Math Solver

The SymPy symbolic math library in Python can do pretty much any kind of math, solving equations, simplifying, factoring, substituting values for variables, pretty printing, converting to LaTeX format, etc. etc. It seems to be a pretty robust solver in my very limited use so far. I recommend trying it out.

If you want to avoid using a graphical interface, but you still want to do computer algebra, then sympy or maxima may cover your needs. (sympy looks very promising, but it still have a long way to go before they can replace mathematica).

Math Solver

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When solving for more than one variable, the order in which you specify the variables defines the order in which the solver returns the solutions. Assign the solutions to variables solv and solu by specifying the variables explicitly. The solver returns an array of solutions for each variable.

By default, solve does not apply simplifications that are not valid for all values of x. In this case, the solver does not assume that x is a positive real number, so it does not apply the logarithmic identity log(3x)=log(3)+log(x). As a result, solve cannot solve the equation symbolically.

solve applies simplifications that allow the solver to find a solution. The mathematical rules applied when performing simplifications are not always valid in general. In this example, the solver applies logarithmic identities with the assumption that x is a positive real number. Therefore, the solutions found in this mode should be verified.

Try to get an explicit solution for such equations by calling the solver with 'MaxDegree'. The option specifies the maximum degree of polynomials for which the solver tries to return explicit solutions. The default value is 2. Increasing this value, you can get explicit solutions for higher order polynomials.

Equation to solve, specified as a symbolic expression or symbolic equation. The relation operator == defines symbolic equations. If eqn is a symbolic expression (without the right side), the solver assumes that the right side is 0, and solves the equation eqn == 0.

Maximum degree of polynomial equations for which solver uses explicit formulas, specified as a positive integer smaller than 5. The solver does not use explicit formulas that involve radicals when solving polynomial equations of a degree larger than the specified value.

Solutions of a system of equations, returned as symbolic variables. The number of output variables or symbolic arrays must be equal to the number of independent variables in a system. If you explicitly specify independent variables vars, then the solver uses the same order to return the solutions. If you do not specify vars, the toolbox sorts independent variables alphabetically, and then assigns the solutions for these variables to the output variables.

If solve cannot find a solution and ReturnConditions is false, the solve function internally calls the numeric solver vpasolve that tries to find a numeric solution. For polynomial equations and systems without symbolic parameters, the numeric solver returns all solutions. For nonpolynomial equations and systems without symbolic parameters, the numeric solver returns only one solution (if a solution exists).

For many students, math can be a particularly challenging subject in school. Math is sequential, in that each lesson is part of the foundation for future learning. If students do not have a solid understanding of each concept as they go, it may impact their ability to build the skills necessary to understand more complex and abstract mathematical concepts in the future.

The impact of Covid-19 has forced students to use more digital learning tools and incorporate their web browser into everyday learning. Students rely on the browser to help them find solutions to their studies, including math. To help these students on their learning journey, we are excited to announce that Microsoft Math Solver will be available as a preview feature starting with Microsoft Edge 91 stable.

We are rolling this out as a preview feature, and are still exploring the possibility of including the feature permanently in the future. Our goal with including Microsoft Math Solver in Microsoft Edge is to bring more equity in learning by democratizing math learning for students who need help but are unable to get access to help.

A new grid-based Boltzmann equation solver, Acuros, was developed specifically for performing accurate and rapid radiotherapy dose calculations. In this study we benchmarked its performance against Monte Carlo for 6 and 18 MV photon beams in heterogeneous media. Acuros solves the coupled Boltzmann transport equations for neutral and charged particles on a locally adaptive Cartesian grid. The Acuros solver is an optimized rewrite of the general purpose Attila software, and for comparable accuracy levels, it is roughly an order of magnitude faster than Attila. Comparisons were made between Monte Carlo (EGSnrc) and Acuros for 6 and 18 MV photon beams impinging on a slab phantom comprising tissue, bone and lung materials. To provide an accurate reference solution, Monte Carlo simulations were run to a tight statistical uncertainty (sigma approximately 0.1%) and fine resolution (1-2 mm). Acuros results were output on a 2 mm cubic voxel grid encompassing the entire phantom. Comparisons were also made for a breast treatment plan on an anthropomorphic phantom. For the slab phantom in regions where the dose exceeded 10% of the maximum dose, agreement between Acuros and Monte Carlo was within 2% of the local dose or 1 mm distance to agreement. For the breast case, agreement was within 2% of local dose or 2 mm distance to agreement in 99.9% of voxels where the dose exceeded 10% of the prescription dose. Elsewhere, in low dose regions, agreement for all cases was within 1% of the maximum dose. Since all Acuros calculations required less than 5 min on a dual-core two-processor workstation, it is efficient enough for routine clinical use. Additionally, since Acuros calculation times are only weakly dependent on the number of beams, Acuros may ideally be suited to arc therapies, where current clinical algorithms may incur long calculation times.

