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

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Maxima

For all I care, at this moment…

Spring 2013

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Content

• Special keys and symbols

• Arithmetic

• Algebra

• Calculus

• Matrix calculations

• Plot

• Linear algebraSpring 2013

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ArithmeticExact(rational) arithmetic

Irrational number kept in symbolic form

Expanding …

Convert to floating point numbers …

Setting (system) floating point precision …

Repeat a previous command …

; end of command% previous output‘’ repeat previous command^ power

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Assignment

VariableList Function specification

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Algebra

Expand, factor, solveTrigexpand, trigreduce, …

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Algebra

Expand/reduce for rational terms

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Polynomials

Gcdex,Gfactorallroots

gcd p/gcd q/gcd

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Calculus

Derivate, partial derivativeIntegral: definite, indefinite, improperinf

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Calculus

Taylor series, limit,

?sin

lim0

x

xx

=Taylor series:

h

xfhxfxf

h

0lim

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ODE

Ode2: solves 1st and 2nd order ODEIc1, ic2, bc: setting conditions‘ do not evaluate

2)0(, yydx

dy0)0(,1)0(,sin

2

2

xxtxdt

dx

dt

xd

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Plot2D• Data points (xi,yi)• Function curve y = f(x)• Parametric curve (x(t), y(t))

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Plot2D (cont)

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Ex: Least Square Fit

Use solve to solve linear systems

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Linear Algebra

Matrix multiplication

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10

1

14

02

10

1

10

02

12

01

10

12

12

01

14

12 21

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TLL

10

21

12

01

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Matrix Factorization

LU(Doolittle) LU(Crout)LDU

Symmetric matrix A = LLT(Cholesky)

LU

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b

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Eigen Problemsnumerical

symbolic

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21b

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Linear Solvers

Compare with general solver: solve

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Use Maxima to …

• Study modified Newton on multiple roots

• Derive PCA …

• Solve symbolic linear systems (give 2 points to get algebraic eqn)

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Index. (matrix multiply) 14,15^ (power) 3^^ (matrix power) 14‘’ (repeat previous cmd) 3: (variable assignment) 4:= (function specification) 4‘ (defer evaluation) 10Allroots 7Bfloat 3Charpoly 16Cholesky 15Determinant 14Diff 8Divide 7Echelon 14Eigenvalues 16Eigenvectors 16Expand 3,6Ezgcd 7Factor 5,7Fpprec 3Gfactor 7

Ic1 10Ic2 10Integrate 8Invert 14Limit 9Linsolve 17Lu_factor 15Matrix 14Ode2 10Plot2d 11,12,13Quotient 7Rank 14Ratexpand 6Ratsimp 6Realroots 7Remainder 7Solve 5,16,17Taylor 9Transpose 14,15Trigexpand 5Trigreduce 5Uniteigenvectors 17

Spring 2013