Math-Solver for Students, Scientists, and Engineers ⬤ Enter a problem in plain text ▶ Press the Solve button ⬤ Get a numeric solution
Curve Fitting Regression
Embracing our vision, we offer a vibrant, free version of our user-friendly Math Solver.
The PolymathPlus solver is available as a web application or a Windows desktop application. A link to the online solver becomes visible on the left menubar after login.
We are encouraging users to switch to the online version while keeping support for the Windows desktop application for paid licenses.
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
Version 7.0.46 (from Feb 14, 2024) has the following key changes:
The student license was upgraded to support up to 50 explicit auxiliary equations
Support for very large number of ODEs (>1000) for pro licenses
Numerical integration of experimental data points
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
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.
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
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:
The solution will be displayed in a tabular format and will also include the integration chart:
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
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
Access to the online solver requires users to be registered and logged in. Once logged in, users can access the online solver. If you're a new user, please fill out the form below to register and gain login access.
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.
For private desktop installation registration please enter the username on the Name field, and the computer name on the Organization field.
Site License Admin Access
This section pertains to organizations purchasing bulk licenses, who may also intend to utilize PolymathPlus on their public lab computers.
To view or renew the site license, please access the site admin page using the form below.
IT Access Form
To initiate the registration of a new site, please reach out to us and provide the following details:
Arizona State University
IT contact email
ABC College 123 University Avenue College Town, CA 98765 United States
Then, we will provide an access key with which you can get invoices, purchase licenses, and read the proliferation instructions.
For cost and further license types details check this licenses section.
We are pleased to announce that we will be offering new site licenses for PolymathPlus. These licenses are
designed for institutions and organizations that require multiple-user access to our software. With a site license,
you will have the flexibility to purchase a bulk quantity of either student or professional licenses, such as 100
student licenses for a site.
Designated site administrators will have online management capabilities through the Site Admin page.
For example, they will be provided with a unique activation key for both the online program and the desktop application.
Site licenses will be sold in bulk quantities of 50 licenses at a 50% discount or 100 licenses at a 70% discount.
per 50 users
per 100 users
per 50 users
per 100 users
Institutions with site licenses may continue to install the desktop version on their public computers. Additional details are available on the Site Admin page.
We are pleased to offer the following individual user license types:
This license will enable users to access a curated set of features that encompass a wide
range of functionalities. We believe it is important to provide an accessible version of our software for
individuals who may have limited resources or are new to mathematical modeling.
As its name suggests, all registered users are automatically granted a free license, enabling them to use the online PolymathPlus web application.
Designed specifically for students, this license offers a comprehensive set of features at
an affordable price. With the student license, users will have access to advanced mathematical tools and
functions, making it an ideal choice for educational purposes.
Tailored to meet the needs of professionals and researchers, the professional
license provides the complete range of features and capabilities offered by PolymathPlus. This license is
priced accordingly to support ongoing product development and customer support.
The following table lists program capacities and features per license.
Capacity & Features
Lines of code
Program file size
Online saved programs
Supporting auxiliary variables
Regression data points
Regression model variables
Intermediate data points table
Solver requests per month
Windows desktop application
Advanced tools ie. Latex
Annual Costsales tax included (USD)
∞ Maximized within reasonable resource limits. ✱ Users who registered for PolymathPlus before August 28, 2023, will maintain their full access until Jan 2024. ✱ The Windows desktop application will be available for Std/Pro licenses during October 2023 following a formal announcement.
Users can purchase individual licenses through their online profile page.
Online and Desktop Programs
The online version of PolymathPlus has several advantages over the traditional desktop version. We advocate using it for the following reasons:
Accessibility: The online version allows users to access the software from any device with internet
connectivity, eliminating the need for software installations and updates.
Cross-Platform Compatibility: Our online version is compatible with various operating systems and
devices, i.e. Windows, macOS, Linux, Android, and iOS, providing users a seamless experience across platforms.
Collaboration and Sharing: With the online version, users can easily collaborate with peers, share
calculations, and work on projects collectively. This fosters a sense of community and encourages
knowledge exchange among users.
Development of the desktop version will be slowed down until we secure adequate funds to align it with our online version.
Click any question below for an answer:
➕ 1. What is PolymathPlus?
PolymathPlus is math-solving software designed for students, scientists, and engineers.
Our goal is to provide the world's leading, user-friendly, and advanced math-solving tool, available and affordable to users globally.
