Let p be prime. Elements of
field = GF(p)
can be constructed as
field(x)
If n>1, elements of
field = GF(p**n)
can be constructed as
field([x1, x2, ..., xn])
This would suggest that for n=1
field([x1])
should work and return the same as
field(x1)
However Sage replies with the following traceback
>>> GF(5)([3])
Traceback (most recent call last):
File "<stdin>", line 1, in <module>
File "sage/structure/parent.pyx", line 900, in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9218)
File "sage/structure/coerce_maps.pyx", line 161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4556)
File "sage/structure/coerce_maps.pyx", line 156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4448)
File "/usr/lib/python3/dist-packages/sage/rings/finite_rings/integer_mod_ring.py", line 1162, in _element_constructor_
return integer_mod.IntegerMod(self, x)
File "sage/rings/finite_rings/integer_mod.pyx", line 199, in sage.rings.finite_rings.integer_mod.IntegerMod (build/cythonized/sage/rings/finite_rings/integer_mod.c:4669)
File "sage/rings/finite_rings/integer_mod.pyx", line 389, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__ (build/cythonized/sage/rings/finite_rings/integer_mod.c:6214)
File "sage/rings/finite_rings/integer_mod.pyx", line 378, in sage.rings.finite_rings.integer_mod.IntegerMod_abstract.__init__ (build/cythonized/sage/rings/finite_rings/integer_mod.c:5963)
File "sage/structure/parent.pyx", line 900, in sage.structure.parent.Parent.__call__ (build/cythonized/sage/structure/parent.c:9218)
File "sage/structure/coerce_maps.pyx", line 161, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4556)
File "sage/structure/coerce_maps.pyx", line 156, in sage.structure.coerce_maps.DefaultConvertMap_unique._call_ (build/cythonized/sage/structure/coerce_maps.c:4448)
File "sage/rings/integer.pyx", line 742, in sage.rings.integer.Integer.__init__ (build/cythonized/sage/rings/integer.c:6946)
TypeError: unable to coerce <class 'list'> to an integer
Is this intentional or a bug? (tested on SageMath version 9.0, Release Date: 2020-01-01 on Kubuntu 20.04)
