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I'm new to sage so forgive me if this is trivial. I want to eventually make a symbol algebras and generic crossed products. The first step would be to make quaternion algebras. I know there is a quaternion algebra function but I want to make one with generators and relations. When I try

F.<i,j> = FreeAlgebra(QQ,2)
A = F.g_algebra({i**2 :-1,j**2:-1,j*i:-i*j})

I get the follow error 'AssertionError: -1'

When I try

F.<i,j> = FreeAlgebra(QQ,2)
A = F.g_algebra({i**2 :-F(1),j**2:-F(1),j*i:-i*j})

I get the error 'ValueError: need more than 1 value to unpack'. Can anyone advise? I want to make the algebra $A=\mathbb{Q}[x,y|x^{n}=a,y^{n}=b,yx =\rho xy]$. If there is a better way to go about it then what I'm doing I would love to hear about that as well. Thanks.

I'm new to sage so forgive me if this is trivial. I want to eventually make a symbol algebras and generic crossed products. The first step would be to make quaternion algebras. I know there is a quaternion algebra function but I want to make one with generators and relations. When I try

F.<i,j> = FreeAlgebra(QQ,2)
A = F.g_algebra({i**2 :-1,j**2:-1,j*i:-i*j})

I get the follow error 'AssertionError: -1'

When I try

F.<i,j> = FreeAlgebra(QQ,2)
A = F.g_algebra({i**2 :-F(1),j**2:-F(1),j*i:-i*j})

I get the error 'ValueError: need more than 1 value to unpack'. Can anyone advise? I want to make the algebra $A=\mathbb{Q}[x,y|x^{n}=a,y^{n}=b,yx =\rho xy]$. If there is a better way to go about it then what I'm doing I would love to hear about that as well. Thanks.

I'm new to sage so forgive me if this is trivial. I want to eventually make a symbol algebras and generic crossed products. The first step would be to make quaternion algebras. I know there is a quaternion algebra function but I want to make one with generators and relations. When I try

F.<i,j> = FreeAlgebra(QQ,2)
A = F.g_algebra({i**2 :-1,j**2:-1,j*i:-i*j})

I get the follow error 'AssertionError: -1'

When I try

F.<i,j> = FreeAlgebra(QQ,2)
A = F.g_algebra({i**2 :-F(1),j**2:-F(1),j*i:-i*j})

I get the error 'ValueError: need more than 1 value to unpack'. Can anyone advise? I want to make the algebra $A=\mathbb{Q}[x,y|x^{n}=a,y^{n}=b,yx =\rho xy]$. If there is a better way to go about it then what I'm doing I would love to hear about that as well. Thanks.