Common Python Code

Author: John J Weber III, PhD

Grouping Symbols

There is at least one different grouping symbols:

• $()$$(\,)$, used for grouping expressions, for example

  • $e\ast \ast (2\ast x)$$e\!*\!*(2\!*\!x)$ to represent $e^{2x}$$e^{2x}$
  • $x\ast \ast 2\ast (x+3)$$x\!*\!*2\!*\!(x + 3)$ to represent $x^2(2+x)$$x^2(2+x)$
  • $1∕(x\ast \ast 2-x-1)$$1∕(x\!*\!*2 - x - 1)$ to represent $\frac{1}{x^2-x-1}$$\frac{1}{x^2-x-1}$

• $()$$(\, )$, domain, for example

  • $(x,-10,10)$$(x,−10, 10)$

• etc.

SymPy Python Library

To import the complete SymPy library:

$\text{from}$${\color{red}\text{from}}$ sympy $\text{import}$${\color{red}\text{import}}$ *

NOTE: The above line of code is needed only once to input the SymPy functions listed below.

NOTE: The above line of code will always be provided, as well as any additional functions from other Python libraries.

Variables

To declare one variable:

$\text{x = symbols(}\mathsf{\text{’}}\text{x}\mathsf{\text{’}}\text{)}$$\text{x = symbols(}\textsf{'}\text{x}\textsf{'}\text{)}$

To declare two variables:

$\text{x, y = symbols(}\mathsf{\text{’}}\text{x, y}\mathsf{\text{’}}\text{)}$$\text{x, y = symbols(}\textsf{'}\text{x, y}\textsf{'}\text{)}$

To declare one variable and one parameter:

$\text{x, a = symbols(}\mathsf{\text{’}}\text{x, a}\mathsf{\text{’}}\text{)}$$\text{x, a = symbols(}\textsf{'}\text{x, a}\textsf{'}\text{)}$

Trigonometric Functions

Where $x$$x$ is in radians:

• sin(x)
• cos(x)
• tan(x)
• csc(x)
• sec(x)
• cot(x)

NOTE: To raise a trig function to a power, e.g., ${\sin }^2(x)$$\sin^2{(x)}$: sin(x)**2

Inverse Trigonometric Functions

Output is in radians:

• ${\sin }^{-1}(x)$$\sin^{−1}{(x)}$: asin(x)
• ${\cos }^{-1}(x)$$\cos^{−1}{(x)}$: acos(x)
• ${\tan }^{-1}(x)$$\tan^{−1}{(x)}$: atan(x)
• ${\csc }^{-1}(x)$$\csc^{−1}{(x)}$: acsc(x)
• ${\sec }^{-1}(x)$$\sec^{−1}{(x)}$: asec(x)
• ${\cot }^{-1}(x)$$\cot^{−1}{(x)}$: acot(x)

Logarithmic Functions

• $\ln (x)$$\ln{(x)}$: ln(x) or log(x)
• ${\log }_{10}(x)$$\log_{10}{\!(x)}$: $\text{from}$${\color{red}\text{from}}$ math $\text{import}$${\color{red}\text{import}}$ log10 log10(x)
• ${\log }_b(x)$$\log_{b}{(x)}$, where $b>0$$b>0$, $b\ne 1$$b\ne 1$: $\text{from}$${\color{red}\text{from}}$ math $\text{import}$${\color{red}\text{import}}$ log log(x,b)

Exponential Function

• $e^x$$e^x$: exp(x)

Radical Functions

• $\sqrt{x}$$\sqrt{x}$: sqrt(x)
• $\sqrt[n]{x}$$\sqrt[n]{x}$: x**(1/n)

Absolute Value Functions

• $\left|x\right|$$\left|\,x\,\right|$: abs(x)

Implicit Multiplication

• $2x$$2x$: 2*x
• $xy$$xy$: x*y

Exponents

• $x^2$$x^2$: x*2
• $2^{x+y}$$2^{x+y}$: 2**(x+y)

Constants

• $\pi$$\pi$: pi
• $e$$e$: $\text{from}$${\color{red}\text{from}}$ math $\text{import}$${\color{red}\text{import}}$ e e

Hyperbolic Functions

• $\sinh (x)$$\sinh{(x)}$: sinh(x)
• $\cosh (x)$$\cosh{(x)}$: cosh(x)
• $\tanh (x)$$\tanh{(x)}$: tanh(x)
• $\mathrm{csch}(x)$$\csch{(x)}$: csch(x)
• $\mathrm{sech}(x)$$\sech{(x)}$: sech(x)
• $\coth (x)$$\coth{(x)}$: coth(x)

Inverse Hyperbolic Functions

• ${\sinh }^{-1}(x)$$\sinh^{−1}{(x)}$: asinh(x)
• ${\cosh }^{-1}(x)$$\cosh^{−1}{(x)}$: acosh(x)
• ${\tanh }^{-1}(x)$$\tanh^{−1}{(x)}$: atanh(x)
• ${\mathrm{csch}}^{-1}(x)$$\csch^{−1}{(x)}$: acsch(x)
• ${\mathrm{sech}}^{-1}(x)$$\sech^{−1}{(x)}$: asech(x)
• ${\coth }^{-1}(x)$$\coth^{−1}{(x)}$: acoth(x)

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Created: Monday, 23 November 2020 6:16 EDT Last Modified: Friday, 07 January 2022 - 15:33 (EST)