6592cd058d
git-subtree-dir: octive-lean git-subtree-mainline:fd3d42ae33git-subtree-split:4b6fcec565
45 lines
2.1 KiB
Matlab
45 lines
2.1 KiB
Matlab
% Symbolic Math Toolbox - cheat sheet walkthrough.
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% Each labeled block produces one line of output.
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x = sym('x'); y = sym('y'); z = sym('z'); t = sym('t');
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a = sym('a'); b = sym('b'); k = sym('k'); n = sym('n');
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% Calculus
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printf("diff: "); disp(diff(sym('sin(x^2 + t)'), x));
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printf("int indef: "); disp(int(sym('x/(1+z^2)'), z));
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printf("int def: "); disp(int(sym('x^2'), x, 0, 1));
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printf("limit left: "); disp(limit(sym('1/x'), x, 0, "left"));
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printf("taylor: "); disp(taylor(sym('exp(-x)')));
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printf("series: "); disp(series(sym('1/sin(x)'), x));
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printf("symsum: "); disp(symsum(k, k, 0, n - 1));
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printf("gradient: "); disp(gradient(sym('x*y + 2*z*x'), sym('[x, y, z]')));
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printf("jacobian: "); disp(jacobian(sym('[x*y*z, y, x+z]'), sym('[x, y, z]')));
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printf("hessian: "); disp(hessian(sym('x*y + 2*z*x'), sym('[x, y, z]')));
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printf("laplacian: "); disp(laplacian(sym('1/x + y^2 + z^3'), sym('[x, y, z]')));
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% Algebra
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printf("double pi: "); disp(double(sym('pi')));
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printf("vpa pi 30: "); disp(vpa(sym('pi'), 30));
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printf("subs: "); disp(subs(sym('a^3 + b'), a, 2));
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printf("solve poly: "); disp(solve(sym('x^2 - 4'), x));
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printf("solve sys: "); disp(solve(sym('[u + v - a, u - v - b]'), sym('[u, v]')));
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printf("isolate: "); disp(isolate(sym('a*x^2 + b*x + c'), x));
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printf("lhs: "); disp(lhs(sym('Eq(x^2, y^2)')));
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printf("rhs: "); disp(rhs(sym('Eq(x^2, y^2)')));
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printf("simplify: "); disp(simplify(sym('sin(x)^2 + cos(x)^2')));
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printf("expand: "); disp(expand(sym('(x+1)^3')));
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printf("factor: "); disp(factor(sym('x^2 - 1')));
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printf("collect: "); disp(collect(sym('x*y + x^2 + 2*x*y + 3'), x));
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printf("rewrite: "); disp(rewrite(sym('tan(x)/cos(x)'), "sin"));
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printf("resultant: "); disp(resultant(sym('x^2 + y'), sym('x - 2*y'), x));
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% ODE - symfun() registers a SymPy Function so f(t) parses as f-of-t
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symfun('f');
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printf("dsolve: "); disp(dsolve(sym('Eq(Derivative(f(t), t), a*f(t))'), sym('f(t)')));
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% Functions
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printf("piecewise: "); disp(piecewise(sym('x < 0'), -1, sym('x >= 0'), 2));
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% Output formats
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printf("latex: "); disp(latex(sym('x^2 + y^2')));
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