You may know a significant amount of code snippets for several of the common tasks such as solutions to quadratic, cubic, transcendental equations, etc. are available at many sites online, especially math and computational departments at universities that have a strong focus on engineering and physics-related disciplines. Also of interest, particularly for the case of your immediate interest, is the Rossetta Code site which offers a worked solution that looks comprehensive: _of_a_quadratic_function#Fortran_90

Many math functions have variants like sqrt, dsqrt, csqrt. These were necessary back in the Fortran 77 days, but they are not necessary any more. On top of that, if you change your program to use higher precision complex numbers, then csqrt will either (a) cause a compiler error or (b) cause a loss of precision in the square root calculation. Whether you get (a) or (b) depends on your compiler and what compilation flags you have set.

To help students, teachers, and others with math problems, you can use structured data to indicate the type of math problems and links to step-by-step walkthroughs for specific math problems. Here's an example of how math solvers may look in Google Search results (the appearance is subject to change):

Here's an example of a math solver home page that has two solver endpoints: one endpoint can solve polynomial equations and the other endpoint can solve trigonometric equations. It is available only in English.

We created these Math Solver content guidelines to ensure that our users are connected with learning resources that are relevant. If we find content that violates these policies, we'll respond appropriately, which may include taking manual action and removing your pages from appearing in the math solver experience on Google.

A placeholder for a mathematical expression (for example: x^2-3x=0) that is sent by Google to your website. You can then "solve" the math expression, which may involve simplifying, transforming, or solving for a specific variable. The string can take many formats (for example: LaTeX, Ascii-Math, or mathematical expressions that you can write with a keyboard).

For some problem types, the math_expression_string indicates both the problem type and parameters of the problem type. Here are some examples of the more complicated problem types so that you can anticipate and parse them correctly.

Use the following list of problem types as either the eduQuestionType for a MathSolver.potentialAction or for the assesses field of a MathSolver when the MathSolver is accompanying a HowTo that walks through a specific math problem.

Over the last few years, variational quantum algorithms (VQAs) have emerged as a leading strategy to realize a quantum advantage on NISQ devices. Specifically, VQAs employ shallow circuit depths to optimize a cost function, expressed in terms of an Ansatz with tunable parameters, through iterative evaluations of expectation values5. Applications of VQAs include the variational quantum eigensolver (VQE) for finding the ground or excited states of a system Hamiltonian6,7,8, the quantum approximate optimization algorithm (QAOA) for solving combinatorial optimization problems9, and solvers for linear10,11,12 and non-linear13 systems of equations.

Consider the second-order homogeneous evolution equation defined on the set \(\Omega \times J\), where \(\Omega \subset \mathbb R^d\) denotes a d-dimensional bounded spatial domain and \(J = [0,T]\), where \(T>0\) denotes a bounded temporal domain, as

A variational quantum solution is to prepare a state \(| u \rangle\) such that \(A | u \rangle\) is proportional to a state \(| b \rangle\) in a way that satisfies Eq. (10). To do that, a canonical approach10,11,12 is to first decompose the matrix A over the Pauli basis \(\mathcal P_n = \{P_1\otimes \cdots \otimes P_n: \forall i,P_i \in \{I,X,Y,Z\} \}\) (where \(X=|1\rangle \!\langle 0| +|0\rangle \!\langle 1|\), \(Y = i|1\rangle \!\langle 0| -i |0\rangle \!\langle 1|\), and \(Z=|0\rangle \!\langle 0| -|1\rangle \!\langle 1|\) are the Pauli matrices and \(I=|0\rangle \!\langle 0| +|1\rangle \!\langle 1|\) is the identity matrix) as 2351a5e196