sql server – SP2007 (All)UserData nvarchar field content garbled for choice fields

In our Sharepoint 2007, one of our lists field is configured as such:

<Field Type="Choice" DisplayName="Standard" Required="FALSE" Format="RadioButtons" FillInChoice="FALSE" Group="gc_xyz" ID="{e5d39160-a777-4d70-b372-a7ca76305adc}" SourceID="{21f217b9-cbc5-44b8-96b7-2c665aecc37f}" StaticName="Standard" Name="Standard" ColName="nvarchar20" RowOrdinal="0"> <CHOICES> <CHOICE>Yes</CHOICE> <CHOICE>No</CHOICE> </CHOICES> </Field>

But when I look in the AllUserData table (or its view), the data for this field is like this:
| nvarchar20 |
|————|
|챂䗅⎑啄獌崿|
|ំ싖줚䎭권䞢⋫|
|嫎⚔潣俎즤떴ಇ긅|
|စ꼨噡䊔ꆫ䐂㪗⋉|
|ᶷ刊ᯉ䯥梋蓊㯕Ꙃ|
|㩝䪿撾럌阶紻|
|ពု帵䙏熦༱䏇䶌|
|왜汵䅩粁ʹ猅|

All values are different, as if hashed. How do I read those values to translate them to Yes/No?

Woocommerce Custom product fields need to be editable after purchase in View Orders Page

I am Using https://stackoverflow.com/questions/46612499/display-a-custom-field-value-in-woocommerce-orders-edit-view/#answer-46615303 answer code, which works fine.

I want to display that checkout custom fields on My Account > View Order Pages, to allow customer to edit its value after purchase, so Customers can change and save the custom field value.

Any help?

Degree of compositum of all number fields under given discriminant

For an integer $ngeq 1$ define $f(n)$ to be the degree of the compositum of all number fields with discriminant at most $n$. What bounds are known on $f(n)$?

forms – Validation for if all fields are required when an optional field has a value

I have a form that has an optional username/password input but when either the username or password has a value it causes them both to be required. Not sure how I should approach this?
So far the validation looks a little wordy:
enter image description here

I considered this kind of validation, but it gives an either/or impression:

enter image description here

8 – How to migrate content (fields and paragraphs) into another content type?

My problem is following:

Initial situation

At my Drupal 8 site I have a node content type (let’s calling it node content type A). node content type A has normal (core) fields included and also holds a field with paragraphs items.

Problem/proposed solution

Now I have to change my data model. Due to it’s not adviced to change node content type machine name in a Drupal 8 site, I should go another way:

  1. Clone the content type (would use Entity type clone module for this step). Let’s calling it node content type B
  2. Clone all already existing content of node content type A into new nodes of node content type B
  3. Modify each content/content type as needed by the requirements of the new data model.

Question

How can I perform step 2, especially with the existing paragraphs items?

Thanks in advance for help and/or alternative ways.

abstract algebra – Suppose $F ⊂ K$ are fields. Let $f(x) ∈ F[x] ⊂ K[x]$. Suppose that $f(x)$ is irreducible in $K[x]$. Prove that $f(x)$ is also irreducible in $F[x]$.

Suppose $F ⊂ K$ are both fields. Let $f(x) ∈ F(x) ⊂ K(x)$. Suppose that $f(x)$ is irreducible in $K(x)$.

$a)$ Prove that $f(x)$ is also irreducible in $F(x)$.

$b)$ Is it true that if $f(x)$ is irreducible in $F(x)$, then it is irreducible in $K(x)$, if not, give an example.

My attempt:

$a)$ Since $f(x)$ is irreducible over $K$, then $K(x)/(f(x))$ is a field (I have previously proven this).

But since $F ⊂ K$, then $F(x) ⊂ K(x)$ and thus, $F(x)/(f(x))⊂K(x)/(f(x))$.

Since $F(x)/(f(x))$ is a subfield, then it is a field, and so $f(x)$ is irreducible over $F$.

Is my attempt correct?

And I don’t think this still holds if $f(x)$ is irreducible over $F$. Can someone please clarify part $(b)$ and give an example? Thank you

plugin development – How to query a nested filed in wordpress api using _fields param

I’m trying to access certain fields which are deeply nested using _fields param which is offerd by wordpress.
what’s wrong with my query?

structure of response.

