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export { "randomSystem" }
randomSystem = method()
randomSystem (ZZ,ZZ,Ring) := (n,d,kk) -> (
R := kk[vars(53..n+52)];
apply(n, i->sum(toList(1..d),j->random(j,R)) - 1)
)
beginDocumentation()
doc ///
Key
randomSystem
(randomSystem,ZZ,ZZ,Ring)
Headline
an example of a 0-dimensional square polynomial system
Usage
F = randomSystem(n,d,K)
Inputs
n:ZZ
positive value representing the number of polynomials
d:ZZ
positive value representing the degree of the polynomials
K:Ring
usually a field, e.g., QQ or CC_{53}
Outputs
F:List
a system of $n$ polynomials random polynomials of degree $d$ in $n$ variables.
Description
Text
This system was solved in May 2020, using @TO track@ in Macaulay2 v1.15
with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.
For a system with 2 polynomials of degree 3 over rationals there were 9 solutions found in 0.06 seconds.
For a system with 5 polynomials of degree 2 over complex numbers there were 32 solutions found in 0.297 seconds.
Example
randomSystem(2,3,QQ)
randomSystem(5, 2, CC_53)
///
-* TEST ///
F = randomSystem(5,2,CC_53)
time sols = solveSystem F
assert(#sols==32)
/// *-
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