A portable way to obtain all gaproots

[orlitzky]

When building a package that uses libgap, it would be helpful if we could easily obtain the argv needed for GAP_Initialize(). We gained --print-gaproot in #4448, but this only prints the primary root with sysinfo.g in it.

There are at least two important gaproots that one might need to know. From Makefile.rules,

# generate a special main.c which sets SYS_DEFAULT_PATHS and then includes
# regular main.c; this is used to build the `gap-install` binary
build/main.c: sysinfo.gap
        @echo "#define SYS_DEFAULT_PATHS \"$(libdir)/gap;$(datarootdir)/gap\"" > $@
        @echo "#include \"$(abs_srcdir)/src/main.c\"" >> $@

(You may also want $HOME/.gap, but that is knowable a priori.) We can actually obtain the first of those without --print-gaproot, by querying pkg-config:

$ echo $(pkg-config --variable=libdir libgap)/gap
/usr/lib/gap

The second however is elusive. When using make install, the build system puts lots of architecture-independent files there... such as lib/init.g... that we need to initialize libgap.

One easy option would be to put the datarootdir into the pkg-config file. Then we could query both it and libdir using pkg-config. Another would be to extend, or add a companion to --print-gaproot, depending on how official you want to make this. Either way would make life a bit easier, thanks :)

[orlitzky]

Two more shower thoughts:

• --print-gaproot tells us where to find sysinfo.gap, so if the second path were in sysinfo.gap, we could get it from there.
• Another option would be to echo SYS_DEFAULT_PATHS into libgap-api.h with a different name. That puts it in the public interface but it could be marked unstable if you don't want to commit to it.

[dimpase]

I would also suggest to have GAP_Initialize_default(), to use these hard-coded paths. I am not quite sure how this should play with the multi-stage installation. Cf. sagemath/sage#41236