# Question:Can Maple solve any (numerical) system of polynomial equations?

## Question:Can Maple solve any (numerical) system of polynomial equations?

Maple 2017

Hi, I have a system of 15 polynomial equations (of 15 variables) of 2nd degree. Meaning, every monomial has at most mulplications of 2 different variables or a single variable squared.

I tried to solve them in Maple but it's been 2 hours and Maple is still thinking.. I don't have any indication if Maple is just stuck or it should return a solution at some point.

Below I wrote the Maple commands that I tried to run (sorry but I'm new here so I didn't know how to write them nicely). I also wrote one of the solutions that I'm expecting to get (15 values for the 15 variables). and you can see that by typing eq7 for example I got -2.5=-2.5 (and the same for the rest of the equations) which means that the values are correct.

I know there is an algorithm for solving any system of numerical polynomial equations of any degree. I don't know if Maple implemented it.

Anyone knows if Maple is able to solve the equations below? and if not, is there any other way that can be done to solve them?

Thanks

David

Here's the commands for Maple (including one of the solutions I'm expecting to get).

The variables are: r11, r12, r13, r21, r22, r23, r31, r32, r33, t1, t2, t3, s1, s2, s3

eq1:=r11^2+r21^2+r31^2 = 1;
eq2:=r12^2+r22^2+r32^2 = 1;
eq3:=r13^2+r23^2+r33^2 = 1;
eq4:=r11*r12+r21*r22+r31*r32 = 0;
eq5:=r11*r13+r21*r23+r31*r33 = 0;
eq6:=r12*r13+r22*r23+r32*r33 = 0;
eq7:=-30*r13-.79382581863774e-1*s1*r11-.95259098236529e-1*s1*r12+.992282273297173*s1*r13 = -.83717247687439e-1*t1;
eq8:=-30*r13+.79382581863774e-1*s2*r11+.95259098236529e-1*s2*r12+.992282273297173*s2*r13 = .76364294519742e-1*t2;
eq9:=-30*r13-.86165283952334e-1*s3*r11+.103398340742801*s3*r12+.990900765451843*s3*r13 = -.81460429387834e-1*t3;
eq10:=-30*r23-.79382581863774e-1*s1*r21-.95259098236529e-1*s1*r22+.992282273297173*s1*r23 = -.107930827800543*t1;
eq11:=-30*r23+.79382581863774e-1*s2*r21+.95259098236529e-1*s2*r22+.992282273297173*s2*r23 = .60269029165473e-1*t2;
eq12:=-30*r23-.86165283952334e-1*s3*r21+.103398340742801*s3*r22+.990900765451843*s3*r23 = .105021268850622*t3;
eq13:=-30*r33-.79382581863774e-1*s1*r31-.95259098236529e-1*s1*r32+.992282273297173*s1*r33 = .990627255252918*t1-30;
eq14:=-30*r33+.79382581863774e-1*s2*r31+.95259098236529e-1*s2*r32+.992282273297173*s2*r33 = .995256820446840*t2-30;
eq15:=-30*r33-.86165283952334e-1*s3*r31+.103398340742801*s3*r32+.990900765451843*s3*r33 = .991128009660183*t3-30;

r11 := 1;
r12 := 0;
r13 := 0;
x := .523598775598299;
r21 := 0;
r22 := cos(x);
r23 := -sin(x);
r31 := 0;
r32 := sin(x);
r33 := cos(x);
t1 := 29.862424638395044;
t2 := 32.737813080348531;
t3 := 30.689747387623886;
s1 := 31.493054789905649;
s2 := 31.493054789905628;
s3 := 29.014005238849720;
eq1;
eq2;
eq3;
eq4;
eq5;
eq6;
eq7;
eq8;
eq9;
eq10;
eq11;
eq12;
eq13;
eq14;
eq15;

unassign('r11', 'r12', 'r13', 'r21', 'r22', 'r23', 'r31', 'r32', 'r33', 't1', 't2', 't3', 's1', 's2', 's3');
solve({eq1, eq10, eq11, eq12, eq13, eq14, eq15, eq2, eq3, eq4, eq5, eq6, eq7, eq8, eq9}, {r11, r12, r13, r21, r22, r23, r31, r32, r33, s1, s2, s3, t1, t2, t3}); ﻿