Introduction | The package in use | Conclusions and further work

Introduction | Lorentz transformations: active and passive | Successive Lorentz transformation | Units in which c is not 1 | Infinite speed of light | Vectorization | Multiple boosts | The stress-energy tensor | Photons | Three-velocities | Conclusions

Introduction | The hypergeo package | Package testing suite | The package in use

keep() and discard() | References

Further properties of Alt() | Wedge product | Further further properties of Alt() | Argument give_kform | References

Wedge products | $$(\mathrm{d}x\wedge\mathrm{d}y)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | $$(\mathrm{d}x\wedge\mathrm{d}y\wedge\mathrm{d}z)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix},\begin{pmatrix}w_1\w_2\w_3\end{pmatrix}\right) | The print method | $$(3\mathrm{d}y\wedge\mathrm{d}z)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | $$(1\mathrm{d}x\wedge\mathrm{d}y)\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | $$X\left(\begin{pmatrix}u_1\u_2\u_3\end{pmatrix},\begin{pmatrix}v_1\v_2\v_3\end{pmatrix}\right) | Configuring the print method | The Hodge dual | Creating elementary one-forms | Package dataset | References

Alternating forms | References

The tensor cross product | Verification | Note on associativity | References

R implementation | Verification | Orientation | Immediate properties | Vector products and the Hodge star operator | Vector cross products in 3 dimensions | Vector cross product identities | Edge-cases | References

References

Digression: function spraycross() | Cut to the chase: wedge2() | Algebraic properties | References

Distributivity | Reconstruction of a given tensor | Function Alt() | References

Some simple examples | Tidyup | References

The Hodge dual on basis elements of $\Lambda^k(V)$ | [\bigcup_ | More complicated examples | Small-dimensional vector spaces | Vector cross product identities | Non positive-definite metrics | Print methods for the Minkowski metric | Specifying the Minkowski metric | References

Package dataset | References

Contraction of products | Repeated contraction | Contraction from first principles | Worked example using contract_elementary() | The "meat" of contract() | References

Antiassociative algebras | The free antiassociative algebra | The evitaicossa package | Extract and replace methods | Note on disordR discipline | Matrix index extraction | Note on generalized antiassociativity | Appendix | References

The stokes package | Package idiom for evaluation of a tensor | Vector space structure of tensors | Numerical verification of multilinearity in the package | Tensor product of general tensors | Alternating forms | Wedge products and the exterior calculus | Formal definition of dx | Formal definition of wedge product | Print methods | Contractions | Transformations and pullback | Exterior derivatives | [ {d}\phi\left({v}i,\ldots,{v}{k+1}\right) | Differential of the differential, $d^2=0$ | Stokes's theorem | References

Matrix-based Jordan algebras, types 1,2,3 | Spin factors, type 5 | Albert algebras, type 4 | Special identities | Numerical verification of Jacobson | Numerical verification of $G_8$ | Numerical verification of $G_9$ | References

References

One-line notation for permutations | Print word as cycle | Commas | Symbols | Cycles in length order | Wrapup | References

Introduction | The package in use | Overloading | Primitive functions | Conclusions | References

Permutations of sets other than integers | Note on identity permutation | References

Introduction | Composition of active permutations | Composition of passive permutations | Permutation matrices | Passive language for permutation matrices | References

Introduction | The package in use | The Gaussian process | Functions of several complex variables | Numerical illustration of these ideas | Conclusions

First method | Second method | Note | Default | References

References

Lorentz transforms in terms of rapidity | $$\begin | Lorentz transforms in Clifford algebra | Numerical methods: Lorentz transforms using the Clifford package | Multiple boosts | Algebra of Clifford representations | References

Implementation | R implementation | Closure | References

Alternative mapping | References

References

References

Points | Sphere, IPNS | Sphere, OPNS | Planes | Circle | Lines and point pairs | References

Using Clifford algebra | Higher dimensional space | References

References

References

Introduction | The package in use | Pseudo-Euclidean spaces | Grassmann algebra | Positive-definite inner product | Left and right contractions | Higher dimensional spaces | Conclusions and further work

Introduction | Sparse arrays | The spray package and multivariate polynomials | Manipulation of coefficients | The package in use: some examples | Conclusions and further work | Package philosophy

Introduction | The package in use | Conclusions and further work | Gallery

Overview

[AB=(\alpha x^2yx + \beta zy)(-\beta zy + \gamma y^4) | [BA=(-\beta zy + \gamma y^4)(\alpha x^2yx + \beta zy) | The freealg package in use | Experimental functionality | References

The package in use | Comparison with mathematica | Further Weyl algebras | Derivations | Low-level considerations and generalizations | Generalized commutator relations | Note on use of disordR package | References

The STL map class | The package in use | Arithmetic operations | Substitution | Pipes | Vectorised substitution | Differentiation | Taylor series | Extraction | Negative powers | The disordR package | Multivariate generating functions | References

Preface | Introduction | Package onion in use | Conclusions

Introduction | onionmat objects | Matrix multiplication | Octonions | Note on the print method

Prologue: table() | Named vectors | The frab package | Note on repeated entries | Two dimensional R tables | Arbitrary-dimensioned R tables | Note on nomenclature | References

Package idiom | References

Island biogeography and biodiversity | Package untb in use | Conclusions

Numerical verification: matrix multiplication | Numerical verification: integration with the cubature package | References

Abstract | Introduction | An R session with the disordR package | An R session with the mvp package | vars() and powers() return disord objects | References

Overview | Introduction | Magic hypercubes | Conclusions

Introduction | The MM package | The package in use | Suggestions for further work | Conclusions

Introduction | Package design philosophy | Package gsl in use | Summary

Introduction | List of objects that the user needs to supply | Data analysis | Data generation

Introduction | Package partitions in use | Conclusions

Introduction | Algorithms | Applications | Note: a gotcha | Conclusions

Introduction | Examples | Conclusions

Introduction | List of objects that the user needs to supply | Data analysis | Data generation

Introduction | Emulation: computer output as a Gaussian process | Bayesian calibration: package calibrator | Design of package calibrator | Package calibrator in use | Bayesian calibration applied to a real problem in climate science | Conclusions

Introduction | List of objects that the user needs to supply | Design matrices | Basis functions | Hyperparameter object | Functions E.theta.int() and Edash.theta.int() | Data | Intermediate results | Estimating the hyperparameters | Calibrated prediction | Metropolis-Hastings

Package ResistorArray in use