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Issue 20919: Wrong behaviour when existence=True for incomplete_orthogonal_array and difference_family

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    "body": "<div id=\"comment:0\"></div>\n\nThe docstring for `designs.incomplete_orthogonal_array` claims that if `existence=True`, the function will return a boolean or `Unknown`. However, for certain values, it returns the array.\n\nFor example,\n\n```\nsage: type(designs.incomplete_orthogonal_array(9,82,[9],existence=True))\n<type 'list'>\n```\n\nI encountered this while working on something else, and I have no idea of the math behind this, but it seems to be incorrect. The problem seems to be in the block starting at line 1371 in `orthogonal_arrays.py` (\"From a quasi-difference matrix\"); all other branches in the function take into account whether `existence` is set, but this one does not.\n\nSimilarly,\n\n```\nsage: type(designs.difference_family(3, 2, 1, existence=True)[0])\n<class 'sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic_with_category'>\n```\n\nCC:  @videlec\n\nComponent: **combinatorial designs**\n\nKeywords: **days78**\n\n_Issue created by migration from https://trac.sagemath.org/ticket/20919_\n\n",
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    "title": "Wrong behaviour when `existence=True` for `incomplete_orthogonal_array` and `difference_family`",
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The docstring for designs.incomplete_orthogonal_array claims that if existence=True, the function will return a boolean or Unknown. However, for certain values, it returns the array.

For example,

sage: type(designs.incomplete_orthogonal_array(9,82,[9],existence=True))
<type 'list'>

I encountered this while working on something else, and I have no idea of the math behind this, but it seems to be incorrect. The problem seems to be in the block starting at line 1371 in orthogonal_arrays.py ("From a quasi-difference matrix"); all other branches in the function take into account whether existence is set, but this one does not.

Similarly,

sage: type(designs.difference_family(3, 2, 1, existence=True)[0])
<class 'sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic_with_category'>

CC: @videlec

Component: combinatorial designs

Keywords: days78

Issue created by migration from https://trac.sagemath.org/ticket/20919


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    "body": "<div id=\"comment:1\" align=\"right\">comment:1</div>\n\nSimilar problem with `designs.difference_family(3, 2, 1, existence=True)`",
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comment:1

Similar problem with designs.difference_family(3, 2, 1, existence=True)


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    "body": "Description changed:\n``````diff\n--- \n+++ \n@@ -1,4 +1,4 @@\n-The docstring for `designs.incomplete_orthogocal_array` claims that if `existence=True`, the function will return a boolean or `Unknown`. However, for certain values, it returns the array.\n+The docstring for `designs.incomplete_orthogonal_array` claims that if `existence=True`, the function will return a boolean or `Unknown`. However, for certain values, it returns the array.\n \n For example,\n \n``````\n",
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Description changed:

--- 
+++ 
@@ -1,4 +1,4 @@
-The docstring for `designs.incomplete_orthogocal_array` claims that if `existence=True`, the function will return a boolean or `Unknown`. However, for certain values, it returns the array.
+The docstring for `designs.incomplete_orthogonal_array` claims that if `existence=True`, the function will return a boolean or `Unknown`. However, for certain values, it returns the array.
 
 For example,
 

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    "body": "Description changed:\n``````diff\n--- \n+++ \n@@ -8,3 +8,10 @@\n ```\n \n I encountered this while working on something else, and I have no idea of the math behind this, but it seems to be incorrect. The problem seems to be in the block starting at line 1371 in `orthogonal_arrays.py` (\"From a quasi-difference matrix\"); all other branches in the function take into account whether `existence` is set, but this one does not.\n+\n+Similarly,\n+\n+```\n+sage: type(designs.difference_family(3, 2, 1, existence=True)[0])\n+<class 'sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic_with_category'>\n+```\n``````\n",
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Description changed:

--- 
+++ 
@@ -8,3 +8,10 @@
 ```
 
 I encountered this while working on something else, and I have no idea of the math behind this, but it seems to be incorrect. The problem seems to be in the block starting at line 1371 in `orthogonal_arrays.py` ("From a quasi-difference matrix"); all other branches in the function take into account whether `existence` is set, but this one does not.
+
+Similarly,
+
+```
+sage: type(designs.difference_family(3, 2, 1, existence=True)[0])
+<class 'sage.rings.finite_rings.integer_mod_ring.IntegerModRing_generic_with_category'>
+```

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