Aggressive Geometry – Regular Rings and Flat Finished Modules

Let $ A $ to be a Noetherian domain. assume $ f: A rightarrow B $ is a homomorphism by injection $ B $ in a flat finished module on $ A $. Yes $ B $ is regular is $ A $ regular too? I've played with some examples: finished covers of elliptic curves, finite field extensions and normalization of the cuspidale curve.

There is a kind of reverse statement, whether $ B $ is not supposed to be flat then if $ A $ is regular $ B $ is flat (Thm 23.1 to Matsumura).

Is the algebra of compact operators flat?

Assume that $ A hookrightarrow B $ is an inclusion of $ C ^ * $algebra and let K be the algebra of the compact operators on a separable space of hilbert. Is it true that the map $ A otimes K hookrightarrow B otimes K $ is injective?

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composition – How can I show a slope? Even the mountain roads seem flat on my photos

You must photograph from an angle. If all the trees / panels are in front of you, they will all appear vertically in the image, regardless of the slope.

It is actually a well-known illusion that gives birth to "Gravity Hill", a sloping road that looks straight ahead in the absence of any visual signal, the brain interprets it as flat / slope, which makes objects appear on a vertical slope. !


(source: flickr.com)

Fluxn's picture

If you pull sideways or at an angle, there would be a clear difference in the line of trees and road, which would give the viewer the information that the road is sloping.

Here is an extreme example:

The slope is clearly visible when you look at the trees. Note that the photo was taken by a friend with my camera because I am in it!

Recursion – Building a flat list from a Java tree

I have a tree represented by a ListI want to get flattened.

I wrote the function below:

List flatTree(List toFlat, List destination) {
    for (Entry entry : toFlat) {
        if (CollectionUtils.isNotEmpty(entry.getEntries())) {
            this.flatEntriesMap(entry.getEntries(), destination);
        } else {
            destination.add(entry);
        }
    }
    return destination;
}

used this way:

List flattenedEntries = this.flatTree(entries, new ArrayList<>());

with this kind of contribution (entries):

(
    {
        key: "level1",
        entries: () 
    },
    {
        key: "level1",
        entries: (
            {
                key: "level2",
                entries: () 
            }
        )   
    },
    {
        key: "level1",
        entries: (
            {
                key: "level2",
                entries: () 
            },
            {
                key: "level2",
                entries: (
                    {
                        key: "level3",
                        entries: () 
                    }
                )   
            }
        )   
    }
)

It works but is there a better way to write it?

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magento2 – Unable to set flat client columns with the help of a source entity

I'm trying to create a customer EAV that is always equal to 0 or 1, never zero. The main problem I encounter is to force the column into the customer_grid_flat table to not be nullable.

$customerSetup->addAttribute(Customer::ENTITY, 'is_company', (
    'type' => 'int',
    'backend' => '',
    'frontend' => '',
    'label' => 'Is a company',
    'input' => 'boolean',
    'class' => '',
    'source' => 'VendorModuleModelEntityAttributeSourceBooleanNotNull',
    'global' => ScopedAttributeInterface::SCOPE_GLOBAL,
    'visible' => true,
    'required' => true,
    'user_defined' => false,
    'default' => '0',
    'searchable' => true,
    'filterable' => true,
    'comparable' => true,
    'visible_on_front' => true,
    'system' => false,
    'is_used_in_grid' => true,
    'is_visible_in_grid' => true,
    'is_filterable_in_grid' => true,
    'is_searchable_in_grid' => true,
    'unique' => false,
    'apply_to' => '',
));

The BooleanNotNull class is as follows. I've intentionally left in my debugging.

class BooleanNotNull extends MagentoEavModelEntityAttributeSourceBoolean
{
    public function getFlatColumns()
    {
        var_dump('getFlatColumns');exit();

        $attributeCode = $this->getAttribute()->getAttributeCode();
        return (
            $attributeCode => (
                'unsigned' => false,
                'default' => 0,
                'extra' => null,
                'type' => MagentoFrameworkDBDdlTable::TYPE_SMALLINT,
                'length' => 1,
                'nullable' => false,
                'comment' => $attributeCode . ' column',
            ),
        );
    }
}

I never see this debug message. It seems that the getFlatColumns function, originally defined in AbstractSource, never get called during the setup:upgrade or indexer:reindex orders, which are when the customer_grid_flat the table is updated.

In fact, watching MagentoFrameworkIndexerGridStructure who is actually rebuilding the flat table, I see this:

foreach ($fields as $field) {
    if ($field('type') === 'searchable') {
        $searchableFields() = $field('name');
    }
    $columnMap = isset($field('dataType')) && isset($this->columnTypesMap($field('dataType')))
        ? $this->columnTypesMap($field('dataType'))
        : ('type' => $field('dataType'), 'size' => isset($field('size')) ? $field('size') : null);
    $name = $field('name');
    $type = $columnMap('type');
    $size = $columnMap('size');
    if ($field('type') === 'filterable') {
        $table->addIndex(
            $this->resource->getIdxName($tableName, $name, AdapterInterface::INDEX_TYPE_INDEX),
            $name,
            ('type' => AdapterInterface::INDEX_TYPE_INDEX)
        );
    }
    $table->addColumn($name, $type, $size);
}

The last line is the question. $options It is not even passed in this function, so there is no way to define it.

My question is: how to define the flat column specification to use when rebuilding the client flat table?