Gröbner bases lie at the heart of many fundamental operations, including solving systems of equations and integration, so performance improvements in Gröbner bases results in faster calculations in other areas as well. Maple 2018 includes new optimizations to the F4 algorithm to increase parallel speedup when computing large total degree Gröbner bases. On a quad core Core i7 with hyperthreading, the new implementation runs 33 percent faster and parallel speedup increases from 1.94x to 2.84x.
memory used=24.08MiB, alloc change=18.98MiB, cpu time=2.73m, real time=25.73s, gc time=0ns
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Maple 2018 also includes a new implementation of the FGLM algorithm for converting total degree Gröbner bases to lexicographical order, with improved performance and lower memory requirements. On this example, the FGLM algorithm runs about 3.5x faster.
memory used=186.80MiB, alloc change=256.00MiB, cpu time=82.03s, real time=26.78s, gc time=93.75ms
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