This is a list of software and programming tools for the C programming language, including libraries, debuggers, compilers, integrated development environments (IDEs), and other related development tools and utilities. == Libraries and tools == Adns — asynchronous DNS resolver library Advanced Linux Sound Architecture — API for sound card device drivers Allegro — cross-platform software library for video game development Apache Portable Runtime — Apache web server tool set of APIs that map to the underlying operating system Argon2 — memory-hard password hashing library Berkeley DB — embedded database software library for key/value data Binary File Descriptor library — binary file manipulation library in the GNU toolchain Boehm garbage collector – conservative garbage collector Borland Graphics Interface — graphics library for Borland compilers BSAFE — FIPS 140-2 validated cryptography library Chipmunk — 2D real-time rigid body physics engine C POSIX library — specification of a C standard library for POSIX systems C standard library – standard library for the C programming language Cairo – vector graphics library API for software developers CFD General Notation System (CGNS) — data format and library for computational fluid dynamics cJSON — lightweight JSON parser CLIPS — public-domain software tool for building expert systems Core Audio — low-level API for dealing with sound in Apple's macOS and iOS operating systems Core Foundation — API for macOS and iOS and other Apple operating systems Core Image — GPU accelerated image processing technology for Apple operating systems with Quartz graphics rendering layer. Core Text — text layout and font rendering API for macOS and iOS. Cryptlib — portable cryptography library cURL / libcurl — CLI app for uploading and downloading individual files, such as a URL from a web server over HTTP. DevIL — cross-platform image library for loading and converting file formats DirectFB — graphics acceleration and input device handling library Dld — dynamic loading library Expat — stream-oriented XML 1.0 parser library, written in C99. FFmpeg — multimedia framework for audio/video processing Fontconfig — font customization and configuration library FreeTDS — database library for Sybase and Microsoft SQL Server FreeType — render text onto bitmaps with a font rasterization engine GD Graphics Library — image creation and manipulation library GDK — graphics abstraction layer for GTK GEGL — graph-based image processing framework GIO — I/O and virtual file system library in GLib GLib — utility library providing data structures, event loops, and portability functions. glibc — GNU implementation of the C standard library GLFW — library for OpenGL contexts, windows, and input device handling GNet — networking library for GLib GNU Libtool — Library management tool GNU portability library — collection of portability routines for GNU software GNU Portable Threads — POSIX/ANSI-C based user space thread library for UNIX for scheduling multithreading GNU Readline — command-line editing library GnuTLS — secure communications (TLS/SSL) library GObject — object system library for GNOME GTK — widget toolkit for creating graphical user interfaces GTK Scene Graph Kit (GSK) — scene graph and rendering toolkit for GTK HDF — file format and library for managing large datasets Integrated Performance Primitives — Intel library of optimized multimedia and data processing routines IUP — portable GUI toolkit J2K-Codec — JPEG 2000 image codec JasPer — reference implementation of the codec specified in the JPEG-2000 Part-1 standard LDAP API — API for interacting with Lightweight Directory Access Protocol LZO — lossless compression library Liba52 — decoder for A/52 (AC-3) audio streams libarchive — reading and writing various archive and compression formats Libart — 2D graphics library Libavcodec — codec library from FFmpeg Libavdevice — library for handling multimedia devices Libavfilter — audio and video filter library Libavformat — library for muxing and demuxing multimedia Libpcap — packet capture library Libdca — decoder for DTS audio Libdvdcss — access to encrypted DVD-Video discs libevent — asynchronous event notification callbacks libffi — foreign function interface libfuse — userspace filesystem Libgegl — programming interface to GEGL image processing libgcrypt — cryptography Libgimp — plug-in development library for GIMP Libhybris — compatibility layer for running Android libraries on Linux Libinput — input device library for Wayland and X.Org libjpeg — JPEG image library libLAS — reading and writing geospatial data encoded in the ASPRS laser (LAS) file format libmicrohttpd — small C library for embedding HTTP server functionality Libmpcodecs — media player codec library from MPlayer Libmpdemux — demultiplexing library from MPlayer libpng — PNG image format Libpostproc — video post-processing library from FFmpeg libpq — PostgreSQL client LibreSSL — fork of OpenSSL for TLS Librsb — parallel library for sparse matrix computations Librsvg — SVG rendering library libsndfile — reading and writing audio files libsodium — easy-to-use cryptography library Libswscale — image scaling and colorspace conversion library LibTIFF — TIFF image handling library Libusb — USB device access library Libuv — asynchronous I/O and event loop library LibVLC — media player engine