gdm force mirror screens : generate monitors.xml by commands

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Hello Gnome Team !

I'm the network administrator of a French high school where I have
many Linux desktop with two connected display :
-> the desktop monitor
-> the interactive whiteboard

I need to mirror the display in gdm because often gdm decide than the
primary screen is the whiteboard (even if off) and my user's can't
login.

I can't setup each client manually as there are too many ( round 50 )
so I need to generate the monitors.xml file by command line.

Actually I have found how to get the majority of the xml entries.
-> connector name OK
-> vendor name OK
-> product name OK
-> serial number OK

The only parameter I don't know how to get is the "rate" value :
<mode>
   <width>1440</width>
   <height>900</height>
   <rate>59.887443542480469</rate>
</mode>

Changing the value to 60 is not accepted by gdm. It's seems that I
need at least 3 good digits after the dot (59.887 works) for the file
being accepted.

But xrandr command give only two digits :
~# xrandr
...
1440x900      59.89

Is anyone have an idea how to get this precise refresh rate value ?
Is there any other possibility to generate this monitors.xml file ?
As gdm is now a classic user maybe this can be done with a dbus request ?
Is there some parameter on gdm to default to mirror screen ?

Thanks if someone can help me. This problem does not affect the
previous version of Debian (stretch) as there is no "rate" parameter.
But I use Buster now.

Regards,

Baptiste.

Here a sample monitors.xml file :

<monitors version="2">
  <configuration>
    <logicalmonitor>
      <x>0</x>
      <y>0</y>
      <scale>1</scale>
      <primary>yes</primary>
      <monitor>
        <monitorspec>
          <connector>DP-1</connector>
          <vendor>ITE</vendor>
          <product>DP2VGA V226</product>
          <serial>0x00000000</serial>
        </monitorspec>
        <mode>
          <width>1440</width>
          <height>900</height>
          <rate>59.887443542480469</rate>
        </mode>
      </monitor>
      <monitor>
        <monitorspec>
          <connector>DP-3</connector>
          <vendor>AOC</vendor>
          <product>2260</product>
          <serial>FZRH7HA040839</serial>
        </monitorspec>
        <mode>
          <width>1440</width>
          <height>900</height>
          <rate>59.887443542480469</rate>
        </mode>
      </monitor>
    </logicalmonitor>
  </configuration>
</monitors>
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