Eigenvalues (Built-in Mathematica Symbol)

Eigenvalues[m] gives a list of the eigenvalues of the square matrix m. Eigenvalues[{m, a}] gives the generalized eigenvalues of m with respect to a. Eigenvalues[m, k] gives ...

ReplacePart (Built-in Mathematica Symbol)

ReplacePart[expr, i -> new] yields an expression in which the i\[Null]\[Null]^th part of expr is replaced by new. ReplacePart[expr, {i_1 -> new_1, i_2 -> new_2, ...}] ...

Some Notes on Internal Implementation (Mathematica Tutorial)

General issues about the internal implementation of Mathematica are discussed in "The Internals of Mathematica". Given here are brief notes on particular features. These ...

Parallel Evaluation (Parallel Package Tutorial)

Recall that connections to remote kernels, as opened by LaunchKernels, are represented as kernel objects. See the chapter Connection Methods for details. The commands in this ...

GraphPlot (Built-in Mathematica Symbol)

GraphPlot[{v i 1 -> v j 1, v i 2 -> v j 2, ...}] generates a plot of the graph in which vertex v_ik is connected to vertex v_jk.GraphPlot[{{v i 1 -> v j 1, lbl_1}, ...}] ...

I (Built-in Mathematica Symbol)

I represents the imaginary unit Sqrt[-1].

Set (Built-in Mathematica Symbol)

lhs = rhs evaluates rhs and assigns the result to be the value of lhs. From then on, lhs is replaced by rhs whenever it appears. {l_1, l_2, ...} = {r_1, r_2, ...} evaluates ...

NumberTheory`NumberTheoryFunctions` (Mathematica Compatibility Information)

SquareFreeQ, PrimePowerQ, KroneckerSymbol, ChineseRemainder and PrimitiveRoot have been added to the built-in Mathematica kernel functions. NextPrime and PreviousPrime are ...

FullSimplify (Built-in Mathematica Symbol)

FullSimplify[expr] tries a wide range of transformations on expr involving elementary and special functions, and returns the simplest form it finds. FullSimplify[expr, assum] ...

ParallelCombine (Built-in Mathematica Symbol)

ParallelCombine[f, h[e_1, e_2, ...], comb] evaluates f[h[e_1, e_2, ...]] in parallel by distributing parts of the computation to all parallel kernels and combining the ...