from VLC LibVNCServer — implementation of the VNC server protocol Libvpx — VP8 and VP9 video codec library Libwww — early World Wide Web protocol library from W3C libxml2 — XML parsing Libxslt — XSLT library for the GNOME Project libzip — ZIP archives Lightning Memory-Mapped Database — fast key–value database engine LittleCMS — open-source color management system LZ4 — fast lossless compression algorithm LZFSE — compression library developed by Apple MatrixSSL — lightweight TLS implementation Mbed TLS — portable cryptography and TLS library MediaLib — Sun Microsystems library for multimedia processing Mesa — OpenGL and Vulkan graphics library Microwindows — small windowing system for embedded devices Ming — library for generating SWF (Flash) files Mongoose — embedded web server and networking library Mpg123 — MP3 audio decoding library MPIR — multiple-precision arithmetic library MsQuic — Microsoft implementation of the QUIC transport protocol MuJoCo — physics engine for robotics and control Mustache — logic-less templating library Ncurses — terminal control library Nettle — low-level cryptography library Newt — text-based user interface library Netpbm — graphics conversion and processing library Nghttp2 — implementation of the HTTP/2 protocol Oniguruma — regular expression library Open Asset Import Library — library to import/export 3D model formats OpenCL — parallel computing API/library OpenCV — computer vision OpenGL — API for rendering 2D and 3D vector graphics OpenGL Utility Library — OpenGL utility functions OpenJPEG — JPEG 2000 image codec OpenSSL — SSL and TLS protocols and cryptography library Pango — layout engine library which works with the HarfBuzz shaping engine for displaying multi-language text perf (Linux) — performance analyzing tool PCRE — regular expression library PROJ — library for map projections and coordinate transforms Quartz 2D — 2D graphics rendering API for macOS and iOS platforms, part of the Core Graphics framework. Raylib — simple library for games and multimedia Redland RDF Application Framework — RDF data storage library S2n-tls — TLS implementation from AWS Setcontext — context switching library functions SDL — Simple DirectMedia Layer systemd — system and service manager libraries for Linux Tk — GUI widgets for building graphical user interfaces VDPAU — video decoding acceleration API Vorbis — audio compression codec library VTD-XML — high-performance XML parser Wimlib — library for handling Windows Imaging Format disk images Windows.h — base Windows API header file WolfSSH — lightweight SSH library WolfSSL — lightweight SSL/TLS library X Toolkit Intrinsics — toolkit library for the X Window System x264 — H.264 video codec library XCB — C binding for the X Window System protocol Xft — font rendering library using FreeType Xlib — low-level X Window System API XMDF — eXtensible Model Data Format for scientific data XMLStarlet — XML command-line toolkit zlib — data compression Zopfli — data compression library that performs deflate, gzip and zlib data encoding. Zstd — fast data compression library == Integrated development environments == Anjuta — GNOME IDE CLion — cross-platform commercial IDE from JetBrains Code::Blocks — cross-platform open-source IDE CodeLite — open-source IDE Dev-C++ Eclipse CDT Geany — text editor with IDE features KDevelop — KDE IDE NetBeans Qt Creator SlickEdit Visual Studio Xcode === Online IDEs === CodeSandbox — online IDE primarily for web development with some C support via containers GitHub Codespaces — cloud-based online IDE developed by GitHub Google Cloud Shell — browser-based shell and editor that can comp
Intelligent agent
In artificial intelligence, an intelligent agent is an entity that perceives its environment, takes actions autonomously to achieve goals, and may improve its performance through machine learning or by acquiring knowledge. AI textbooks define artificial intelligence as the "study and design of intelligent agents," emphasizing that goal-directed behavior is central to intelligence. A specialized subset of intelligent agents, agentic AI (also known as an AI agent or simply agent), expands this concept by proactively pursuing goals, making decisions, and taking actions over extended periods. Intelligent agents can range from simple to highly complex. A basic thermostat or control system is considered an intelligent agent, as is a human being, or any other system that meets the same criteria—such as a firm, a state, or a biome. Intelligent agents operate based on an objective function, which encapsulates their goals. They are designed to create and execute plans that maximize the expected value of this function upon completion. For example, a reinforcement learning agent has a reward function, which allows programmers to shape its desired behavior. Similarly, an evolutionary algorithm's behavior is guided by a fitness function. Intelligent agents in artificial intelligence are closely related to agents in economics, and versions of the intelligent agent paradigm are studied in cognitive science, ethics, and the philosophy of practical reason, as well as in many interdisciplinary socio-cognitive modeling and computer social simulations. Intelligent agents are often described schematically as abstract functional systems similar to computer programs . To distinguish theoretical