Solving multiple system of equation in sagemath
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a,b,c,d,x,f,g,h,k,p,q,r,s,u,v,l,m,n= var('a b c d x f g h k p q r s u v l m n')
f1 = a*p+b*q+c*r+1
f2 = d*s+u*x+f*v-1
f3 = g*l+h*m+k*n-1
f4 = a*s+b*u+c*v
f5=a*l+b*m+c*n
f6=d*l+x*m+f*n
f7=a*p+d*s+g*l-1
f8=b*p+x*s+h*l+2
f9=c*p+f*s+k*l-1
f10=a*q+d*u+g*m
f11=b*q+x*u+h*m-1
f12= c*q+f*u+k*m
f13= a*r+d*v+g*n
f14= b*r+x*v+h*n-2
f15= c*r+f*v+k*n+1
solve([f1==0,f2==0,f3==0,f4==0,f5==0,f6==0,f7==0,f8==0,f9==0,f10==0,f11==0,f12==0,f13==0,f14==0,f15==0],a,b,c,d,x,f,g,h,k,p,q,r,s,u,v)
I am trying to solve these 15 system of equations but I am not getting any result. Is there any wrong here?
I don't know if it is a typo but you need to put * for multiplication. a*p instead of ap, etc.
and use PolynomialRing + Groebner bases and not the symbolic ring.
@FrédéricC, can you please gave me the code. It will help me if possible. Thanks
See example in https://ask.sagemath.org/question/64672/
As for your system, at very least it has the following partial solution:
{g: k, l: 1/k, x: 1/v, u: v, b: -c, r: 1/(-c), n: 0, m: 0, q: 0, p: 0, a: 0, s: (-h*v - 2*k*v)/k, d: 0, f: 0}.@Max Alekseyev, Thank you so much for your solutions. This is great