[+] added python env and python script for figures, and continued ex3 for td4

chapters/td4.typ

@@ -19,4 +19,53 @@
   +
   +
   +
-  + Calcul des poids : $omega_i = product _(j=0 \ j!=i) ^(n-1)$
\ No newline at end of file
+  + Calcul des poids : $omega_i = product _(j=0 \ j!=i) ^(n-1) (x_i-x_j) forall i in [|0 ,n-1|].$
+
+    Algorithme :
+    ```
+  poids(x) -> omega
+    n <- length(x)
+    omega <- [null for i in range(n)]
+    pour i=0 à n-1 faire
+      omega[i] <- 1
+      pour j de 0 à n-1 faire
+        si j != i alors
+          omega[i] <- omega[i] * (x[i] - x[j])
+    retourner omega
+    ```
+    Evaluation par la formule barycentrique de Lagrange :
+
+    ```
+  eval_poly_bary(x, y, t, omega) -> ?
+    n <- length(x)
+    pour i=0 à n-1 faire
+      si t=x[i] alors
+        retourner y[i]
+      sinon 
+        calcule p(t)
+      num <- 0
+      denum <- 0
+      pour k=0 à n-1 faire
+        temp <- (t-x[k])*omega[k]
+        num <- num + y[k]/temp
+        denum <- denum + 1/temp
+    retourner num/denum
+    ```
+
+== Exercice 3
++ #align(center)[#image(width: 75%, "../data/td4_e3_q1.png")]
+  - Sinus est $2 pi$ périodique. On peut donc se placer sur l'intervalle $[0, 2 pi]$.
+  $forall x in RR, x mod 2 pi, "soit" X | x equiv X [2 pi] "i.e." x = 2k pi + X.$ \
+  Alors, $sin(x) = sin(X)$
+
+  - Sinus est impair en $pi$ sur l'intervalle $[0, 2 pi]$. \
+    - si $X in [pi, 2pi]$, alors $sin(x) = sin(X) = -sin(2pi X)$ \
+      Posons $Y = 2pi - X$, \
+      Alors, $Y in [0, pi]$  et $sin(x)  = sin(X) = -sin(Y)$
+    - si $X in [0, pi]$, alors on pose $Y = X$. \
+    Alors, $sin(x) = sin(X) = sin(Y)$
+
+    Ainsi, on peut se placer sur l'intervalle $[0, pi]$.
+  
+  - Sinus est pair en $pi/2$ sur l'intervalle $[0, pi]$. \
+    #align(center)[#image(width: 75%, "../data/td4_e3_q1_bis.png")]
\ No newline at end of file

