Remove backslash hack in doctest

[user202729]

Would fix #39058 . I think it's cleaner to remove this thing anyway (given that it doesn't work in the real Sage command prompt either)

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• The description explains in detail what this PR is about.
• I have linked a relevant issue or discussion.
• I have created tests covering the changes.
• I have updated the documentation and checked the documentation preview.

⌛ Dependencies

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[user202729]

There's a little issue e.g. with the book_stein_ent file…

This file contains all the example code from the published book
'Elementary Number Theory: Primes, Congruences, and Secrets' by
William Stein, Springer-Verlag, 2009.

This modifies the code however. Is it a problem (factually incorrect)?

Then there are other cases where the file is autogenerated… (I don't know where the source is)

This file (./integration_doctest.sage) was *autogenerated* from ./integration.tex,
with sagetex.sty version 2011/05/27 v2.3.1.

Helper script:

from pathlib import Path
import re

backslash_replacer = re.compile(r"^( *)sage:(.*)\\\ *\n((?:\ *\.\.\.\.\:.*\\\ *\n)*)(\ *)(.*)", flags=re.MULTILINE)

def do_replace(string):
    m = backslash_replacer.search(string)
    while m is not None:
        g = m.groups()
        if g[4].startswith(("sage:", "....:")):
            m = backslash_replacer.search(string, m.start()+1)
        else:
            string = (string[:m.start()] + g[0] + "sage:" + g[1] + "\\\n" + g[2] + 
            g[0] + "....: " +
            " " * max(0, len(g[3])-len(g[0])-6) + 
            g[4] + string[m.end():])
            m = backslash_replacer.search(string)  # may have exponential complexity
    return string

for f in """
src/doc/en/developer/coding_basics.rst
src/doc/en/thematic_tutorials/lie/crystals.rst
src/doc/en/thematic_tutorials/lie/branching_rules.rst
src/doc/en/thematic_tutorials/sandpile.rst
src/sage/coding/delsarte_bounds.py
src/sage/coding/extended_code.py
src/sage/coding/information_set_decoder.py
src/sage/coding/linear_code.py
src/sage/coding/linear_code_no_metric.py
src/sage/combinat/designs/gen_quadrangles_with_spread.pyx
src/sage/doctest/parsing.py
src/sage/dynamics/arithmetic_dynamics/affine_ds.py
src/sage/dynamics/arithmetic_dynamics/wehlerK3.py
src/sage/doctest/forker.py
src/sage/features/__init__.py
src/sage/dynamics/arithmetic_dynamics/projective_ds.py
src/sage/geometry/polyhedron/base4.py
src/sage/graphs/graph.py
src/sage/groups/conjugacy_classes.py
src/sage/groups/group.pyx
src/sage/interfaces/qepcad.py
src/sage/knots/knotinfo.py
src/sage/libs/ntl/ntl_mat_GF2.pyx
src/sage/manifolds/differentiable/affine_connection.py
src/sage/matrix/matrix_polynomial_dense.pyx
src/sage/numerical/backends/interactivelp_backend.pyx
src/sage/numerical/backends/glpk_backend.pyx
src/sage/rings/multi_power_series_ring.py
src/sage/rings/multi_power_series_ring_element.py
src/sage/rings/polynomial/multi_polynomial.pyx
src/sage/rings/polynomial/multi_polynomial_ideal.py
src/sage/rings/polynomial/pbori/gbcore.py
src/sage/schemes/jacobians/abstract_jacobian.py
src/sage/schemes/product_projective/rational_point.py
src/sage/schemes/product_projective/subscheme.py
src/sage/schemes/projective/projective_space.py
src/sage/symbolic/expression.pyx
src/sage/tensor/modules/tensor_with_indices.py
src/sage/tests/book_stein_ent.py
src/sage/tests/books/computational-mathematics-with-sagemath/float_doctest.py
src/sage/tests/books/computational-mathematics-with-sagemath/integration_doctest.py
src/sage/topology/simplicial_complex.py
""".strip().splitlines():
    f = Path("~/sage").expanduser()/f
    if f.is_file() and f.suffix not in (".pyc",):
        string = f.read_text(errors="ignore")
        string1 = do_replace(string)
        if string1 != string:
            #print(string)
            f.write_text(string1)
            print("Changed:", f)
        else: print("No changes:", f)
    else: assert False