2019-06-09 11:29:37 +0100 asked a question Directory problems Hi everybody. I would like to create some kind of structure(packages) in sage. Let's say I have the following directory structure: Main_Dir which contains: subdirectories [Dir_A, Dir_B, ...,Test ] Dir_A contains some sage files/classes file1.sage, file2.sage. In file1.sage I have load('file2.sage') My Test directory is the place where I would like to test all the functions I have created. It contains some test files test1.sage, test2.sage, ...., assemble_all.sage. In test1.sage I have the line load('../Dir_A/file1.sage'). And here I got the following error: raise IOError('did not find file %r to load or attach' % filename) IOError: did not find file './file2.sage' to load or attach I hope somebody has an answer to this kind of problems. 2019-06-09 11:28:44 +0100 asked a question Create new sage project Hi everybody. I would like to create some kind of structure(packages) in sage. Let's say I have the following directory structure: Main_Dir which contains: subdirectories [Dir_A, Dir_B, ...,Test ] Dir_A contains some sage files/classes file1.sage, file2.sage. In file1.sage I have load('file2.sage') My Test directory is the place where I would like to test all the functions I have created. It contains some test files test1.sage, test2.sage, ...., assemble_all.sage. In test1.sage I have the line load('../Dir_A/file1.sage'). And here I got the following error: raise IOError('did not find file %r to load or attach' % filename) IOError: did not find file './file2.sage' to load or attach I hope somebody has an answer to this kind of problems. 2018-02-18 15:15:17 +0100 asked a question Pullback of ideals Hi. I have the the following question and I hope that somebody of you has a good idea for the implementation and an explanation of the error. Offset: A number field K (in general non Galois) L the Galois closure of K phi: K --> L an arbitrary embedding of K into L I a fractional ideal in K and IL = phi(I) Question: How to compute the pullback of IL for (general) fractional ideals of K? My approach: Let V, W be two QQ vector spaces and f: V --> W a linear map (morphism). Let further V' and W' be subspaces of V and W. The aim is to identify the subspace V' = f^(-1)(W') as the preimage of W' under f. Let p: V x W' --> W be a linear map definied by (v,w')|--> f(v) - w' with ker(p):={(v,w')in V x W'| f(v)-w' = 0_W} = {(v,w'): f(v) = w'}. Such vectors v are the vectors in the preimage of W'. def inverseImage(IL, K, phi): ZK = K.maximal_order() dK = K.degree() BZK = ZK.basis() M = Matrix(QQ, [ list(phi(b)) for b in BZK ]) BJ = IL.basis() N = Matrix(QQ, [ list(b) for b in BJ ]) vs = M.stack(N).integer_kernel().basis() BI = [ sum([ v[i]*BZK[i] for i in [0..(dK - 1)] ]) for v in vs ] IK = ZK.fractional_ideal([num_IL/denom_IL, BI]) return IK  EXAMPLE 1: sage: K = NumberField(x^6 - 2*x^5 - 6*x^3 + 151*x^2 + 76*x + 861, 'a') sage: L. = K.galois_closure() sage: phi = K.embeddings(L)[1] sage: I = K.fractional_ideal([129, x - 54]) sage: I_ = inverseImage(IL, K, phi) sage: I_ == I TRUE  EXAMPLE 2 (and the first problem, loosing the denominator) sage: I = K.fractional_ideal([2/3]) sage: I Fractional ideal (2/3) sage: I_ = inverseImage(phi(I), K, phi) sage: I_ Fractional ideal (2) sage: I == I_ FALSE  My improvement approach: ... num_IL = IL.numerator().gens()[0] denom_IL = IL.denominator().gens()[0] IK = ZK.fractional_ideal([num_IL/denom_IL, BI]) return IK  Now EXAMPLE 2 returns the corresponding fractional ideal I_ BUT with an incorrect ideal I_ in EXAMPLE 1. Thanks for helping! 2017-12-06 22:37:56 +0100 received badge ● Student (source) 2017-12-05 19:58:40 +0100 received badge ● Scholar (source) 2017-12-05 19:54:39 +0100 received badge ● Editor 2017-12-05 19:53:37 +0100 answered a question Morphism between Klein four group and additive abelian group or order 4 Thank you for the fast answer. C is the always the class group of a quartic/sextic CM filed and G is the corresponding abstract group "printed by sage". Yes, I assume that I have to construct the inverse image too. 2017-12-05 11:03:14 +0100 asked a question Morphism between Klein four group and additive abelian group or order 4 Hi. Let's say I have an ideal class C with structure G := C2 x C2. I want now to construct a morphism phi: G --> C, s.t. phi(g1) = c1 and phi(g2) = c2.