I'm in the US and want to build an Ubuntu PC for around $1200. I have a monitor but need a case and the rest of the system.
I'll use C, C++, Rust, GAP, Wolfram and Python for FEA, large graphs and matrices, finite-field arithmetic and depth-first searches. What specs should I prioritize?
Start with the programs that are actually slow, because those jobs can want very different hardware. Check whether they use multiple CPU cores, a GPU, or mostly one core, and watch memory usage on a representative run.
For FEA, also check the solver's licensing before paying for lots of cores. Some licenses are priced by core or socket, so the fastest-looking CPU might not be the best fit for the software budget.
I'd put memory capacity high on the list and consider 64GB if your current jobs are close to filling 32GB. A 196,883 by 196,883 dense matrix with 8-byte entries alone would take roughly 310GB, so check whether your data is sparse and what the software actually stores.
DDR4 may leave more room in the budget than DDR5, depending on the CPU and motherboard you choose. Check compatibility as a set, and don't assume laptop memory can be reused in a desktop.
Don't buy a GPU just because the work involves matrices. First check which of your programs and code paths can use it, and how much GPU memory they need. A job that doesn't fit in GPU memory may not benefit much from a faster card.
If Wolfram GPU support matters, check its current requirements and compatibility for the specific functions you use. NVIDIA may be worth considering, but the card, drivers and Ubuntu support all need to line up with your software.
For the CPU, look at both per-core performance and core count. Depth-first search and other sequential work won't necessarily get much faster just from adding cores, while parallel code may benefit. I'd pick the processor after checking the workloads, then fit the motherboard, case, power supply and storage around it.
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Viblet-9h:
My current laptop has an i7 and 32GB of RAM. Large GPU array work is slow, and it also struggles with parallel tasks and simplicial homology calculations.
n307+foldmark_8:
That gives you a useful baseline. Compare a few representative runs for CPU utilization, RAM use and GPU memory use before deciding where the desktop budget should go.