2018-06-27 11:43:31 +0100 commented answer Pari error when factoring polynomial Thanks! I will look into it. 2018-06-26 21:58:15 +0100 asked a question Pari error when factoring polynomial I ran the following code to factor a polynomial over a number field: U. = CyclotomicField(32) P. = PolynomialRing(U) f = x^16-256 print f.factor()  This code works for all substitutions of 256 by another value I have tried, but this one gives an error: Traceback (most recent call last): File "p_is_2_test.sage.py", line 10, in print f.factor() File "sage/rings/polynomial/polynomial_element.pyx", line 4199, in sage.rings.polynomial.polynomial_element.Polynomial.factor (build/cythonized/sage/rings/polynomial/polynomial_element.c:39418) File "cypari2/auto_gen.pxi", line 17246, in cypari2.gen.Gen_auto.nffactor File "cypari2/handle_error.pyx", line 196, in cypari2.handle_error._pari_err_handle cypari2.handle_error.PariError: inconsistent concatenation t_COL (8 elts) , t_VEC (8 elts)  This seems like some bug in sage, but I am not quite sure what to make of the error. Does anyone know how to deal with this error and to properly let sage factor this polynomial? 2018-06-26 21:50:25 +0100 received badge ● Scholar (source) 2018-06-26 21:44:16 +0100 received badge ● Supporter (source) 2018-06-19 12:36:08 +0100 received badge ● Nice Question (source) 2018-06-17 16:10:17 +0100 commented answer Possible bug with identity morphism Is there any way to coerce the formal composite map to one of the former type? I compute the product of O(n) morphisms as f = one and for phi in l: f = phi*f, and the latter becomes an unreadable block of composite maps when I print the result, and it doesn't help the algorithmic complexity either when trying to evaluate the function I presume. I can work around this by reverse iterating the list and doing right multiplication with phi instead, but this feels like a hack. Furthermore, my question was whether any piece of documentation justifies this counter intuitive result. 2018-06-17 12:47:03 +0100 asked a question Possible bug with identity morphism I have a number field U for which I consider its automorphisms through Hom(U,U). The identity one=Hom(U,U).identity() behaves weirdly under right multiplication: U = CyclotomicField(3) f = Hom(U,U)[1] print f print "--------------------" one = Hom(U,U).identity() print f*one print "--------------------" print one*f print "--------------------" print f*f  When I run this code, I expect f to be printed thrice, followed by the identity morphism. However, while the first and third output do in fact both print f, the second prints Composite map: From: Cyclotomic Field of order 3 and degree 2 To: Cyclotomic Field of order 3 and degree 2 Defn: Identity endomorphism of Cyclotomic Field of order 3 and degree 2 then Ring endomorphism of Cyclotomic Field of order 3 and degree 2 Defn: zeta3 |--> -zeta3 - 1  Is this a bug or is this this behaviour explained somewhere in the documentation? 2018-01-28 02:03:02 +0100 received badge ● Student (source) 2018-01-27 12:42:28 +0100 commented answer Computation of homomorphisms of number fields Maybe I should have included this, but at print K.gens(), L.gens()' sage answers with (gen1, zeta3) (gen2, zeta3) so clearly K has two generators, I think? Secondly, how does it decide where to send zeta3? In this case there is little room, but if we take P. = PolynomialRing(QQ) R. = QQ.extension(X^2-2) K. = R.extension(X^2-3) print K.gens() H = K.hom( [-s3,-s2], K ) print H  this should also give a valid morphism instead of the one returned by K.hom([-s3]) that maps s2 to itself. 2018-01-27 12:25:40 +0100 asked a question Computation of homomorphisms of number fields Given two number fields, I want to construct a morphism between them. For this I tried to use the hom member-function of the NumberField object as follows: R. = CyclotomicField(3) P. = PolynomialRing(R) K. = R.extension(X^3-zeta3) L. = R.extension(X^3-zeta3^2) print K.gens(), L.gens() H = K.hom( [gen2,zeta3^2], L ) print H  The help page of hom specifies: Return the unique homomorphism from self to codomain that sends self.gens() to the entries of im_gens`. Raises a TypeError if there is no such homomorphism. However, instead of TypeError, I get an incomprehensible error: File "/home/sage/bin/sage2/local/lib/python2.7/site-packages/sage/rings/number_field/number_field.py", line 1670, in _element_constructor_ raise ValueError("Length must be equal to the degree of this number field") ValueError: Length must be equal to the degree of this number field What am I doing wrong? Is there a better way to define this morphism?