Polymath^Plus

Math-Solver for students, scientists, and engineers
⬤ Enter a problem in plain text ▶ Press the Solve button ⬤ Get a numeric solution

Linear Equations	Nonlinear Equations
Differential Equations	Curve Fitting Regression

Polymath^Plus is free and will always remain free for students and professionals.

The Polymath^Plus solver is available as a web application. A link to the solver becomes visible on the left menubar after login. Please note that the Windows desktop application is no longer supported.

Our internal algorithms have been extensively used over the years by many engineering faculties in universities across the world. Students and professionals will appreciate the ease of use and the comprehensive solution reports of our application.

Supported Web Browsers

Chrome	85	Safari	14
Edge	85	Firefox	79
Opera	71

** Internet-Explorer is not supported.

Modules

Linear Equations

PolymathPlus can solve linear equations of any size. The number of equations should be equal to the number of unknown linear variables. Here's an example of 3 linear equations to be solved simultaneously:

Below are the equations entered into the PolymathPlus problem input text box (note that the # sign indicates user remarks and is being ignored by the program):

# linear equations a + 2*c = 50 b = -2 + c a + 23*c = 12 + b

Nonlinear Equations

When solving simultaneous nonlinear equations, the equations have to be written as root expressions (expressions that are equal to zero in the solution). In addition, an initial guess should be provided for each nonlinear variable.
Below is a sample problem and data entry for solving 2 nonlinear equations:

When entering the problem into PolymathPlus, we should enter the root expressions, each associated to a nonlinear variable function. We should also provide an initial estimate for each nonlinear variable. In the example below, we have 2 nonlinear variables x and y, hence 2 root functions, and we provide an initial guess of 1 for both x, and y.

f(x) = x^2 + y - 12 f(y) = 2*x + log(y+2) - 5 x(0)=1 y(0)=1

Note that we may also define any number of auxiliary expressions, to simplify long expressions, in this example we define a as an auxiliary expression:

f(x) = x^2 + y - 12 f(y) = 2*x + a a = log(y+2) - 5 x(0)=1 y(0)=1

In case we only have one nonlinear equation to solve (with any number of auxiliary expressions), we need to provide a min/max estimates for the nonlinear variable. For example, below is a PolymathPlus program for solving one nonlinear equation where we need to evaluate V:

f(V) = (P+a/(V^2))*(V-b)-R*T P=56 R=0.08206 T=450 Tc=405.5 Pc=111.3 Pr=P/Pc a=27*(R^2*Tc^2/Pc)/64 b=R*Tc/(8*Pc) Z=P*V/(R*T) V(min)=0.4 V(max)=1

Differential Equations

Entering and solving ordinary differential equations with PolymatPlus is simple.
Consider this set of equations to be solved:

Given the initial conditions x₀=1, y₀=4, at t₀=0, and having the integration finish at t_f=1,
the text below should be entered into PolymathPlus:

x' = x + 4*t^2 y' = sqrt(y) - x/(5-y) x|1 y|4 t|0:1

The following alternative compatible syntax can also be used for the same problem:

d(x)/d(t) = x + 4*t^2 d(y)/d(t) = sqrt(y) - x/(5-y) x(0)=1 y(0)=4 t(0)=0 t(f)=1

The solution will be displayed in a tabular format and will also include the integration chart:

Curve Fitting

PolymathPlus supports curve fitting for polynomial, multi-linear, and nonlinear regression. The report evaluates the model variables, generates a regression chart, residual plots, and provides statistics on the accuracy of the model.

Here is an example of the data entry required for solving a linear regression model for a given set of data points.
We solve a polynomial regression model with the order of 1 (hence linear regression) which best fits the linear equation matching the given data points.

polyfit <x> <y> <order> [origin]

# Linear regression example # Straight line fit to BOD data # BOD = a0 + a1*Time [ t BOD 1 0.6 2 0.7 4 1.5 6 1.9 8 2.1 10 2.6 12 2.9 14 3.7 16 3.5 18 3.7 20 3.8 ] Time = t + 10 polyfit Time BOD 1

Below is an example of a data entry for solving nonlinear regression model for a given set of data points. The model variables to be found are a and b, for which we should also provide an initial guess.

# Example: Nonlinear Regression [ x y g 0.5 1.255 1.2 0.387 1.25 1.3 0.24 1.189 1.4 0.136 1.124 2.0 0.04 0.783 2.1 0.011 0.402 2.2 ] # Nonlinear regression model nlinfit y = a * x / (b + x) # Initial guess of the # regression model variables a,b m(a)= 2 m(b)= 1

More examples can be found in this Help file.

Register

User registration is needed to access the online solver which becomes visible after login.

Contact Email

Name

Organization

Student Professional

Please don't use the form above to register the application on a public or cloud computers, site IT administrators should get a site registration license instead.

Site Admin Access

This section is relevant for academic/other organizations looking to use Polymath^Plus on their public lab or cloud computers.

To register a new site, first contact us with the following details: (1) Site name (2) IT contact email (3) Alternate email (4) Email extension/s for the organization. Then, we will provide an access key for the site. The instructions to install and register Polymath^Plus over multiple computers will be available via the access form below.

IT Access Form for Site Computers Registration

Sample Library

Linear and Explicit Equations

Nonlinear Equations

Differential Equations

Linear/Polynomial Regression

Multilinear Regression

Nonlinear Regression

Notes

Polymath^Plus is an initiative to create the best user-friendly, yet advanced math solver. We started with a Windows desktop application and extended it with an online web application.

Recently we decided to stop supporting the desktop version due to resource limitations. We want to keep PolymathPlus free, but we're short on resources. If you wish to support our effort, please contact us ✉ via email.

Recent Enhancements

Simplified user interface and input text syntax
Formatted equations presentation
Expanded examples menu
Optional comma as a decimal separator
Scalable Vector Graphics (SVG) formatted charts
Improved text editor
Settings per problem and default global setting
Text-based tables can be copied across spreadsheets
Self contained html solution report files
Variablea rename option
Performance improvement >30% faster execution
Record historical problems in log file
Online site registration for IT professionals

Long-Term Enhancements

We plan to expand the program's capabilities as community demand and support grows.
Here is a list of potential enhancements:

New algorithms e.g., Optimization
Embedded general purpose chart formatting utility
Embedded general purpose LaTex like math expressions writer
Enhanced calculator (matrix algebra, interpolation, derivative, integration)
Symbolic derivatives
Algebraic expressions pre-solution optimization
Cross platform package (Windows, Mac, Android, iPhone)
The online version has limited support for custom settings; for example - it only supports dot as a decimal separator, unlike the former desktop version that supports either dot or comma, based on the local culture.

Terms and Conditions

PolymathPlus does not warrant that the functions contained in the program will meet your requirements or that the operation of the program will be uninterrupted or error-free. In no event will PolymathPlus or its distributors or their dealers be liable to you for any damages, including any lost profit, lost savings, lost patience, or other incidental or consequential damage.
You may use PolymathPlus As Is and As Available on your own responsibility.
Data may be temporarily collected internally to improve performance and reliability.