scripts_python/env/bin/Activate.ps1

+<#
+.Synopsis
+Activate a Python virtual environment for the current PowerShell session.
+
+.Description
+Pushes the python executable for a virtual environment to the front of the
+$Env:PATH environment variable and sets the prompt to signify that you are
+in a Python virtual environment. Makes use of the command line switches as
+well as the `pyvenv.cfg` file values present in the virtual environment.
+
+.Parameter VenvDir
+Path to the directory that contains the virtual environment to activate. The
+default value for this is the parent of the directory that the Activate.ps1
+script is located within.
+
+.Parameter Prompt
+The prompt prefix to display when this virtual environment is activated. By
+default, this prompt is the name of the virtual environment folder (VenvDir)
+surrounded by parentheses and followed by a single space (ie. '(.venv) ').
+
+.Example
+Activate.ps1
+Activates the Python virtual environment that contains the Activate.ps1 script.
+
+.Example
+Activate.ps1 -Verbose
+Activates the Python virtual environment that contains the Activate.ps1 script,
+and shows extra information about the activation as it executes.
+
+.Example
+Activate.ps1 -VenvDir C:\Users\MyUser\Common\.venv
+Activates the Python virtual environment located in the specified location.
+
+.Example
+Activate.ps1 -Prompt "MyPython"
+Activates the Python virtual environment that contains the Activate.ps1 script,
+and prefixes the current prompt with the specified string (surrounded in
+parentheses) while the virtual environment is active.
+
+.Notes
+On Windows, it may be required to enable this Activate.ps1 script by setting the
+execution policy for the user. You can do this by issuing the following PowerShell
+command:
+
+PS C:\> Set-ExecutionPolicy -ExecutionPolicy RemoteSigned -Scope CurrentUser
+
+For more information on Execution Policies: 
+https://go.microsoft.com/fwlink/?LinkID=135170
+
+#>
+Param(
+    [Parameter(Mandatory = $false)]
+    [String]
+    $VenvDir,
+    [Parameter(Mandatory = $false)]
+    [String]
+    $Prompt
+)
+
+<# Function declarations --------------------------------------------------- #>
+
+<#
+.Synopsis
+Remove all shell session elements added by the Activate script, including the
+addition of the virtual environment's Python executable from the beginning of
+the PATH variable.
+
+.Parameter NonDestructive
+If present, do not remove this function from the global namespace for the
+session.
+
+#>
+function global:deactivate ([switch]$NonDestructive) {
+    # Revert to original values
+
+    # The prior prompt:
+    if (Test-Path -Path Function:_OLD_VIRTUAL_PROMPT) {
+        Copy-Item -Path Function:_OLD_VIRTUAL_PROMPT -Destination Function:prompt
+        Remove-Item -Path Function:_OLD_VIRTUAL_PROMPT
+    }
+
+    # The prior PYTHONHOME:
+    if (Test-Path -Path Env:_OLD_VIRTUAL_PYTHONHOME) {
+        Copy-Item -Path Env:_OLD_VIRTUAL_PYTHONHOME -Destination Env:PYTHONHOME
+        Remove-Item -Path Env:_OLD_VIRTUAL_PYTHONHOME
+    }
+
+    # The prior PATH:
+    if (Test-Path -Path Env:_OLD_VIRTUAL_PATH) {
+        Copy-Item -Path Env:_OLD_VIRTUAL_PATH -Destination Env:PATH
+        Remove-Item -Path Env:_OLD_VIRTUAL_PATH
+    }
+
+    # Just remove the VIRTUAL_ENV altogether:
+    if (Test-Path -Path Env:VIRTUAL_ENV) {
+        Remove-Item -Path env:VIRTUAL_ENV
+    }
+
+    # Just remove VIRTUAL_ENV_PROMPT altogether.
+    if (Test-Path -Path Env:VIRTUAL_ENV_PROMPT) {
+        Remove-Item -Path env:VIRTUAL_ENV_PROMPT
+    }
+
+    # Just remove the _PYTHON_VENV_PROMPT_PREFIX altogether:
+    if (Get-Variable -Name "_PYTHON_VENV_PROMPT_PREFIX" -ErrorAction SilentlyContinue) {
+        Remove-Variable -Name _PYTHON_VENV_PROMPT_PREFIX -Scope Global -Force
+    }
+
+    # Leave deactivate function in the global namespace if requested:
+    if (-not $NonDestructive) {
+        Remove-Item -Path function:deactivate
+    }
+}
+
+<#
+.Description
+Get-PyVenvConfig parses the values from the pyvenv.cfg file located in the
+given folder, and returns them in a map.
+
+For each line in the pyvenv.cfg file, if that line can be parsed into exactly
+two strings separated by `=` (with any amount of whitespace surrounding the =)
+then it is considered a `key = value` line. The left hand string is the key,
+the right hand is the value.
+
+If the value starts with a `'` or a `"` then the first and last character is
+stripped from the value before being captured.
+
+.Parameter ConfigDir
