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export{"puma"}
puma = method()
puma (Ring) := kk -> (
x := symbol x;
R := kk[x_1..x_8];
{ x_1^2 + x_2^2 - 1,
x_3^2 + x_4^2 - 1,
x_5^2 + x_6^2 - 1,
x_7^2 + x_8^2 - 1,
0.004731*x_1*x_3 - 0.3578*x_2*x_3 - 0.1238*x_1 - 0.001637*x_2 - 0.9338*x_4 + x_7 - 0.3571,
0.2238*x_1*x_3 + 0.7623*x_2*x_3 + 0.2638*x_1 - 0.07745*x_2 -0.6734*x_4 -0.6022,
x_6*x_8 + 0.3578*x_1 + 0.004731*x_2,
-0.7623*x_1 + 0.2238*x_2 + 0.3461 }
)
beginDocumentation()
doc ///
Key
puma
(puma,Ring)
Headline
hand position and orientation of PUMA robot
Usage
puma(kk)
Inputs
kk:Ring
the coefficient ring
Outputs
:List
of polynomials in the system
Description
Text
This system was solved in May 2020, using @TO solveSystem@ in Macaulay2 v1.15
with an Intel(R) Core(TM) i5-5250U CPU at 1.60GHz.
There were 16 solutions found in 0.531 seconds (with a Bezout bound of 128).
Reference: "Box-Bisection for solving second-degree systems and the problem of clustering', ACM Transactions on Mathematical Software" by A. Morgan and V. Shapiro. (p. 152-167).
See also: http://homepages.math.uic.edu/~jan/Demo/puma.html.
Example
puma(RR_53)
///
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