PowerPoint

Python SyMPYMoon Yong Joon1

Pythonsympy

Moon Yong Joon2

Symbolic mathematics3

sympy SymPy symbolic mathematics python . SymPy a full-featured computer algebra system (CAS) 4

sympy SymPy symbolic mathematics 5

Sympy pi (evalf)

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python sympy Python sympy 7 sympy sympy

Sympy : Sympy python 8

Symbol 9

sympy Sympy 10

Symbol name symbol

sympy SymPy symbolic mathematics 11

Sympy pi (evalf)

Sympy symbol 12

sympy.abc sympy.abc symbol 13

symbol Sympy x = Symbol(x) a, b, c = symbols(a, b, c) 14

Symbol 15

symbol : symbols 16

symbol : symbols cls Function 17

Sympy symbol 18

symbol : evalf symbol 19

Pythonsympy

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init_printing: . sympy pprint 22

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pprint: 24

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print_tree: sympy tree 26

Pythonsympy

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: sympy(, integer) (1, 2, 3, ...) (1, 2, 3, ...) 0 . 29

: sympy(, rational number) (p) (q) 30

1 : sympy [, real number] 31

2 : sympySympify sympy 32

: sympySympify sympy I( I) Python complex

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/pi sympy oo , pi 35

Pythonsympy

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: sympy () 38

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radsimp : () 40

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Numerical evaluation42

evalf 43

evalf 2 subs evalf 44

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: +/- subs, evalf, replace 46

: *, / subs, evalf, replace 47

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Add49

Add Add Add 50

Mul51

Mul Mul Mul 52

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Mul ( ) 55

Mul ( ) 56

Integer 57

Pow () 58

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: srepr61

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: srepr 63

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: func 66

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: Add Mul 68

: func 69

: func .func args expr 70

:args 71

: args 72

:atoms 73

: atoms 74

:args/atoms 75

: args args args 76

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1 add, mul 79

2 add, mul dict 80

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commutative , . A,B False 82

args_cnc ( , )83

PythonsympyPython / sympy

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Sympify python sympy 86

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Sympify sympy 88

Sympify . 2x 2*x 89

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apart apart (denomimator) (numerator) 92

apart simplify apart simpify 93

PythonsympyAlgebraic manipulations

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polynomial95

polynomial . (expand), (factor) 96

: multinomial=True expand multinomial 97

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expand : expand 99

expand : expand 100

force=True

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expand : complex=True 102

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factor factor 104

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factor factor expand solve 106

factor : modulus modulus 107

factor : (Gau, Gaussian integer) .(a+bi)(a-bi)=a2+b2 108

= (0+i)(0 i)= -i*I= -(i)**2= 1X**2+1

factor : extension 109

check110

Simplify 0 simplify 0 111

Simplify : 112

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cancel : cancel 114

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trigsimp : trigsimp 116

simplify : trigsimp/cancel simplify 117

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collect : 119

collect cancel . simplify cancel . 120

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Solve : solve 123

2 expand solve 124

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expand : expand func=True 127

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plotting129

1 1 plot 130

2 2 plot 131

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1,2 plot 133

plot line_color 134

x 135

1 : x 1 plot (x,-5,5) x 136

Plot 1 2 x 137

Plot 1 2 x x 138

y 139

1 : y 1 plot ylim=(y,-5,5) y 140

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:legend legend142

1 (title, xlabel, ylabel) 143

show 144

sympy plot . show=False 145

Show 146

show sympy plot . show=False 147

Multi plot 148

plot 1 plot plot 149

plot : 2 plot 150

plot plot 151

Multi plot 152

append plot append plot 153

extend plot extend plot 154

Pythonsympy3d

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3d 156

plot3d: 3D 157

plot3d: 2 3D 158

3D 159

plot3d: 3D 160

Pythonsympy/

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Pow : e 162

Pow base**a Pow base 163

Exp : e164

exp e e**x 165

log base:e 166

log : base(e) sympy base e exp(x) log 167

log base:10 168

log : base(10) sympy base e 10 base log x,y x , y base 169

log : base(10) log evaluate=False x, base simplipy 170

log 171

log : x*y log positive log (x*y) expand 2 log Expand log=True 172

log : x/y log positive log (x*y) expand 2 log 173

log : log force=True 174

expand_log 175

expand_log : symbol positive log 176

expand_log : symbol positive force=True 177

logcombine 178

logcombine : symbol positive log , force=True 179

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expand : trig=True 182

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Sin sin

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Sin sin

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Python sympy

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FiniteSet : sympy FiniteSet 188

FiniteSet : list list unpack 189

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FiniteSet : 191

FiniteSet : is_subset , is_superset 192

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FiniteSet : A B 194

FiniteSet : A B 195

FiniteSet : A B A 196

FiniteSet : product A B 197

Python sympy

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Summation()199

Sum : 200

Product : 201

(Linear algebra)

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(, determinant .203

dot 204

Python sympy/

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Die: 207

given : 208

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density : dict 210

density : lambdas 211

Python sympy

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limit : limit214

Python sympy

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diff : diff 217

: sympy 0 218

: sympy c 219

: sympy n xn nxn-1 220

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: sympy 222

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f(x) g(x) + f(x) g(x) 224

x*x f(x) = x, g(x)= x = 1*x + x*1= x + x= 2x

: sympy f(x) g(x) + f(x) g(x) 225

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1 227

:sympy 228

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2 :sympy 230

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:sympy 232

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:sympy diff 234

(integration)

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: sympy nxn-1 X 1/n+1*x**n+1 237

*x2 = 2*1/2 x 2-1= x

: sympy 238

n : sympy 239

: sympy 240

: sympy 241

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:sympy 243