+Path to the directory that contains the `pyvenv.cfg` file.
+#>
+function Get-PyVenvConfig(
+    [String]
+    $ConfigDir
+) {
+    Write-Verbose "Given ConfigDir=$ConfigDir, obtain values in pyvenv.cfg"
+
+    # Ensure the file exists, and issue a warning if it doesn't (but still allow the function to continue).
+    $pyvenvConfigPath = Join-Path -Resolve -Path $ConfigDir -ChildPath 'pyvenv.cfg' -ErrorAction Continue
+
+    # An empty map will be returned if no config file is found.
+    $pyvenvConfig = @{ }
+
+    if ($pyvenvConfigPath) {
+
+        Write-Verbose "File exists, parse `key = value` lines"
+        $pyvenvConfigContent = Get-Content -Path $pyvenvConfigPath
+
+        $pyvenvConfigContent | ForEach-Object {
+            $keyval = $PSItem -split "\s*=\s*", 2
+            if ($keyval[0] -and $keyval[1]) {
+                $val = $keyval[1]
+
+                # Remove extraneous quotations around a string value.
+                if ("'""".Contains($val.Substring(0, 1))) {
+                    $val = $val.Substring(1, $val.Length - 2)
+                }
+
+                $pyvenvConfig[$keyval[0]] = $val
+                Write-Verbose "Adding Key: '$($keyval[0])'='$val'"
+            }
+        }
+    }
+    return $pyvenvConfig
+}
+
+
+<# Begin Activate script --------------------------------------------------- #>
+
+# Determine the containing directory of this script
+$VenvExecPath = Split-Path -Parent $MyInvocation.MyCommand.Definition
+$VenvExecDir = Get-Item -Path $VenvExecPath
+
+Write-Verbose "Activation script is located in path: '$VenvExecPath'"
+Write-Verbose "VenvExecDir Fullname: '$($VenvExecDir.FullName)"
+Write-Verbose "VenvExecDir Name: '$($VenvExecDir.Name)"
+
+# Set values required in priority: CmdLine, ConfigFile, Default
+# First, get the location of the virtual environment, it might not be
+# VenvExecDir if specified on the command line.
+if ($VenvDir) {
+    Write-Verbose "VenvDir given as parameter, using '$VenvDir' to determine values"
+}
+else {
+    Write-Verbose "VenvDir not given as a parameter, using parent directory name as VenvDir."
+    $VenvDir = $VenvExecDir.Parent.FullName.TrimEnd("\\/")
+    Write-Verbose "VenvDir=$VenvDir"
+}
+
+# Next, read the `pyvenv.cfg` file to determine any required value such
+# as `prompt`.
+$pyvenvCfg = Get-PyVenvConfig -ConfigDir $VenvDir
+
+# Next, set the prompt from the command line, or the config file, or
+# just use the name of the virtual environment folder.
+if ($Prompt) {
+    Write-Verbose "Prompt specified as argument, using '$Prompt'"
+}
+else {
+    Write-Verbose "Prompt not specified as argument to script, checking pyvenv.cfg value"
+    if ($pyvenvCfg -and $pyvenvCfg['prompt']) {
+        Write-Verbose "  Setting based on value in pyvenv.cfg='$($pyvenvCfg['prompt'])'"
+        $Prompt = $pyvenvCfg['prompt'];
+    }
+    else {
+        Write-Verbose "  Setting prompt based on parent's directory's name. (Is the directory name passed to venv module when creating the virtual environment)"
+        Write-Verbose "  Got leaf-name of $VenvDir='$(Split-Path -Path $venvDir -Leaf)'"
+        $Prompt = Split-Path -Path $venvDir -Leaf
+    }
+}
+
+Write-Verbose "Prompt = '$Prompt'"
+Write-Verbose "VenvDir='$VenvDir'"
+
+# Deactivate any currently active virtual environment, but leave the
+# deactivate function in place.
+deactivate -nondestructive
+
+# Now set the environment variable VIRTUAL_ENV, used by many tools to determine
+# that there is an activated venv.
+$env:VIRTUAL_ENV = $VenvDir
+
+if (-not $Env:VIRTUAL_ENV_DISABLE_PROMPT) {
+
+    Write-Verbose "Setting prompt to '$Prompt'"
+
+    # Set the prompt to include the env name
+    # Make sure _OLD_VIRTUAL_PROMPT is global
+    function global:_OLD_VIRTUAL_PROMPT { "" }
+    Copy-Item -Path function:prompt -Destination function:_OLD_VIRTUAL_PROMPT
+    New-Variable -Name _PYTHON_VENV_PROMPT_PREFIX -Description "Python virtual environment prompt prefix" -Scope Global -Option ReadOnly -Visibility Public -Value $Prompt
+
+    function global:prompt {
+        Write-Host -NoNewline -ForegroundColor Green "($_PYTHON_VENV_PROMPT_PREFIX) "
+        _OLD_VIRTUAL_PROMPT
+    }
+    $env:VIRTUAL_ENV_PROMPT = $Prompt
+}
+
+# Clear PYTHONHOME
+if (Test-Path -Path Env:PYTHONHOME) {
+    Copy-Item -Path Env:PYTHONHOME -Destination Env:_OLD_VIRTUAL_PYTHONHOME
+    Remove-Item -Path Env:PYTHONHOME
+}
+
+# Add the venv to the PATH
+Copy-Item -Path Env:PATH -Destination Env:_OLD_VIRTUAL_PATH
+$Env:PATH = "$VenvExecDir$([System.IO.Path]::PathSeparator)$Env:PATH"

