polynomials be reduced? If yes, how do you do it with sagemath? Can the coef

Can the coefficients of these two pairs of polynomials be reduced? If yes, how do you do it with sagemath? Can the coef

Please reopen

I was able to cut the time on my computer in half The first OUTPUT was (x, y, p, a, A, b, B, c, C, d, D, f, z, Z, w,

correct is eq6 = y + (q-p) / 2 -a == 0 but we are missing some other changes

there is an error in eq6

@Max Alekseyev I did it in O (log_2) I finally solved the factorization problem This is the system for factoring N = 17

How do I filter only integer solutions in sagemath?

import time
Start_Time = time.time()
var('x y N M F f G g L l Q q S s U u')

eq0 = N-1019 == 0 



eq3 = (32*((2*(3*3/4*M+1)-3*(-x)+1)/24)+3*(2*f-1)^2-3)/8-F==0
eq4 = ((2*(3*3/4*M+1)-3*(-x)+1)/24)+3/4*M- F == 0
eq5 = (32*((2*(3*F+1)-3*(f)+1)/24)+3*(2*g-1)^2-3)/8-G==0
eq6 = ((2*(3*F+1)-3*(f)+1)/24)+3/4*M- G == 0
eq7 = (32*((2*(3*G+1)-3*(g)+1)/24)+3*(2*l-1)^2-3)/8-L==0
eq8 = ((2*(3*G+1)-3*(g)+1)/24)+3/4*M- L == 0
eq9 = (32*((2*(3*L+1)-3*(l)+1)/24)+3*(2*q-1)^2-3)/8-Q==0
eq10 = ((2*(3*L+1)-3*(l)+1)/24)+3/4*M- Q == 0
eq11 = (32*((2*(3*Q+1)-3*(q)+1)/24)+3*(2*s-1)^2-3)/8-S==0
eq12 = ((2*(3*Q+1)-3*(q)+1)/24)+3/4*M- S == 0
eq13 = (32*((2*(3*S+1)-3*(s)+1)/24)+3*(2*u-1)^2-3)/8-U==0
eq14 = ((2*(3*S+1)-3*(s)+1)/24)+3/4*M- U == 0

eq15 =u+1==0


eq16 = (N-3)/8+y*(y-1)/2-M == 0

eq17 = 2*x*(x+1)-M == 0 

solutions = solve([eq0,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,eq13,eq14,eq15,eq16,eq17],x,y,N,M,F,f,G,g,L,l,Q,q,S,s,U,u)
sol = solutions  
Execution_Time = time.time() - Start_Time
print (Execution_Time)
print(sol)

How do I filter only integer solutions in sagemath? How do I filter only integer solutions in sagemath? import time Sta

How do I filter only integer solutions in sagemath? import time Start_Time = time.time() var('x y N M F

How do I filter only integer solutions in sagemath? import time Start_Time = time.time() var('x y N M F f G g L

How do I filter only integer solutions in sagemath? import time Start_Time = time.time() var('x y N M F f G g L

How do I filter only integer solutions in sagemath? import time Start_Time = time.time() var('x y N M F f G g L

How do I filter only integer solutions in sagemath? import time Start_Time = time.time() var('x y N M D d F f G g L l Q

@Max Alekseyev thank you

@Max Alekseyev One last favor, kindly. As you may have noticed, the system will have 12+4*[Integer_Part[log_2 (p+q-4)/8

UPDATE: I tried to solve it in linear time i.e. the factorization of N happens in log N Italian language https://www.academia.edu/96992548/Fat...

I found a system (which varies its length as a function of (p + q-4) / 8) which generates all the numbers N = 8 * G + 3 = p * q so by inserting our number to factor in the underlying system instead of N we will have our p, factor of N.

System example up to x = (p + q-4) / 8 <= 3

var('x y p a A b B c z Z w W N v V')

eq0 = N -27 == 0

eq1 = (2*(3*x+1)-3*(a)+1)/24+3/2*x*(x+1) - A == 0
eq2 = A+b*(b-1)/2 - (2*x*(x+1)) == 0
eq3 = (2*(3*(A)+1)-3*(b)+1)/24+3/2*x*(x+1) - B == 0
eq4 = B+c*(c-1)/2 - (2*x*(x+1)) == 0
eq5 = (2*(3*(B)+1)-3*(c)+1)/24+3/2*x*(x+1) - (2*x*(x+1)) == 0
eq6 = a-(2*x+1) == 0

eq7 = (2*(3*(N-3)/8+1)-3*(z)+1)/24+3/2*x*(x+1) -((N-3)/8+Z) == 0
eq8 = (N-3)/8+z*(z-1)/2 - (2*x*(x+1)) == 0
eq9 = (2*(3*((N-3)/8+Z)+1)-3*(w)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W) == 0
eq10 = (N-3)/8+Z+w*(w-1)/2 - (2*x*(x+1)) == 0
eq11 = (2*(3*((N-3)/8+Z+W)+1)-3*(v)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W+V) == 0
eq12 = (N-3)/8+Z+W+v*(v-1)/2 - (2*x*(x+1)) == 0
eq13 = (N-3)/8+Z+W+V - (2*x*(x+1)) == 0

eq14 = (N-3)/8+y*(y-1)/2 - 2*x*(x+1) == 0
eq15 = 4*x+1-2*(y-1)-p == 0


solutions = solve([eq0,eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,eq13,eq14,eq15],x,y,p,a,A,b,B,c,z,Z,w,W,N,v,V)
sol = solutions 
print(sol)