models from real-world implementations, abstract descriptions of intelligent agents are called abstract intelligent agents. Intelligent agents are also closely related to software agents—autonomous computer programs that carry out tasks on behalf of users. They are also referred to using a term borrowed from economics: a "rational agent". == Intelligent agents as the foundation of AI == The concept of intelligent agents provides a foundational lens through which to define and understand artificial intelligence. For instance, the influential textbook Artificial Intelligence: A Modern Approach (Russell & Norvig) describes: Agent: Anything that perceives its environment (using sensors) and acts upon it (using actuators). E.g., a robot with cameras and wheels, or a software program that reads data and makes recommendations. Rational Agent: An agent that strives to achieve the best possible outcome based on its knowledge and past experiences. "Best" is defined by a performance measure – a way of evaluating how well the agent is doing. Artificial Intelligence (as a field): The study and creation of these rational agents. Other researchers and definitions build upon this foundation. Padgham & Winikoff emphasize that intelligent agents should react to changes in their environment in a timely way, proactively pursue goals, and be flexible and robust (able to handle unexpected situations). Some also suggest that ideal agents should be "rational" in the economic sense (making optimal choices) and capable of complex reasoning, like having beliefs, desires, and intentions (BDI model). Kaplan and Haenlein offer a similar definition, focusing on a system's ability to understand external data, learn from that data, and use what is learned to achieve goals through flexible adaptation. Defining AI in terms of intelligent agents offers several key advantages: Avoids Philosophical Debates: It sidesteps arguments about whether AI is "truly" intelligent or conscious, like those raised by the Turing test or Searle's Chinese Room. It focuses on behavior and goal achievement, not on replicating human thought. Objective Testing: It provides a clear, scientific way to evaluate AI systems. Researchers can compare different approaches by measuring how well they maximize a specific "goal function" (or objective function). This allows for direct comparison and combination of techniques. Interdisciplinary Communication: It creates a common language for AI researchers to collaborate with other fields like mathematical optimization and economics, which also use concepts like "goals" and "rational agents." == Objective function == An objective function (or goal function) specifies the goals of an intelligent agent. An agent is deemed more intelligent if it consistently selects actions that yield outcomes better aligned with its objective function. In effect, the objective function serves as a measure of success. The objective function may be: Simple: For example, in a game of Go, the objective function might assign a value of 1 for a win and 0 for a loss. Complex: It might require the agent to evaluate and learn from past actions, adapting its behavior based on patterns that have proven effective. The objective function encapsulates all of the goals the agent is designed to achieve. For rational agents, it also incorporates the trade-offs between potentially conflicting goals. For instance, a self-driving car's objective function might balance factors such as safety, speed, and passenger comfort. Different terms are used to describe this concept, depending on the context. These include: Utility function: Often used in economics and decision theory, representing the desirability of a state. Objective function: A general term used in optimization. Loss function: Typically used in machine learning, where the goal is to minimize the loss (error). Reward Function: Used in reinforcement learning. Fitness Function: Used in evolutionary systems. Goals, and therefore the objective function, can be: Explicitly defined: Programmed directly into the agent. Induced: Learned or evolved over time. In reinforcement learning, a "reward function" provides feedback, encouraging desired behaviors and discouraging undesirable ones. The agent learns to maximize its cumulative reward. In evolutionary systems, a "fitness function" determines which agents are more likely to reproduce. This is analogous to natural selection, where organisms evolve to maximize their chances of survival and reproduction. Some AI systems, such as nearest-neighbor, reason by analogy rather than being explicitly goal-driven. However, even these systems can have goals implicitly defined within their training data. Such systems can still be benchmarked by framing the non-goal system as one whose "goal" is to accomplish its narrow classification task. Systems not traditionally considered agents, like knowledge-representation systems, are sometimes included in the paradigm by framing them as agents with a goal of, for example, answering questions accurately. Here, the concept of an "action" is extended to encompass the "act" of providing an answer. As a further extension, mimicry-driven systems can be framed as agents optimizing a "goal function" based on how closely the agent mimics the desired behavior. In generative adversarial networks (GANs) of the 2010s, an "encoder"/"generator" component attempts to mimic and improvise human text composition. The generator tries to maximize a function representing how well it can fool an antagonistic "predictor"/"discriminator" component. While symbolic AI systems often use an explicit goal function, the paradigm also applies to neural networks and evolutionary computing. Reinforcement learning can generate intelligent agents that appear to act in ways intended to maximize a "reward function". Sometimes, instead of setting the reward function directly equal to the desired benchmark evaluation function, machine learning programmers use reward shaping to initially give the machine rewards for incremental progress. Yann LeCun stated in 2018, "Most of the learning algorithms that people have come up with essentially consist of minimizing some objective function." AlphaZero chess had a simple objective function: +1 point for each win, and -1 point for each loss. A self-driving car's objective function would be more complex. Evolutionary computing can evolve intelligent agents that appear to act in ways intended to maximize a "fitness function" influencing how many descendants each agent is allowed to leave. The mathematical formalism of AIXI was proposed as a maximally intelligent agent in this paradigm. However, AIXI is uncomputable. In the real world, an intelligent agent is constrained by finite time and hardware resources, and scientists compete to produce algorithms that achieve progressively higher scores on benchmark tests with existing hardware. == Agent function == An intelligent agent's behavior can be described mathematically by an agent function. This function determines what the agent does based on what it has seen. A percept refers to the agent's sensory inputs at a single point in time. For example, a self-driving car's percepts might include camera images, lidar data, GPS coordinates, and speed r
Argument Web
The Argument Web is a large-scale Web of interconnected arguments created by individuals as they express their opinions and interact with the opinions of others. The Argument Web aims to make online debate intuitive for participants such as mediators, students, academics, broadcasters and bloggers, to create a Web infrastructure that allows for the storage, automatic retrieval and analysis of linked argument data, and to improve the quality of online argument and debate. The Argument Web can be described as a portion of a larger Semantic Web. == AIFdb == AIFdb is a database implementation or ‘reification’ of the Argument Interchange Format (AIF), which allows for the storage and retrieval of AIF compliant argument structures. This database solution was provided as a foundation for an open, integrated Argument Web. It offers an extensive range of web services for interacting with stored argument data, while also offering search and argument visualisation features that are all consistent with the formal ontology of AIF. At a basic level, the AIFdb web services allow for the insertion and querying of basic components of an AIF argument, such as nodes, edges and schemes. Building upon this basis, it also facilitates more complex interactions with these AIF argument structures. Such complex queries could make it possible, for example, to determine all the statements made by a particular person in support a given I-Node. While, at its highest level of interaction, AIFdb can handle the import and export of many standard file formats, including SVG, DOT, RDF/XML and other formats of argument theory tools, like Carneades, Rationale and Araucaria. == Argument blogging == ArguBlogging is software which allows its users to select portions of hypertext on webpages in their Web browsers and to agree or disagree with the selected content, posting their arguments to their blogs with linked argument data. It is implemented as a bookmarklet, adding functionality to Web browsers and interoperating with blogging platforms such as Blogger and Tumblr.
Polyworld
Polyworld is a cross-platform (Linux, Mac OS X) program written by Larry Yaeger to evolve Artificial Intelligence through natural selection and evolutionary algorithms. It uses the Qt graphics toolkit and OpenGL to display a graphical environment in which a population of trapezoid agents search for food, mate, have offspring, and prey on each other. The population is typically only in the hundreds, as each individual is rather complex and the environment consumes considerable computer resources. The graphical environment is necessary since the individuals actually move around the 2-D plane and must be able to "see." Since some basic abilities, like eating carcasses or randomly generated food, seeing other individuals, mating or fighting with them, etc., are possible, a number of interesting behaviours have been observed to spontaneously arise after prolonged evolution, such as cannibalism, predators and prey, and mimicry. Each individual makes decisions based on a neural net using Hebbian learning; the neural net is derived from each individual's genome. The genome does not merely specify the wiring of the neural nets, but also determines their size, speed, color, mutation rate and a number of other factors. The genome is randomly mutated at a set probability, which are also changed in descendant organisms.