{
    "_embedded" : {
    
        wp:featuredmedia : [
            {
                "id": 21917,
                 "date": "2021-02-27T11:56:48",
                 "slug": "SLUG",
                 "type": "attachment",
                 "link": "https://SITENAME.net/POST/POST/",
                  "title": {
                     rendered": "SLUG NAME"
                 },
            
            }
            
        ]
    }
}

Desired response :

{
    "_embedded" : {

        wp:featuredmedia : [
            {
                 "link": "https://SITENAME.net/POST/POST/",
            }

        ]
    }
}

Query I’m Trying to use:

http://yoursite.com/wp-json/wp/v2/posts?_embed&_filter=_embedded.wp:featuredmedia[0].link

Tits reductive groups over local fields, 1.15/3.11. Problem with affine root subgroups of $SU_3$ ramified, residue characteristic p=2

Let $L/K$ be ramified quadratic extension of local fields, and let characteristic of the residue field of $K$ be $2$. Let $mathbb{G}=SU_3$, $G=mathbb{G}(K)$. Let $text{val}$ be a valuation on $K$ so that $text{val}(K^times) = mathbb{Z}$ (and $text{val}(L^times) = frac{1}{2}mathbb{Z}$).

Following Tits 1.15 and 3.11, I have been trying to work out the parahoric subgroups of $G$ attached to the special vertices $nu_0$ and $nu_1$ in the building of $G$.

Firstly, I’ll start with a description of the root subgroups of $G$. I’m using a slightly different notation from Tits’. Let $$u_+(c,d) = begin{pmatrix} 1 & -bar{c} & d \ 0 & 1 & c \ 0 & 0 & 1 end{pmatrix},$$
with $bar{c}c+d+bar{d}=0$.
Similarly, $$u_-(c,d) = begin{pmatrix} 1 & 0 & 0 \ c & 1 & 0 \ d & -bar{c} & 1 end{pmatrix},$$
with $bar{c}c+d+bar{d}=0$.

We have the root subgroups $U_{pm a}(K) = { u_pm(c,d) text{ : } c,d in L }$ and $U_{pm 2a} = { u_pm(0,d) text{ : } d in L}$.

Tits later defines $delta = sup{text{val}(d) text{ : } d in L, , bar{d}+d+1=0}$. $delta=0$ in the unramified case and in the ramified, residue characteristic $pneq 2$ case. However, when $L/K$ is ramified with residue characteristic $2$, $delta$ is strictly negative.

From here, Tits finds the set of affine roots of $G$ as $$Big{pm a + frac{1}{2}mathbb{Z} +frac{delta}{2}Big} cup Big{pm 2a +mathbb{Z}+ frac{1}{2} + delta Big}.$$

Affine root subgroups are given by $$U_{pm a + gamma/2} = { u_pm(c,d) text{ : } text{val}(d) geq gamma},$$
$$U_{pm 2a+ gamma} = { u_pm(0,d) text{ : } text{val}(d) geq gamma}.$$

The special points $nu_0$ and $nu_1$ i the standard apartment are defined by $$a(nu_1)=frac{delta}{2}, , a(nu_0) = frac{delta}{2} + frac{1}{4}.$$

From here, one can find that $$G_{nu_1} = langle T_0, U_{a-frac{delta}{2}}, U_{-a+frac{delta}{2}}, U_{2a+frac{1}{2}-delta}, U_{-2a+frac{1}{2}+delta} rangle,$$
$$G_{nu_0} = langle T_0, U_{a-frac{delta}{2}}, U_{-a+frac{1}{2}+frac{delta}{2}}, U_{2a-frac{1}{2}-delta}, U_{-2a+frac{1}{2}+delta} rangle.$$

In 3.11, Tits takes a $lambda in L$ with $text{val}(lambda) = delta$, satisfying $lambda+bar{lambda}+1=0$ in a way such that $lambda varpi_L + overline{(lambda varpi_L)}=0$ for some uniformizer $varpi_L$ of the ring of integers $mathcal{O}_L$ of $L$.

In 3.11, Tits defines the lattices $$Lambda_{nu_1} = mathcal{O}_L oplus mathcal{O}_L oplus lambdamathcal{O}_L,$$
$$Lambda_{nu_0} = varpi_L^{-1}mathcal{O}_L oplus mathcal{O}_L oplus lambdamathcal{O}_L.$$ Let $P_{nu_1}$ and $P_{nu_0}$ be their respective stabilizers.
Tits then states that $G_{nu_i} = P_{nu_i} cap G_{nu_i}$ for $i=0,1$.

Here’s where my problem comes in.

