fix: broken doctests and typos

[Fe-r-oz]

This PR implements minor fixes in doctests.

Edit:

• The code is properly formatted and commented.
• Substantial new functionality is documented within the docs.
• All new functionality is tested.
• All of the automated tests on github pass.
• We recently started enforcing formatting checks. If formatting issues are reported in the new code you have written, please correct them.

[Krastanov]

These fixes are much appreciated! But I am also a bit confused: any idea how come these problems were not detected by the test runner?

[Fe-r-oz]

The test runner didn't detect these errors because it did not construct the code to check the parameters: the parameters (108,12) were given to it on the platter.

QuantumClifford.jl/ext/QuantumCliffordHeckeExt/lifted_product.jl

Lines 254 to 255 in 7b444e9

	julia> B = 𝜋^8 + 𝜋^14 + 𝜋^47;
	(108, 12)

To the test runner, this was correct because it was the expected result. It didn't calculate the parameters to verify it, as the calculation step - the code construction => to calculate the parameters was missing. This was a silly error. My bad.

[Fe-r-oz]

In the first doctest fix, the group algebra, GA and the generators x and y are not constructed. For multivariate bicycle code, the condition is to have a z = x*y as the third generator. This doctest should have thrown an error because x and y are not provided to it when constructing the third generator.

QuantumClifford.jl/ext/QuantumCliffordHeckeExt/lifted_product.jl

Lines 218 to 230 in 7b444e9

	julia> import Hecke: group_algebra, GF, abelian_group, gens; # hide
	julia> l=4; m=6;
	julia> z = x*y;
	julia> A = x^3 + y^5;
	julia> B = x + z^5 + y^5 + y^2;
	julia> c = two_block_group_algebra_codes(A, B);
	julia> code_n(c), code_k(c)

[Krastanov]

That does not seem to be the correct explanation. It seems these doctests, because they were in an extension, were actually never executed. Hopefully the last commit I pushed fixes that.

Thanks for flagging this issue! That would have been unresolved and untested for a long time otherwise. Good catch!