scripts_python/env/bin/activate

+# This file must be used with "source bin/activate" *from bash*
+# you cannot run it directly
+
+deactivate () {
+    # reset old environment variables
+    if [ -n "${_OLD_VIRTUAL_PATH:-}" ] ; then
+        PATH="${_OLD_VIRTUAL_PATH:-}"
+        export PATH
+        unset _OLD_VIRTUAL_PATH
+    fi
+    if [ -n "${_OLD_VIRTUAL_PYTHONHOME:-}" ] ; then
+        PYTHONHOME="${_OLD_VIRTUAL_PYTHONHOME:-}"
+        export PYTHONHOME
+        unset _OLD_VIRTUAL_PYTHONHOME
+    fi
+
+    # Call hash to forget past commands. Without forgetting
+    # past commands the $PATH changes we made may not be respected
+    hash -r 2> /dev/null
+
+    if [ -n "${_OLD_VIRTUAL_PS1:-}" ] ; then
+        PS1="${_OLD_VIRTUAL_PS1:-}"
+        export PS1
+        unset _OLD_VIRTUAL_PS1
+    fi
+
+    unset VIRTUAL_ENV
+    unset VIRTUAL_ENV_PROMPT
+    if [ ! "${1:-}" = "nondestructive" ] ; then
+    # Self destruct!
+        unset -f deactivate
+    fi
+}
+
+# unset irrelevant variables
+deactivate nondestructive
+
+VIRTUAL_ENV="/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env"
+export VIRTUAL_ENV
+
+_OLD_VIRTUAL_PATH="$PATH"
+PATH="$VIRTUAL_ENV/bin:$PATH"
+export PATH
+
+# unset PYTHONHOME if set
+# this will fail if PYTHONHOME is set to the empty string (which is bad anyway)
+# could use `if (set -u; : $PYTHONHOME) ;` in bash
+if [ -n "${PYTHONHOME:-}" ] ; then
+    _OLD_VIRTUAL_PYTHONHOME="${PYTHONHOME:-}"
+    unset PYTHONHOME
+fi
+
+if [ -z "${VIRTUAL_ENV_DISABLE_PROMPT:-}" ] ; then
+    _OLD_VIRTUAL_PS1="${PS1:-}"
+    PS1="(env) ${PS1:-}"
+    export PS1
+    VIRTUAL_ENV_PROMPT="(env) "
+    export VIRTUAL_ENV_PROMPT
+fi
+
+# Call hash to forget past commands. Without forgetting
+# past commands the $PATH changes we made may not be respected
+hash -r 2> /dev/null

scripts_python/env/bin/activate.csh

+# This file must be used with "source bin/activate.csh" *from csh*.
+# You cannot run it directly.
+# Created by Davide Di Blasi <davidedb@gmail.com>.
+# Ported to Python 3.3 venv by Andrew Svetlov <andrew.svetlov@gmail.com>
+
+alias deactivate 'test $?_OLD_VIRTUAL_PATH != 0 && setenv PATH "$_OLD_VIRTUAL_PATH" && unset _OLD_VIRTUAL_PATH; rehash; test $?_OLD_VIRTUAL_PROMPT != 0 && set prompt="$_OLD_VIRTUAL_PROMPT" && unset _OLD_VIRTUAL_PROMPT; unsetenv VIRTUAL_ENV; unsetenv VIRTUAL_ENV_PROMPT; test "\!:*" != "nondestructive" && unalias deactivate'
+
+# Unset irrelevant variables.
+deactivate nondestructive
+
+setenv VIRTUAL_ENV "/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env"
+
+set _OLD_VIRTUAL_PATH="$PATH"
+setenv PATH "$VIRTUAL_ENV/bin:$PATH"
+
+
+set _OLD_VIRTUAL_PROMPT="$prompt"
+
+if (! "$?VIRTUAL_ENV_DISABLE_PROMPT") then
+    set prompt = "(env) $prompt"
+    setenv VIRTUAL_ENV_PROMPT "(env) "
+endif
+
+alias pydoc python -m pydoc
+
+rehash