Consider $G_{nu_1} = langle T_0, U_{a-frac{delta}{2}}, U_{-a+frac{delta}{2}}, U_{2a+frac{1}{2}-delta}, U_{-2a+frac{1}{2}+delta} rangle.$ The stabilizer of the lattice $Lambda_{nu_1}$ in $GL_3(L)$ has the form
$$begin{pmatrix} mathcal{O}_L & mathcal{O}_L & mathfrak{p}_L^{-2delta} \ mathcal{O}_L & mathcal{O}_L & mathfrak{p}_L^{-2delta} \ mathfrak{p}_L^{2delta} & mathfrak{p}_L^{2delta} & mathcal{O}_L end{pmatrix}.$$
Since $text{val}(delta) < 0$, intersecting this stabilizer with $G$ would give us a matrix roughly looking like
$$begin{pmatrix} mathcal{O}_L & mathfrak{p}_L^{-2delta} & mathfrak{p}_L^{-2delta} \ mathcal{O}_L & mathcal{O}_L & mathfrak{p}_L^{-2delta} \ mathfrak{p}_L^{2delta} & mathcal{O}_L & mathcal{O}_L end{pmatrix},$$

Presumeably, this would tell us that $$U_{a-frac{delta}{2}} = { u_+(c,d) text{ : } c,d in L, , text{val}(d) geq -delta textbf{ and } text{val}(c) geq -delta },$$
$$U_{-a+frac{delta}{2}} = {u_{-}(c,d) text{ : } c,d in L, , text{val}(d) geq delta textbf{ and } text{val}(c) geq 0 }.$$
Normally, one would expect that if $text{val}(d) = gamma$, then $text{val}(d) = frac{gamma}{2}$ or $frac{gamma}{2}+frac{1}{4}$, as whether $gamma in mathbb{Z}$ or just $frac{1}{2}mathbb{Z}$.

I cannot work out algebraically why we have these improved bounds on the valuation of $c$ for these affine root subgroups. I assume it involves some manipulation with $lambda$, but I am not making any progress.

Thank you

python – Eliminar MEDIA Files antiguos, es decir, archivos que ya no estén referenciados en los File Fields de los Modelos de Django

Heredé un sistema web en el que se encuentran varios archivos viejos que ya no están referenciados en la Base de Datos. Es decir, se borraron instancias de modelos en los que se borraba la referencia a un Media File pero el Media File en si mismo, nunca fue borrado. Me gustaría saber si conocen alguna librería ya probada que no genere errores para lograr el objetivo de borrar esos archivos.

Actualmente, codifique unos signals que sirven para borrar Media Files cuando sus respectivas referencias en la base de datos son eliminadas, o bien, cuando son actualizadas.

import uuid

from django.db import models
from django.dispatch import receiver
from django.utils.translation import ugettext_lazy as _


class MediaFile(models.Model):
    file = models.FileField(_("file"),
        upload_to=lambda instance, filename: str(uuid.uuid4()))


# These two auto-delete files from filesystem when they are unneeded:

@receiver(models.signals.post_delete, sender=MediaFile)
def auto_delete_file_on_delete(sender, instance, **kwargs):
    """
    Deletes file from filesystem
    when corresponding `MediaFile` object is deleted.
    """
    if instance.file:
        if os.path.isfile(instance.file.path):
            os.remove(instance.file.path)

@receiver(models.signals.pre_save, sender=MediaFile)
def auto_delete_file_on_change(sender, instance, **kwargs):
    """
    Deletes old file from filesystem
    when corresponding `MediaFile` object is updated
    with new file.
    """
    if not instance.pk:
        return False

    try:
        old_file = MediaFile.objects.get(pk=instance.pk).file
    except MediaFile.DoesNotExist:
        return False

    new_file = instance.file
    if not old_file == new_file:
        if os.path.isfile(old_file.path):
            os.remove(old_file.path)

Pero ese código me sirve solamente con los Media Files que son borrados actualmente, no los viejos que ya no estaban referenciados.

¿Alguna idea?

ag.algebraic geometry – Covering abelian varieties over finite fields with the product of curves

Question. Given an $n$-dimensional abelian variety $X$ over a finite field, is it possible to find smooth projective curves
$C_1,ldots, C_n$ such that there exists a finite regular map
$C_1times ldots times C_nrightarrow X$?

I was thinking maybe using the space filling curve, we have a sequence of space-filling curves that cover all rational points, picking $n$ of them we can define a map from their product to $X$, by first mapping the product to the product of $n$-copies of $X$ and then taking the sum of it. This gives a regular map from product of $n$ curves to $X$ which is surjective let’s say on $mathbb{F}_{p^m}$ points, which we can take $m$ to be arbitrarily large. The only problem is that one needs to verify that image of this map is $n$-dimensional. Although I don’t know how to prove it, it seems intuitively obvious.