System example up to x = (p + q-4) / 8 <= 7

var('x y p a A b B c C d z Z w W N v V u U')

eq0 = N-59 == 0

eq1 = (2*(3*x+1)-3*(a)+1)/24+3/2*x*(x+1) - A == 0
eq2 = A+b*(b-1)/2 - (2*x*(x+1)) == 0
eq3 = (2*(3*(A)+1)-3*(b)+1)/24+3/2*x*(x+1) - B == 0
eq4 = B+c*(c-1)/2 - (2*x*(x+1)) == 0
eq5 = (2*(3*(B)+1)-3*(c)+1)/24+3/2*x*(x+1) - C == 0
eq6 = C+d*(d-1)/2 - (2*x*(x+1)) == 0
eq7 = (2*(3*(C)+1)-3*(d)+1)/24+3/2*x*(x+1) - (2*x*(x+1)) == 0
eq8 = a-(2*x+1) == 0

eq9 = (2*(3*(N-3)/8+1)-3*(z)+1)/24+3/2*x*(x+1) -((N-3)/8+Z) == 0
eq10 = (N-3)/8+z*(z-1)/2 - (2*x*(x+1)) == 0
eq11 = (2*(3*((N-3)/8+Z)+1)-3*(w)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W) == 0
eq12 = (N-3)/8+Z+w*(w-1)/2 - (2*x*(x+1)) == 0
eq13 = (2*(3*((N-3)/8+Z+W)+1)-3*(v)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W+V) == 0
eq14 = (N-3)/8+Z+W+v*(v-1)/2 - (2*x*(x+1)) == 0
eq15 = (2*(3*((N-3)/8+Z+W+V)+1)-3*(u)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W+V+U) == 0
eq16 = (N-3)/8+Z+W+V+u*(u-1)/2 - (2*x*(x+1)) == 0
eq17 = (N-3)/8+Z+W+V+U - (2*x*(x+1)) == 0

eq18 = (N-3)/8+y*(y-1)/2 - 2*x*(x+1) == 0
eq19 = 4*x+1-2*(y-1)-p == 0


solutions = solve([eq0,eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,eq13,eq14,eq15,eq16,eq17,eq18,eq19],x,y,p,a,A,b,B,c,C,d,z,Z,w,W,N,v,V,u,U)
sol = solutions 
print(sol)

System example up to x = (p + q-4) / 8 <= 15

var('x y p a A b B c C d D f z Z w W N v V u U t T')

eq0 = N - 123 == 0

eq1 = (2*(3*x+1)-3*(a)+1)/24+3/2*x*(x+1) - A == 0
eq2 = A+b*(b-1)/2 - (2*x*(x+1)) == 0
eq3 = (2*(3*(A)+1)-3*(b)+1)/24+3/2*x*(x+1) - B == 0
eq4 = B+c*(c-1)/2 - (2*x*(x+1)) == 0
eq5 = (2*(3*(B)+1)-3*(c)+1)/24+3/2*x*(x+1) - C == 0
eq6 = C+d*(d-1)/2 - (2*x*(x+1)) == 0
eq20 = (2*(3*(C)+1)-3*(d)+1)/24+3/2*x*(x+1) - D == 0
eq21 = D+f*(f-1)/2 - (2*x*(x+1)) == 0
eq7 = (2*(3*(D)+1)-3*(f)+1)/24+3/2*x*(x+1) - (2*x*(x+1)) == 0
eq8 = a-(2*x+1) == 0

eq9 = (2*(3*(N-3)/8+1)-3*(z)+1)/24+3/2*x*(x+1) -((N-3)/8+Z) == 0
eq10 = (N-3)/8+z*(z-1)/2 - (2*x*(x+1)) == 0
eq11 = (2*(3*((N-3)/8+Z)+1)-3*(w)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W) == 0
eq12 = (N-3)/8+Z+w*(w-1)/2 - (2*x*(x+1)) == 0
eq13 = (2*(3*((N-3)/8+Z+W)+1)-3*(v)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W+V) == 0
eq14 = (N-3)/8+Z+W+v*(v-1)/2 - (2*x*(x+1)) == 0
eq15 = (2*(3*((N-3)/8+Z+W+V)+1)-3*(u)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W+V+U) == 0
eq16 = (N-3)/8+Z+W+V+u*(u-1)/2 - (2*x*(x+1)) == 0
eq22 = (2*(3*((N-3)/8+Z+W+V+U)+1)-3*(t)+1)/24+3/2*x*(x+1) -((N-3)/8+Z+W+V+U+T) == 0
eq23 = (N-3)/8+Z+W+V+U+t*(t-1)/2 - (2*x*(x+1)) == 0
eq17 = (N-3)/8+Z+W+V+U+T - (2*x*(x+1)) == 0

eq18 = (N-3)/8+y*(y-1)/2 - 2*x*(x+1) == 0
eq19 = 4*x+1-2*(y-1)-p == 0


solutions = solve([eq0,eq1,eq2,eq3,eq4,eq5,eq6,eq7,eq8,eq9,eq10,eq11,eq12,eq13,eq14,eq15,eq16,eq17,eq18,eq19,eq20,eq21,eq22,eq23],x,y,p,a,A,b,B,c,C,d,D,f,z,Z,w,W,N,v,V,u,U,t,T)
sol = solutions 
print(sol)

What mathematical procedure does sagemath use to solve these types of systems?

Is there a better process?

@Max Alekseyev do you have any advice for me?

What mathematical procedure does sagemath use to solve these types of systems? Is there a better process? I found a sys