How do we cut multiple objects with multiple colors at the edge of a shape? Without clipping!

Question

I got a similar problem as this post: This Post ;-)
And the difference is i've got multiple objects (actually paths) with different colors. Also, i want to know if i can do this without clipping, 'cause clipping creates an object that cannot be converted to a path, which adds a lot of limitations. Please look at [this post] for further info: So, once again, how can i cut the objects that is out of the model shape （which is colored in purple in the image below）, or we say, cut them at the edge.
So here are those objects with different colors:

And the purple box is the model object,

and i want those circles to disappear at the edge of the purple square, so i can get a square filled with colorful circles!

And i create an example with gimp (which creates bitmaps) and show you what is the thing i exactly i want:

Answer 1

You need the Multi-Bool addon (download by clicking on the arrow ↓ right of the headline).

Install the plugin as described on the linked site. Restart Inkscape.

1. Completely ungroup all circles.
2. Select everything (circles and rectangle).
3. Click Extensions > Boolean > Multiple Division.
   (In contrast to Inkscapes native boolean functions, this does not remove the rectangle on the top. You may remove the rectangle manually.)
4. Select the outer parts of the circles and remove them.

Selecting the outer parts is actually more work than one expects. But there is an easy way around this: Use the negation of the rectangle and multi-difference.

1. Draw a rectangle over the complete canvas.
2. Place your original rectangle on top of it.
3. Select both rectangles.
4. Subtract (Path > Difference or ctrl+-).
5. Select everything (circles and negated rectangle).
6. Click Extensions > Boolean > Multiple Difference.