The challenge of conciliating reliability with efficiency and the convergence of interests for experimental mathematics and applications is an opportunity to bring together end-users of computer algebra (in mathematics, theoretical physics, mechanism design, and other applications) with computer algebra experts. Fostering these exchanges will allow these communities to identify the different specifications, levels of certification and ways to harness computational power required by the core research of the community and in various application contexts and tackle the different complexity models. This will pave the way to the next generation of computer algebra algorithms and software. One of the main goals of this series of events is to push forward the current limits by investigating recent trends of this broad area, such as the design of algorithms exploiting and discovering structural properties, the hybridization of exact computing through rigorous numerical approximations, the guess-and-prove paradigms, as well as high performance computing issues. These are our means to provide better algorithmic and computer algebra software solutions to topical trans-disciplinary applications in engineering sciences, experimental mathematics and theoretical physics. These issues will be broadly covered with various computer algebra events we organize in 2023 in Lyon and Paris.