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Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

EDIT: Thanks to @H. Zhou, I am editing this question with additional constraints given by four inequalities $|x\pm y| \le |1\pm z|$ which simplify to $z \ge x+y-1; ~z\le -x+y+1;~z\le x-y+1;~z \ge -x-y-1.$

Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

EDIT: Thanks to @H. Zhou, I am editing this question with additional constraints given by four inequalities $|x\pm y| \le |1\pm z|$ which simplify to $z \ge x+y-1; ~z\le -x+y+1;~z\le x-y+1;~z \ge -x-y-1.$

Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

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seeker
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Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

EDIT: Thanks to @H. Zhou, I am editing this question with additional constraints given by four inequalities $|x\pm y| \le |1\pm z|$ which simplify to $z \ge x+y-1; ~z\le -x+y+1;~z\le x-y+1;~z \ge -x-y-1.$

Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

EDIT: Thanks to @H. Zhou, I am editing this question with additional constraints given by four inequalities $|x\pm y| \le |1\pm z|$ which simplify to $z \ge x+y-1; ~z\le -x+y+1;~z\le x-y+1;~z \ge -x-y-1.$

Jeopardy compliance. Fixed the question formation - missing auxiliary (or helping) verb - see e.g. <https://www.youtube.com/watch?v=t4yWEt0OSpg&t=1m49s> (see also <https://www.youtube.com/watch?v=kS5NfSzXfrI> (QUASM)) - alternatively, drop the question mark.
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edit approved Aug 9, 2022 at 12:37
Peter Mortensen
edit approved Aug 9, 2022 at 12:37
Peter Mortensen
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How tocan I generate a large number of data points of a function and plot them?

Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I want to randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$.?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

How to generate large number of data points of a function and plot them?

Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), I want to randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$. I am sure this is doable in Mathematica, but have no idea how to proceed.

How can I generate a large number of data points of a function and plot them?

Given a function f[x_,y_,z_,a_]:=x^2 + xy+ yz + z^3+a^2 (just for example), how can I randomly choose values of x,y,z,a (with constraints that all $x,y,z$, and $a$ are positive, and Sqrt[x^2+y^2+z^2]<=1) and plot f[x,y,z,a] against Sqrt[x^2+y^2+z^2] for say 100 points $(x,y,z,a)$?

I am sure this is doable in Mathematica, but I have no idea how to proceed.

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