# Benchmarks#

sage.misc.benchmark.bench0()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench0()[0])
Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
```
sage.misc.benchmark.bench1()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench1()[0])
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
```
sage.misc.benchmark.bench2()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench2()[0])
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
```
sage.misc.benchmark.bench3()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench3()[0])
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
```
sage.misc.benchmark.bench4()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench4()[0])
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
```
sage.misc.benchmark.bench5()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench5()[0])
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
```
sage.misc.benchmark.bench6()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench6()[0])
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
```
sage.misc.benchmark.bench7()#

Run a benchmark.

BENCHMARK:

```sage: from sage.misc.benchmark import *
sage: print(bench7()[0])
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
```
sage.misc.benchmark.benchmark(n=- 1)#

Run a well-chosen range of Sage commands and record the time it takes for each to run.

INPUT:

n – int (default: -1) the benchmark number; the default

of -1 runs all the benchmarks.

OUTPUT:

list – summary of timings for each benchmark. int – if n == -1, also return the total time

EXAMPLES:

```sage: from sage.misc.benchmark import *
sage: _ = benchmark()
Running benchmark 0
Benchmark 0: Factor the following polynomial over
the rational numbers: (x^97+19*x+1)*(x^103-19*x^97+14)*(x^100-1)
Time: ... seconds
Running benchmark 1
Find the Mordell-Weil group of the elliptic curve 5077A using mwrank
Time: ... seconds
Running benchmark 2
Some basic arithmetic with very large Integer numbers: '3^1000001 * 19^100001
Time: ... seconds
Running benchmark 3
Some basic arithmetic with very large Rational numbers: '(2/3)^100001 * (17/19)^100001
Time: ... seconds
Running benchmark 4
Rational polynomial arithmetic using Sage. Compute (x^29+17*x-5)^200.
Time: ... seconds
Running benchmark 5
Rational polynomial arithmetic using Sage. Compute (x^19 - 18*x + 1)^50 one hundred times.
Time: ... seconds
Running benchmark 6
Compute the p-division polynomials of y^2 = x^3 + 37*x - 997 for primes p < 40.
Time: ... seconds
Running benchmark 7
Compute the Mordell-Weil group of y^2 = x^3 + 37*x - 997.
Time: ... seconds
Running benchmark 8
```