Dominic Harris
Dominic Harris (born 16 November 1976) is a British artist known for integrating modern technology and classical design in his interactive artworks. == Background == Dominic Harris was born in London on 16 November 1976, and grew up in London, Brussels, and Michigan before returning to London in 1995. Harris attended the Cranbrook Kingswood Upper School, and then trained as an architect at the Bartlett School of Architecture, and has been ARB registered since 2011. Harris designs and fabricates his artworks at Dominic Harris Studio, a multi-disciplinary practice he founded in 2007. This studio consists of 25 people with diverse backgrounds including architecture, product design, electronics, programming, graphic design, and workshop skills. Harris uses the resources of his studio for the ongoing development, prototyping and production of his artworks. Harris also oversees the studio's international projects where his fascinations are translated into larger scale projects that span residential, retail, and public art projects. In 2015, Harris was granted permission by the Walt Disney Company to use their Intellectual Property for the purpose of making new interactive artworks. Harris is the only artist to gain permission to use Disney's back catalogue of characters, and led him to creating his interactive versions of "Snow White and the Seven Dwarfs" and "Mickey and Minnie: An Interactive Diptych". Harris is fascinated by the idea of using data streams, algorithms, and computer code to generate dynamic and ever-changing artworks. He sees data as a raw material that can be transformed into visual poetry. Many of his installations and sculptures are interactive, responding to the presence and movement of viewers/participants. This creates an immersive experience where the observer becomes part of the artwork itself. Harris is also the founding partner of a sister studio in London called Cinimod Studio that creates large commissioned installations, interactive events and lighting designs for large brands. == Works == == Exhibitions == The works of Dominic Harris have been exhibited internationally, both through direct and gallery representation. Solo shows: "Feeding Consciousness" at Halcyon Gallery, Mayfair, London, UK – 2023 "US: NOW" at Halcyon Gallery, Mayfair, London, UK – 2020 "Imagine" at Halcyon Gallery, Mayfair, London, UK – 2019 "5 Year Celebration", Priveekollektie Contemporary Art | Design, London, UK – 2016. "Moments of Reflection" at PHOS ART + DESIGN, Mayfair, London, UK – 2015 Recent exhibitions include: In Plain Sight, 2024 Halcyon Gallery Victoria & Albert Museum Dublin Science Museum Design Miami / Basel Design Miami Art Miami Art 14, London PAD Paris PAD London Art Geneva == Gallery Representation == 2010 to 2019: Dominic Harris was represented by Priveekollektie Contemporary Art | Design, a Dutch gallery based in Heusden, the Netherlands, and with a regular presence on the international art and design circuits. 2015: Dominic Harris was shown with PHOS ART + DESIGN Gallery, in Mayfair, London, UK. 2019 – ongoing: Dominic Harris is exclusively represented by the Halcyon Gallery, an established international gallery based in Mayfair, London. == Collections == The majority of Harris's work has been bought by private collectors. Since 2012 Harris's work is also being acquired by several large institutional collections, including the Borusan Contemporary Art Collection in Istanbul. Harris's artworks include some of the biggest and most respected international art collectors and are also displayed in public spaces. == Books == Dominic Harris: Feeding Consciousness. Halcyon Gallery, 2023. Imagine: Dominic Harris (exhibition catalogue). Halcyon Gallery, 2019. A Touch Of Code: Documents the "Beacon" art installation and "Flutter" artwork (ISBN 978-3899553314) Dominic Harris, Artworks, Edition Eight. (ISBN 978-0957306325) Digital Real: Kunst & Nachhaltigkeit Vol 8.
Tensor operator
In pure and applied mathematics, quantum mechanics and computer graphics, a tensor operator generalizes the notion of operators which are scalars and vectors. A special class of these are spherical tensor operators which apply the notion of the spherical basis and spherical harmonics. The spherical basis closely relates to the description of angular momentum in quantum mechanics and spherical harmonic functions. The coordinate-free generalization of a tensor operator is known as a representation operator. == The general notion of scalar, vector, and tensor operators == In quantum mechanics, physical observables that are scalars, vectors, and tensors, must be represented by scalar, vector, and tensor operators, respectively. Whether something