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"body": "<div id=\"comment:0\"></div>\n\nIf a number field is equipped with structural morphisms, these are lost when applying the functorial construction of the number field (via `NumberField.construction()` and `AlgebraicExtensionFunctor`), which happens for example in the construction of push-outs:\n\n```\nsage: R.<x> = ZZ[]\nsage: K.<a> = NumberField(x^2 - 3)\nsage: L0.<b> = K.change_names()\nsage: L0.structure()\n(Isomorphism given by variable name change map:\n From: Number Field in b with defining polynomial x^2 - 3\n To: Number Field in a with defining polynomial x^2 - 3,\n Isomorphism given by variable name change map:\n From: Number Field in a with defining polynomial x^2 - 3\n To: Number Field in b with defining polynomial x^2 - 3)\nsage: L1 = (b*x).parent().base_ring()\nsage: L1.structure()\n(Ring Coercion endomorphism of Number Field in b with defining polynomial x^2 - 3,\n Ring Coercion endomorphism of Number Field in b with defining polynomial x^2 - 3)\n```\nThis currently does not cause too much trouble because the two fields (with and without the structural morphisms) are considered equal, although they are not identical:\n\n```\nsage: L1 is L0\nFalse\nsage: L1 == L0\nTrue\n```\nHowever, this becomes a nuisance when implementing \"equality is identity\" for number fields on ticket #20827.\n\nComponent: **number fields**\n\nAuthor: **Peter Bruin**\n\nBranch/Commit: **[`c30f1eb`](https://github.com/sagemath/sagetrac-mirror/commit/c30f1ebd35df510a699e851468625b9aff7a6364)**\n\nReviewer: **Julian R\u00fcth**\n\n_Issue created by migration from https://trac.sagemath.org/ticket/20826_\n\n",
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"title": "AlgebraicExtensionFunctor should include number field structure",
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}If a number field is equipped with structural morphisms, these are lost when applying the functorial construction of the number field (via NumberField.construction() and AlgebraicExtensionFunctor), which happens for example in the construction of push-outs:
sage: R.<x> = ZZ[]
sage: K.<a> = NumberField(x^2 - 3)
sage: L0.<b> = K.change_names()
sage: L0.structure()
(Isomorphism given by variable name change map:
From: Number Field in b with defining polynomial x^2 - 3
To: Number Field in a with defining polynomial x^2 - 3,
Isomorphism given by variable name change map:
From: Number Field in a with defining polynomial x^2 - 3
To: Number Field in b with defining polynomial x^2 - 3)
sage: L1 = (b*x).parent().base_ring()
sage: L1.structure()
(Ring Coercion endomorphism of Number Field in b with defining polynomial x^2 - 3,
Ring Coercion endomorphism of Number Field in b with defining polynomial x^2 - 3)
This currently does not cause too much trouble because the two fields (with and without the structural morphisms) are considered equal, although they are not identical:
sage: L1 is L0
False
sage: L1 == L0
True
However, this becomes a nuisance when implementing "equality is identity" for number fields on ticket #20827.
Component: number fields
Author: Peter Bruin
Branch/Commit: c30f1eb
Reviewer: Julian Rüth
Issue created by migration from https://trac.sagemath.org/ticket/20826
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"body": "Description changed:\n``````diff\n--- \n+++ \n@@ -24,4 +24,4 @@\n sage: L1 == L0\n True\n ```\n-However, this becomes a nuisance when trying to implement \"equality is identity\" for number fields (to be done on a future ticket).\n+However, this becomes a nuisance when implementing \"equality is identity\" for number fields on ticket #20827.\n``````\n",
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---
+++
@@ -24,4 +24,4 @@
sage: L1 == L0
True
```
-However, this becomes a nuisance when trying to implement "equality is identity" for number fields (to be done on a future ticket).
+However, this becomes a nuisance when implementing "equality is identity" for number fields on ticket #20827.archive/issue_comments_302045.json:
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"body": "<div id=\"comment:3\" align=\"right\">comment:3</div>\n\n(seen in `AlgebraicExtensionFunctor`) For comparisons you can simplify\n\n```\nc = cmp(a1,b1)\nif c == 0:\n c = cmp(a2,b2)\nif c == 0:\n c = cmp(a3,b3)\n...\nreturn c\n```\nby\n\n```\nreturn cmp(a1,b1) or cmp(a2,b2) or cmp(a3,b3) or ...\n```",
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(seen in AlgebraicExtensionFunctor) For comparisons you can simplify
c = cmp(a1,b1)
if c == 0:
c = cmp(a2,b2)
if c == 0:
c = cmp(a3,b3)
...
return c
by
return cmp(a1,b1) or cmp(a2,b2) or cmp(a3,b3) or ...
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"body": "<div id=\"comment:4\"></div>\n\nBranch pushed to git repo; I updated commit sha1. New commits:\n<table><tr><td><a href=\"https://github.com/sagemath/sagetrac-mirror/commit/c30f1ebd35df510a699e851468625b9aff7a6364\"><code>c30f1eb</code></a></td><td><code>Trac 20826: simplify AlgebraicExtensionFunctor.__cmp__()</code></td></tr></table>\n",
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c30f1eb | Trac 20826: simplify AlgebraicExtensionFunctor.__cmp__() |
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