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Maxima

Maxima. For all I care, at this moment…. Content. Special keys and symbols Arithmetic Algebra Calculus Matrix calculations Plot Linear algebra. ; end of command % previous output ‘’ repeat previous command ^ power. Arithmetic. Exact(rational) arithmetic.

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Maxima

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  1. Maxima For all I care, at this moment… Spring 2013

  2. Content • Special keys and symbols • Arithmetic • Algebra • Calculus • Matrix calculations • Plot • Linear algebra Spring 2013

  3. ; end of command % previous output ‘’ repeat previous command ^ power Arithmetic Exact(rational) arithmetic Irrational number kept in symbolic form Expanding … Convert to floating point numbers … Setting (system) floating point precision … Repeat a previous command … Spring 2013

  4. Variable List Function specification Assignment Spring 2013

  5. Expand, factor, solve Trigexpand, trigreduce, … Algebra Spring 2013

  6. Expand/reduce for rational terms Algebra Spring 2013

  7. Gcdex, Gfactor allroots Polynomials q/gcd p/gcd gcd Spring 2013

  8. Derivate, partial derivative Integral: definite, indefinite, improper inf Calculus Spring 2013

  9. = Taylor series: Taylor series, limit, Calculus Spring 2013

  10. Ode2: solves 1st and 2nd order ODE Ic1, ic2, bc: setting conditions ‘ do not evaluate ODE Spring 2013

  11. Data points (xi,yi) Function curve y = f(x) Parametric curve (x(t), y(t)) Plot2D Spring 2013

  12. Plot2D (cont) Spring 2013

  13. Use solve to solve linear systems Ex: Least Square Fit Spring 2013

  14. Linear Algebra Matrix multiplication Spring 2013

  15. U L Matrix Factorization c LU(Doolittle) LU(Crout) LDU b Symmetric matrix A = LLT(Cholesky) Spring 2013

  16. Eigen Problems numerical symbolic Spring 2013

  17. Linear Solvers Compare with general solver: solve Spring 2013

  18. Use Maxima to … • Study modified Newton on multiple roots • Derive PCA … • Solve symbolic linear systems (give 2 points to get algebraic eqn) Spring 2013

  19. . (matrix multiply) 14,15 ^ (power) 3 ^^ (matrix power) 14 ‘’ (repeat previous cmd) 3 : (variable assignment) 4 := (function specification) 4 ‘ (defer evaluation) 10 Allroots 7 Bfloat 3 Charpoly 16 Cholesky 15 Determinant 14 Diff 8 Divide 7 Echelon 14 Eigenvalues 16 Eigenvectors 16 Expand 3,6 Ezgcd 7 Factor 5,7 Fpprec 3 Gfactor 7 Ic1 10 Ic2 10 Integrate 8 Invert 14 Limit 9 Linsolve 17 Lu_factor 15 Matrix 14 Ode2 10 Plot2d 11,12,13 Quotient 7 Rank 14 Ratexpand 6 Ratsimp 6 Realroots 7 Remainder 7 Solve 5,16,17 Taylor 9 Transpose 14,15 Trigexpand 5 Trigreduce 5 Uniteigenvectors 17 Index Spring 2013

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