is a scalar, vector, or tensor depends on how it is viewed by two observers whose coordinate frames are related to each other by a rotation. Alternatively, one may ask how, for a single observer, a physical quantity transforms if the state of the system is rotated. Consider, for example, a system consisting of a molecule of mass M {\displaystyle M} , traveling with a definite center of mass momentum, p z ^ {\displaystyle p{\mathbf {\hat {z}} }} , in the z {\displaystyle z} direction. If we rotate the system by 90 ∘ {\displaystyle 90^{\circ }} about the y {\displaystyle y} axis, the momentum will change to p x ^ {\displaystyle p{\mathbf {\hat {x}} }} , which is in the x {\displaystyle x} direction. The center-of-mass kinetic energy of the molecule will, however, be unchanged at p 2 / 2 M {\displaystyle p^{2}/2M} . The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p{\mathbf {\hat {x}} }} . The kinetic energy on the other hand must be represented by a scalar operator, whose expected value must be the same in the initial and the rotated states. In the same way, tensor quantities must be represented by tensor operators. An example of a tensor quantity (of rank two) is the electrical quadrupole moment of the above molecule. Likewise, the octupole and hexadecapole moments would be tensors of rank three and four, respectively. Other examples of scalar operators are the total energy operator (more commonly called the Hamiltonian), the potential energy, and the dipole-dipole interaction energy of two atoms. Examples of vector operators are the momentum, the position, the orbital angular momentum, L {\displaystyle {\mathbf {L} }} , and the spin angular momentum, S {\displaystyle {\mathbf {S} }} . (Fine print: Angular momentum is a vector as far as rotations are concerned, but unlike position or momentum it does not change sign under space inversion, and when one wishes to provide this information, it is said to be a pseudovector.) Scalar, vector and tensor operators can also be formed by products of operators. For example, the scalar product L ⋅ S {\displaystyle {\mathbf {L} }\cdot {\mathbf {S} }} of the two vector operators, L {\displaystyle {\mathbf {L} }} and S {\displaystyle {\mathbf {S} }} , is a scalar operator, which figures prominently in discussions of the spin–orbit interaction. Similarly, the quadrupole moment tensor of our example molecule has the nine components Q i j = ∑ α q α ( 3 r α , i r α , j − r α 2 δ i j ) . {\displaystyle Q_{ij}=\sum _{\alpha }q_{\alpha }\left(3r_{\alpha ,i}r_{\alpha ,j}-r_{\alpha }^{2}\delta _{ij}\right).} Here, the indices i {\displaystyle i} and j {\displaystyle j} can independently take on the values 1, 2, and 3 (or x {\displaystyle x} , y {\displaystyle y} , and z {\displaystyle z} ) corresponding to the three Cartesian axes, the index α {\displaystyle \alpha } runs over all particles (electrons and nuclei) in the molecule, q α {\displaystyle q_{\alpha }} is the charge on particle α {\displaystyle \alpha } , and r α , i {\displaystyle r_{\alpha ,i}} is the i {\displaystyle i} -th component of the position of this particle. Each term in the sum is a tensor operator. In particular, the nine products r α , i r α , j {\displaystyle r_{\alpha ,i}r_{\alpha ,j}} together form a second rank tensor, formed by taking the outer product of the vector operator r α {\displaystyle {\mathbf {r} }_{\alpha }} with itself. == Rotations of quantum states == === Quantum rotation operator === The rotation operator about the unit vector n (defining the axis of rotation) through angle θ is U [ R ( θ , n ^ ) ] = exp ( − i θ ℏ n ^ ⋅ J ) {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right)} where J = (Jx, Jy, Jz) are the rotation generators (also the angular momentum matrices): J x = ℏ 2 ( 0 1 0 1 0 1 0 1 0 ) J y = ℏ 2 ( 0 i 0 − i 0 i 0 − i 0 ) J z = ℏ ( − 1 0 0 0 0 0 0 0 1 ) {\displaystyle J_{x}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&1&0\\1&0&1\\0&1&0\end{pmatrix}}\,\quad J_{y}={\frac {\hbar }{\sqrt {2}}}{\begin{pmatrix}0&i&0\\-i&0&i\\0&-i&0\end{pmatrix}}\,\quad J_{z}=\hbar {\begin{pmatrix}-1&0&0\\0&0&0\\0&0&1\end{pmatrix}}} and let R ^ = R ^ ( θ , n ^ ) {\displaystyle {\widehat {R}}={\widehat {R}}(\theta ,{\hat {\mathbf {n} }})} be a rotation matrix. According to the Rodrigues' rotation formula, the rotation operator then amounts to U [ R ( θ , n ^ ) ] = 1 1 − i sin θ ℏ n ^ ⋅ J − 1 − cos θ ℏ 2 ( n ^ ⋅ J ) 2 . {\displaystyle U[R(\theta ,{\hat {\mathbf {n} }})]=1\!\!1-{\frac {i\sin \theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} -{\frac {1-\cos \theta }{\hbar ^{2}}}({\hat {\mathbf {n} }}\cdot \mathbf {J} )^{2}.