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In the Clifford algebra squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) above. Am I missing something?

In the Clifford algebra squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) above. Am I missing something?

In the Clifford algebra squared, tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) $

as some anticommutation rule, but this is not what happens in mathematics (if I'm not mistaken) and renaming by creating a copy of the Clifford algebra with new-names for generators doesn't work.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) $

as some anticommutation rule, but this is not what happens in mathematics (if I'm not mistaken) and renaming by creating a copy of the Clifford algebra with new-names for generators doesn't work.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) $

as some anticommutation rule, but this is not what happens in mathematics (if I'm not mistaken) and renaming by creating a copy of the Clifford algebra with new-names for generators doesn't work.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) $

as some anticommutation rule, but this is not what happens in mathematics (if I'm not mistaken) and renaming by creating a copy of the Clifford algebra with new-names for generators doesn't work.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) $

as some anticommutation rule, but this is not what happens in mathematics (if I'm not mistaken) and renaming by creating a copy of the Clifford algebra with new-names for generators doesn't work.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the Cl(Z,2) $\mathrm{Cl}(\mathbb Z,2) \otimes \mathrm{Cl}(\mathbb Z,2) $ above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) $

as some anticommutation rule, but this is not what happens in mathematics (if I'm not mistaken) and renaming by creating a copy of the Clifford algebra with new-names for generators doesn't work.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the $\mathrm{Cl}(\mathbb Z,2) \otimes \mathrm{Cl}(\mathbb Z,2) $ above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) = a_0^2\otimes a_1^2 $

as some anticommutation rule, anti-commutation rule ($a_0a_1 + a_1 a_0 =0$, hence the minus), but this is not what happens such products never happened in mathematics the computation (if I'm not mistaken) and mistaken). I tried renaming by creating a copy of the Clifford algebra with new-names for generators generators, but that doesn't work.work either.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the $\mathrm{Cl}(\mathbb Z,2) \otimes \mathrm{Cl}(\mathbb Z,2) $ above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) = a_0^2\otimes a_1^2 $

as some anti-commutation rule ($a_0a_1 + a_1 a_0 =0$, hence the minus), but such products never happened in the computation (if (i.e. they must not occur for this example, if I'm not mistaken). I tried renaming creating a copy of the Clifford algebra with new-names for generators, but that doesn't work either.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the $\mathrm{Cl}(\mathbb Z,2) \otimes \mathrm{Cl}(\mathbb Z,2) $ above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) = a_0^2\otimes a_1^2 $

as some anti-commutation rule ($a_0a_1 + a_1 a_0 =0$, hence the minus), but such products never happened in the computation (i.e. they must not occur for this example, if I'm not mistaken). I tried renaming creating a copy of the Clifford algebra with new-names for generators, but that doesn't work either.

In the Clifford algebra tensor-squared, I find a minus I cannot explain:

C.<a0,a1>=CliffordAlgebra(DiagonalQuadraticForm(ZZ,[1,1])) ; C.rename('Cl(Z,2)')
a0.tensor(a0) in C.tensor(C)     
a0.tensor(a1) * a0.tensor(a1)
# result: -1#1    ( why? )

In mathematics $a_0\otimes a_1$ squared equals its components squared, so $a_0^2\otimes a_1^2$ which should be the unit of the $\mathrm{Cl}(\mathbb Z,2) \otimes \mathrm{Cl}(\mathbb Z,2) $ above. Am I missing something?

I supposed first that Sage interprets the wandering of the, say, left $a_1$ to the 'right of the second' $a_0$ in

$ (a_0\otimes a_1) \cdot (a_0\otimes a_1) = a_0^2\otimes a_1^2 $= 1\otimes 1$ (trivial quad. form)

as some anti-commutation rule ($a_0a_1 + a_1 a_0 =0$, hence the minus), but such products never happened in the computation (i.e. they must not occur for this example, if I'm not mistaken). I tried renaming creating a copy of the Clifford algebra with new-names for generators, but that doesn't work either.