使用 CX CAS 求解方程组时避免资源耗尽错误

Question

I am attempting to solve the following system of 2 equations (2 unknowns) using a Ti-Nspire CX CAS calculator:

I have already solved it using Mathematica:

Solve[v*Sqrt[1+0.5^2 + 2*0.5*Cos[2*(2*Pi/(8*10^-3))*(-3*10^-3) + p]]==2 && v*Sqrt[1+0.5^2 + 2*0.5*Cos[2*(2*Pi/(8*10^-3))*(-1*10^-3) + p]]==6 && 0<=p<=2*Pi, {v,p}];

So I know that v=4 and p=Pi/2 but I get a "Resource exhaustion; Cannot complete calculation" error when I try to solve the system on the calculator with the following 3 steps:

Answer 1

I suggest that you insert constrains within solve command instead when defining functions:

solve(l(p,v)=2 and u(p,v)=6 and 0≤p and p≤2*π,{p,v})

answer: v=4. and p=1.5707964860087 Also use expressions instead of functions, unless you have very good reason for, like:

u:=v*√(1+(0.5)^(2)+2*0.5*cos(((2*−0.001*2*π)/(0.008))+p))
l:=v*√(1+(0.5)^(2)+2*0.5*cos(((2*−0.003*2*π)/(0.008))+p))

solve command and result are the same as above. Of course, in this case solve will find the correct solution without any constrains:

solve(l=2 and u=6,{p,v})

answer: v=4. and p=1.5707964860087 But it wont find any other solutions, and for some reason this doesnt work for the solution between 2 π and 4 π

solve(l=2 and u=6 and 2*π≤p and p≤4*π,{p,v})

In that case, you can use zeros

zeros({l-2,u-6},{p,v})|2*π≤p and p≤4*π

answer: [[7.8539817931882,4.]]