} An operator Ω ^ {\displaystyle {\widehat {\Omega }}} is invariant under a unitary transformation U if Ω ^ = U † Ω ^ U ; {\displaystyle {\widehat {\Omega }}={U}^{\dagger }{\widehat {\Omega }}U;} in this case for the rotation U ^ ( R ) {\displaystyle {\widehat {U}}(R)} , Ω ^ = U ( R ) † Ω ^ U ( R ) = exp ( i θ ℏ n ^ ⋅ J ) Ω ^ exp ( − i θ ℏ n ^ ⋅ J ) . {\displaystyle {\widehat {\Omega }}={U(R)}^{\dagger }{\widehat {\Omega }}U(R)=\exp \left({\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right){\widehat {\Omega }}\exp \left(-{\frac {i\theta }{\hbar }}{\hat {\mathbf {n} }}\cdot \mathbf {J} \right).} === Angular momentum eigenkets === The orthonormal basis set for total angular momentum is | j , m ⟩ {\displaystyle |j,m\rangle } , where j is the total angular momentum quantum number and m is the magnetic angular momentum quantum number, which takes values −j, −j + 1, ..., j − 1, j. A general state within the j subspace | ψ ⟩ = ∑ m c j m | j , m ⟩ {\displaystyle |\psi \rangle =\sum _{m}c_{jm}|j,m\rangle } rotates to a new state by: | ψ ¯ ⟩ = U ( R ) | ψ ⟩ = ∑ m c j m U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =U(R)|\psi \rangle =\sum _{m}c_{jm}U(R)|j,m\rangle } Using the completeness condition: I = ∑ m ′ | j , m ′ ⟩ ⟨ j , m ′ | {\displaystyle I=\sum _{m'}|j,m'\rangle \langle j,m'|} we have | ψ ¯ ⟩ = I U ( R ) | ψ ⟩ = ∑ m m ′ c j m | j , m ′ ⟩ ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle |{\bar {\psi }}\rangle =IU(R)|\psi \rangle =\sum _{mm'}c_{jm}|j,m'\rangle \langle j,m'|U(R)|j,m\rangle } Introducing the Wigner D matrix elements: D ( R ) m ′ m ( j ) = ⟨ j , m ′ | U ( R ) | j , m ⟩ {\displaystyle {D(R)}_{m'm}^{(j)}=\langle j,m'|U(R)|j,m\rangle } gives the matrix multiplication: | ψ ¯ ⟩ = ∑ m m ′ c j m D m ′ m ( j ) | j , m ′ ⟩ ⇒ | ψ ¯ ⟩ = D ( j ) | ψ ⟩ {\displaystyle |{\bar {\psi }}\rangle =\sum _{mm'}c_{jm}D_{m'm}^{(j)}|j,m'\rangle \quad \Rightarrow \quad |{\bar {\psi }}\rangle =D^{(j)}|\psi \rangle } For one basis ket: | j , m ¯ ⟩ = ∑ m ′ D ( R ) m ′ m ( j ) | j , m ′ ⟩ {\displaystyle |{\overline {j,m}}\rangle =\sum _{m'}{D(R)}_{m'm}^{(j)}|j,m'\rangle } For the case of orbital angular momentum, the eigenstates | ℓ , m ⟩ {\displaystyle |\ell ,m\rangle } of the orbital angular momentum operator L and solutions of Laplace's equation on a 3d sphere are spherical harmonics: Y ℓ m ( θ , ϕ ) = ⟨ θ , ϕ | ℓ , m ⟩ = ( 2 ℓ + 1 ) 4 π ( ℓ − m ) ! ( ℓ + m ) ! P ℓ m ( cos θ ) e i m ϕ {\displaystyle Y_{\ell }^{m}(\theta ,\phi )=\langle \theta ,\phi |\ell ,m\rangle ={\sqrt {{(2\ell +1) \over 4\pi }{(\ell -m)! \over (\ell +m)!}}}\,P_{\ell }^{m}(\cos {\theta })\,e^{im\phi }} where Pℓm is an associated Legendre polynomial, ℓ is the orbital angular momentum quantum number, and m is the orbital magnetic quantum number which takes the values −ℓ, −ℓ + 1, ... ℓ − 1, ℓ The formalism of spherical harmonics have wide applications in applied mathematics, and are closely related to the formalism of spherical tensors, as shown below. Spherical harmonics are functions of the polar and azimuthal angles, ϕ and θ respectively, which can be conveniently collected into a unit vector n(θ, ϕ) pointing in the direction of those angles, in the Cartesian basis it is: n ^ ( θ , ϕ ) = cos ϕ sin θ e x + s
Hostile Waters: Antaeus Rising
Hostile Waters, released as Hostile Waters: Antaeus Rising in America, is a hybrid vehicle and strategy game developed and published by Rage Software for Microsoft Windows. It was inspired by Carrier Command (Realtime Games, 1988). It has won several awards and one unofficial award from Rock Paper Shotgun as a "lost classic" or "The best game you've never played". == Plot == Hostile Waters takes place in a Utopian future where war has been abolished. In the year 2012, a revolutionary war takes place between the corrupt and power-hungry politicians, leaders and businessmen (described as the "Old Guard") and the people. The Old Guard were defeated, with only a few of their leaders escaping. By 2032, the world has been rebuilt as a utopia, with the help of nano-technological assemblers, which are used in "creation engines" to create matter from energy and waste, for free. The newly united world is governed from a capital city known as Central. Missile attacks are suddenly launched against major cities all over the world from an unknown location. This is eventually discovered to be an island chain in the South Pacific Ocean. A response to the missile attacks was a special forces team sent in to investigate the area for preliminary investigations. The Ministry of Intelligence (MinIntel) loses contact with it shortly thereafter. The world government authorises a reactivation of the Antaeus program, a series of warships able to create any weapon of their choosing using their on-board nano-technological creation engine. Two