Can't find SAGE_ROOT

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It seems you want to install csdp using sage -i.

Your operating system's package manager might have it packaged.

In Debian or Ubuntu, use the following command in a terminal:

sudo apt install coinor-csdp

I think you're talking about https://github.com/jsliacan/flagmatic. The first instruction there is sage -i csdp, and this fails for me with Sage installed by apton Ubuntu. The only safe way to do this, and in my experience, the only reliable way to be able to build other packages for Sage, is to build Sage from scratch, but fortunately that is not too complicated. Follow the directions at https://doc.sagemath.org/html/en/inst..., and in particular at https://doc.sagemath.org/html/en/inst.... (I recommend all four of the sudo apt-get install ... commands given there.)

This is normal. the sage executable is a shell script which defines some environment variables (among them SAGE_ROOT) then launches Sage's version of Python with the necessary libraries.

Similarly, sage -sh lauvhes the same shell script, whose argument sh launches a subshell where SAGE_ROOT is defined (among others, most notably the path).

The Python session implementing the Sage REPL doesn't need a SAGE_ROOT identifier, but it is defined in the underlying environment :

charpent@zen-book-flip:~$ sage
┌────────────────────────────────────────────────────────────────────┐
│ SageMath version 9.8.beta1, Release Date: 2022-09-29               │
│ Using Python 3.10.7. Type "help()" for help.                       │
└────────────────────────────────────────────────────────────────────┘
┏━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┓
┃ Warning: this is a prerelease version, and it may be unstable.     ┃
┗━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━┛
sage: !echo $SAGE_ROOT
/usr/local/sage-9
sage: quit
charpent@zen-book-flip:~$ echo $SAGE_ROOT

HTH,

Running export SAGE_ROOT=/usr/local/sage-9.6 (or alike) will make this variable available for the current shell session and descendant processes.