scripts_python/env/bin/activate.fish

+# This file must be used with "source <venv>/bin/activate.fish" *from fish*
+# (https://fishshell.com/); you cannot run it directly.
+
+function deactivate  -d "Exit virtual environment and return to normal shell environment"
+    # reset old environment variables
+    if test -n "$_OLD_VIRTUAL_PATH"
+        set -gx PATH $_OLD_VIRTUAL_PATH
+        set -e _OLD_VIRTUAL_PATH
+    end
+    if test -n "$_OLD_VIRTUAL_PYTHONHOME"
+        set -gx PYTHONHOME $_OLD_VIRTUAL_PYTHONHOME
+        set -e _OLD_VIRTUAL_PYTHONHOME
+    end
+
+    if test -n "$_OLD_FISH_PROMPT_OVERRIDE"
+        set -e _OLD_FISH_PROMPT_OVERRIDE
+        # prevents error when using nested fish instances (Issue #93858)
+        if functions -q _old_fish_prompt
+            functions -e fish_prompt
+            functions -c _old_fish_prompt fish_prompt
+            functions -e _old_fish_prompt
+        end
+    end
+
+    set -e VIRTUAL_ENV
+    set -e VIRTUAL_ENV_PROMPT
+    if test "$argv[1]" != "nondestructive"
+        # Self-destruct!
+        functions -e deactivate
+    end
+end
+
+# Unset irrelevant variables.
+deactivate nondestructive
+
+set -gx VIRTUAL_ENV "/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env"
+
+set -gx _OLD_VIRTUAL_PATH $PATH
+set -gx PATH "$VIRTUAL_ENV/bin" $PATH
+
+# Unset PYTHONHOME if set.
+if set -q PYTHONHOME
+    set -gx _OLD_VIRTUAL_PYTHONHOME $PYTHONHOME
+    set -e PYTHONHOME
+end
+
+if test -z "$VIRTUAL_ENV_DISABLE_PROMPT"
+    # fish uses a function instead of an env var to generate the prompt.
+
+    # Save the current fish_prompt function as the function _old_fish_prompt.
+    functions -c fish_prompt _old_fish_prompt
+
+    # With the original prompt function renamed, we can override with our own.
+    function fish_prompt
+        # Save the return status of the last command.
+        set -l old_status $status
+
+        # Output the venv prompt; color taken from the blue of the Python logo.
+        printf "%s%s%s" (set_color 4B8BBE) "(env) " (set_color normal)
+
+        # Restore the return status of the previous command.
+        echo "exit $old_status" | .
+        # Output the original/"old" prompt.
+        _old_fish_prompt
+    end
+
+    set -gx _OLD_FISH_PROMPT_OVERRIDE "$VIRTUAL_ENV"
+    set -gx VIRTUAL_ENV_PROMPT "(env) "
+end

scripts_python/env/bin/f2py

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from numpy.f2py.f2py2e import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/fonttools

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from fontTools.__main__ import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/pip

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pip._internal.cli.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/pip3

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pip._internal.cli.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/pip3.11

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from pip._internal.cli.main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/pyftmerge

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from fontTools.merge import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/pyftsubset

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from fontTools.subset import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/pylupdate5

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from PyQt5.pylupdate_main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/pyrcc5

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from PyQt5.pyrcc_main import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())

scripts_python/env/bin/python

+python3
\ No newline at end of file

scripts_python/env/bin/python3

+/usr/bin/python3
\ No newline at end of file

scripts_python/env/bin/python3.11

+python3
\ No newline at end of file

scripts_python/env/bin/pyuic5

+#!/home/dolhen/Documents/backup_usb/1_Cours/1_Ecole_inge/TelecomNancyEleves/1a-mn/scripts_python/env/bin/python3
+# -*- coding: utf-8 -*-
+import re
+import sys
+from PyQt5.uic.pyuic import main
+if __name__ == '__main__':
+    sys.argv[0] = re.sub(r'(-script\.pyw|\.exe)?$', '', sys.argv[0])
+    sys.exit(main())