Wolfram

Getting started

Wolfram Language

If you are new to the Wolfram Language, or even if you aren't, honestly, you should check out Prof. Richard Gaylord's three lecture series on titled Wolfram Language Fundamentals. Trust me, it's worth it.

WolframScript

First, you'll need to install Wolfram's suite of tools to your machine. You will need to install the following applications:

WolframScript
Wolfram Engine
Wolfram Desktop

After you have completed this step, search within the application's package contents, and look for an executable file titled wolframscript. Add the directory containing this file to your shell's search path, preferrably doing so in your shell's runtime configuration file.

After you have authenticated to the server, you will need to provide wolframscript with the path to the kernel file. It is located within your Wolfram Engine installation.

wolframscript -config WOLFRAMSCRIPT_KERNELPATH=/Applications/Wolfram\ Desktop.app/Contents/MacOS/WolframKernel

Alternatively, you can set the kernel path as an environment variable

export WOLFRAMSCRIPT_KERNELPATH=/Applications/Wolfram\ Desktop.app/Contents/MacOS/WolframKernel

I recommend you place your configuration files somewhere more standard, similar to what I have below:

export WOLFRAMSCRIPT_CONFIGURATIONPATH=${XDG_CONFIG_HOME}/wolfram/config.txt
export WOLFRAMSCRIPT_AUTHORIZATIONPATH=${XDG_CONFIG_HOME}/wolfram/auth.txt

Next, in order for wolframscript to generate our credentials at the authorization path provided above, we will need to authenticate ourselves to the cloud server.

wolframscript -authenticate

From here, you're good to go!

wolframscript -l -c '1+1'

The expected output of this command is:

At long last, we have found the answer.

Getting Help

Get information on a given Wolfram Language Symbol:
```
Entity["WolframLanguageSymbol", "LinearSolve"]
```

Determinant

Det[{{1, 2, 1}, {1, 1, 0}, {0, 1, 1}}]

Cross Product

Cross[{1, 2, 3}, {3, 4, 5}]

Matrix Product

{{1, 2}, {3, 4}} . {{-1, 1}, {0, 2}}

Row Reduction

Get the matrix in reduced row echelon form:

RowReduce[{{1, -3, 3, -4}, {2, 3, -1, 15}, {4, -3, -1, 19}}]

Matrix Rank

Get the rank of a matrix

MatrixRank[{{1, 2, 1}, {-2, -3, 1}, {3, 5, 0}}]

Eigenvalues

Eigenvalues[{{3, -1}, {0, 2}}]

Eigenvectors

Eigenvectors[{{-2, 5, 7}, {3, 11, 15}, {-4, -3, 10}}]

Jordan Decomposition

JordanDecomposition[{{-1, 5}, {-3, 11}}]

Kernel

The kernel of a matrix is just its null space

Null Space

NullSpace[{{1, 3, 3}, {-3, -5, -3}, {3, 3, 0}}]

Positive Definite

PositiveDefiniteMatrixQ[{{3, -3}, {-3, 5}}]

Probability

Distributions

Wolfram Alpha Reference

Normal distribution of μ and σ
```
NormalDistribution[\[Mu], \[Sigma]]
```

Probability Distribution

First example

PDF[NormalDistribution[\[Mu], \[Sigma]], x]

Second example

Plot[PDF[NormalDistribution[2, 3], x], {x, -5, 10}]

Wolfram Client Library for Python

If you'd like to stay in Python, and have the features of Wolfram Engine, you can install the Wolfram Client Library for Python

pip install wolframclient

from wolframclient.evaluation import WolframLanguageSession
from wolframclient.language import wl, wlexpr

sesh.evaluate(wl.WolframAlpha("temperature in los angeles", "Result"))
# Quantity[55.0, 'DegreesFahrenheit']
sesh.evaluate(wl.WolframAlpha("stock price of GME", "Result"))
# (DateObject[(2021, 4, 1), 'Day', 'Gregorian', -7.0], Quantity[191.4499969482422, 'USDollars'])
sesh.evaluate(wl.WolframAlpha("value of chinese yuan in dollars", "Result"))
# Quantity[0.15, 'USDollars']