Mathematica can process many different formulas of all types, including polynomials containing millions of terms to complex combinations of advanced mathematical functions. It provides transformation and simplification functions that will automatically refer to thousands of rules and algorithms, many of which are original to Wolfram Research. Below are a few examples of various formula...

Article Id:
13548

Category: Basic Features & How To's

Function (&) — specify a pure function (e.g. (#+1)&)
#, ##, #name — slots for variables in a pure function
Applying Functions to Lists
Map (/@) — map across a list:...

Article Id:
19590

Category: Basic Features & How To's

To integrate symbolic matrices in Mathematica, use the following...

Article Id:
13535

Category: Basic Features & How To's

Constructing Lists:
{a,b,...} (List) -- specify a list explicitly
Table -- make a table of values of an expression
Array -- make an array of any dimension from a function
Range
Subdivide
SparseArray
Tuples
...

Article Id:
19589

Category: Basic Features & How To's

Boolean expressions and functions in Mathematica can not only be evaluated, but may also be symbolically manipulated and transformed. Mathematica provides a extensive structure for expressions dealing with Boolean algebra.
Below are various commands associated with computing Boolean expressions, as well as their corresponding function to which the...

Article Id:
13803

Category: Basic Features & How To's

Equality & Inequality:
Equal(==), Unequal(!=) -- numerical equality
SameQ(===), UnsameQ(=!=) -- literal symbolic identity
Less(<)
Greater(>)
LessEqual(<=)
GreaterEqual(>=)
Between
Logical...

Article Id:
19586

Category: Basic Features & How To's

The large volume mathematical data provided by Mathematica is created and specially organized for application for a wide range of forms, capable of direct integration in wide variety of computations in Mathematica. Below are various commands associated with these computations and their corresponding mathematical function:
...

Article Id:
13804

Category: Basic Features & How To's

Mathematica has one of the most extensive collections of mathematical functions ever, most of which are from the results and algorithms developed at Wolfram Research over the past 20 years. Each function supports a wide range of symbolic operations for all complex values.
Below are a few examples of various commands under their corresponding mathematical...

Article Id:
13538

Category: Basic Features & How To's

Mathematica, using many of the original methods developed by Wolfram Research, automatically evaluates both numeric and symbolic matrices. Thanks to these methods, Mathematica can operate numerical matrices of any precision, handling both dense and sparse matrices, and can operate on matrices containing millions of entries.
Below are a few examples of various commands and...

Article Id:
13583

Category: Basic Features & How To's

Factoring Primes:
Prime
NextPrime
PrimePi
EulerPhi
MoebiusMu
JacobiSymbol....
FactorInteger -- find the factors of an integer
PrimeQ -- test whether an integer is prime
Congruences & Modular...

Article Id:
13795

Category: Basic Features & How To's

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