of these were left on the seabed in the case of an emergency, capable of being re-activated and refloating itself. On board are a series of "soulcatcher" chips, a classified 1990s military program researched into for the storage of human brain functions on a silicon chip. The soulcatcher technology was used to store the minds of every crew member ever assigned to an Antaeus vessel. It is soon discovered that one of the cruisers does not respond to the awakening signal. The other cruiser, however, is refloated and re-activated, with heavy damage to vital ship components. A course is plotted for a nearby disused wet-dock. As the Antaeus progresses from the wet-dock, unusual biological life-forms are discovered amongst the enemy bases on the islands. The identity of the aggressor firing the missiles is confirmed as the leftovers of the old, pre-Central forces, known as the Cabal. Outnumbering Central's army a thousand to one, they are fighting with thousands of troops and weapons that they hid away when it was apparent that the war was lost. The Antaeus is deployed into the chicane to stop the Cabal's operations there. It's later discovered that along with their superior numbers, they have also biologically engineered a species of organic machines, designed in the popular likeness of extraterrestrials, which they intend to use to create the fear of an alien invasion, to facilitate their taking over the world and the removal of the public use of creation engines. The Cabal later lose control of the species, which eventually turns on its masters, destroying them. The species starts spreading, modifying the planetary climate and geographical features in an attempt to exterminate humanity and make the planet more hospitable to itself. Having exterminated its creators, the species resolves to cleanse humanity as a whole from the planet using a massive 'disassembler cannon', only to be stopped by the Antaeus. The species subsequently attempts to flee into the cosmos and colonise the surrounding planets and stars, by launching a massive number of 'culture stones' (information devices that also double as creation engines) into space from an enormous, artificially-grown organic "island", the final staging point. Central's only option is to bind the Antaeus' creation engine and the disassembler cannon stolen from the aliens together to create a makeshift bomb, and detonate it at the central "column" containing the culture stones. The plan succeeds, and the Antaeus is sacrificed to save the world. The final cinematic show the organic disassembler cannon and the Antaeus' creation engine moving closer together and fusing, creating something new. A post-credits scene also shows that two of the species' culture stones have managed to get into space. == Gameplay == Each Mission takes place on and or near a fortified enemy island containing various forms of anti-air and ground defence, with scattered unit-production complexes powered by oil-derricks and fuel containers (which are dependent on the oil-derricks) that the player can destroy to keep the enemy from replacing destroyed forces. Vehicles are built on the Antaeus and, if desired, land vehicles can be delivered to a location by the air-lifting "magpie". Units are created by providing Antaeus with a number of resources which are obtained at the beginning of the level and debris which are taken from destroyed enemy units and structures. Transport helicopters such as the "Pegasus" can fly to an object and airlift it to the ship-board recycling system with little resources required. The carrier can analyse objects it disassembles at the rear of the Antaeus cruiser, and several of the game's vehicles and items are unlocked by "sampling" them in this fashion. The game has a number of vehicles that are progressively unlocked as the missions progress. Vehicles contain a number of slots for equipment and a selection of different types of weapons to use in the vehicle. A variety of vehicle equipment combinations can be designed. Vehicles have an individual damage multiplier such that different vehicles with the same weapon will do different damage. In addition to this, each soul-chip personality specializes in one unit along with specific equipment, which, if equipped will gain them a bonus in efficiency. == Development == The game was developed by 12 people. == Reception == The game received "favourable" reviews according to the review aggregation website Metacritic. Carla Harker of NextGen said, "You'll feel like a real battlefield general when you take to the field in Antaeus Rising." Jake The Snake of GamePro said, "If the usual game categories leave you unscathed, get bloodied in these Hostile Waters."