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Acanti gravatar image

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}:=\langle k^4\vert k\in K\backslash 0 \rangle,Iwanttofind(all?)aandbinFsuchthatp1==1moduloK^{4}andp2==1moduloK^{*4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}:=\langle k^4\vert k\in K\backslash 0 \rangle$, \ranglei.e.thegroupof4thpowersofnonzeroelementsofK$. I want to find (all?) a and b in F such that p1==1 p11 modulo $K^{4}$ and p2==-1 p2-1 modulo K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}:=\langle k^4\vert k\in K\backslash 0 \rangle$ i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}andp2\equiv1moduloK^{*4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}:=\langle k^4\vert k\in K\backslash 0 \rangle$ \rangle$. i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}andp2\equiv1moduloK^{*4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}:=\langle 4}:=( k^4\vert k\in K\backslash 0 \rangle$. )$. i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}andp2\equiv1moduloK^{*4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}:=( k^4\vert k\in K\backslash K\setminus 0 ).i.e.thegroupof4thpowersofnonzeroelementsofK.Iwanttofind(all?)aandbinFsuchthatp1\equiv1moduloK^{4}andp2\equiv1moduloK^{*4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}:=( k^4\vert k\in K\setminus 0 )$. 4}$, i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}andp2\equiv1moduloK^{*4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{$K4}$, ^{4}$, i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}andp2\equiv1moduloK^{*4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{4}$, K4

i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}andp2\equiv$-1 modulo K4.$K^{4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and K4

i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}$ K4 and p2-1 modulo $K^{4}$.K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and K4K4

i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo K4 $K^{4}$ and p2-1 modulo K4.$K^{4}$.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and K4

i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo $K^{4}$ K4 and p2-1 modulo $K^{4}$.K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and K4K4:=(k4|kK0)

i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo K4 and p2-1 modulo K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{\ast4}:=( $K^{\ast4}:=\langle k^4\vert k\in K\setminus 0 )$\rangle$

i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo K4 and p2-1 modulo K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and $K^{\ast4}:=\langle k^4\vert k\in K\setminus 0 \rangle$

\rangle$ i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo K4 and p2-1 modulo K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and K4:=k4|kK0 i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo K4 and p2-1 modulo K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

click to hide/show revision 17
retagged

updated 5 years ago

FrédéricC gravatar image

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and K4:=k4|kK0 i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo K4 and p2-1 modulo K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.

click to hide/show revision 18
retagged

updated 5 years ago

FrédéricC gravatar image

solving system of equations over number field modulo another number field

I am trying to solve two, 2-variable polynomial equations over F:=Q(i) modulo K:=F(2). Specifically, if p1 = a2+6b2, p2 = 3a2+2b2, and K4:=k4|kK0 i.e. the group of 4th powers of nonzero elements of K. I want to find (all?) a and b in F such that p11 modulo K4 and p2-1 modulo K4.

Any amount of walk through or pointing in the right direction, or telling me this might not be doable would be great! I am relatively new to sage, or at least it has been years since I've used it.