With PolymathPlus, you can:
Enter a math problem in plain text.
Press the 'Solve' button.
Get a numeric solution report.
➕ 2. Is PolymathPlus free?
PolymathPlus offers a free online package designed to solve various numerical problems. This includes tackling challenges such as nonlinear equations, ordinary differential equations, linear, polynomial, and nonlinear curve fitting, and more.
Additionally, PolymathPlus offers premium packages that are equipped to handle more complex tasks. For instance, these packages are capable of solving larger problems, such as situations involving more than five simultaneous nonlinear equations or ordinary differential equations.
To access these solver packages, users are required to sign up by following a free simple registration process which grants users the access they need to leverage the capabilities offered by PolymathPlus.
Please note that the free package is designed for individual users. Organizations interested in utilizing our software are kindly requested to add their site to our database and purchase site licenses for their student and/or professional users.
➕ 3. Can I use PolymathPlus from my Windows/Mac laptop?
Yes. The online version of PolymathPlus is accessible from all modern browsers and devices. This includes laptops and desktops running Windows or macOS, utilizing any of the following supported web browsers: Chrome, Safari, Opera, Firefox, and Edge.
The software can also be used on Android and iOS smartphones, as well as tablets, using the Chrome, Safari, Opera, and Firefox browsers.
Additionally, we offer a dedicated desktop version, currently available exclusively for Windows computers.
➕ 4. How can I try the online solver?
Simply visit the PolymathPlus main page and register by clicking the Register menu item on the left panel. Upon submission, a login password will be sent to your email. Registration is free and simple.
After receiving the password, you can log in and access the online solver package by clicking the Solver button in the left menu bar.
➕ 5. What type of licenses does PolymathPlus offer?
PolymathPlus provides three types of individual user licenses:
The Student and Pro licenses are priced at 15 USD and 50 USD per year respectively.
PolymathPlus also offers site licenses that come with a discounted rate for bulk licenses.
Check ☛ this link for more details on the capabilities of each license.
➕ 6. Which mathematical algorithms does PolymathPlus use?
PolymathPlus utilizes finely tuned solver algorithms that have been derived from renowned numerical recipes.
These algorithms have undergone rigorous testing over the course of more than 20 years, effectively solving practical problems.
➕ 7. What is the history of PolymathPlus?
The core development team of PolymathPlus also created the earlier Polymath application, which was widely utilized as a numerical solver package within the global community of Chemical Engineers.
The development was also encouraged by:
CACHE The Computer Aids for Chemical Engineering Education Corporation, as part of the
AIChE The American Institute of Chemical Engineers
After the dissolution of the Polymath team/organization, the principal developer took the initiative to rekindle the project. Drawing from more than 25 years of software development and extensive research in numerical packages, a new package was crafted.
The new organization has its foundation in Georgia , specifically in Tbilisi. Our office, though modest, serves as a hub for our dedicated staff.
We maintain ties with many US-based universities and others worldwide.
➕ 8. Does PolymathPlus offer a desktop version package?
Indeed, we offer a Windows desktop version for both Student and Pro individual licenses, which can be downloaded from the user profile page. However, the free license does not include the desktop package. Sites with an active site license can install the desktop version on their public lab computers, but users covered by the site license can only use the desktop version on those public computers.
Access to the Windows desktop application mandates a login using your online user account.
At present, our focus remains on the online and Windows desktop platforms, and there aren't immediate plans for a desktop version compatible with Mac or Linux. Nonetheless, this direction could be influenced by user demand and available resources.
It's worth highlighting that the online version is platform agnostic. This means that users across Windows, Mac, Linux, iOS, and Android can seamlessly use the platform-independent online version.
➕ 9. What is the user profile page?
The user profile page displays user preferences and provides insight into the license status. In addition, it offers users the ability to upgrade their license by purchasing an individual student or professional license or claiming a site license.
For claiming a site license, the user is required to possess the access key. This access key is exclusively available to members of sites that have procured a bulk site license.
➕ 10. What is the 'Site Admin' page, and who can use it?
The 'Site Admin' page is specifically designed for IT site administrators who have acquired a site license for their organization. Access to the Site Admin page necessitates the use of a dedicated access key.
This page is designed to provide essential information about configuring the site license, as well as the distribution and utilization of various packages.
➕ 11. I am interested in procuring a site license for my organization. What steps should I take?
To initiate the registration of a new site, kindly ✉ contact us and furnish the following information:
Site name (i.e. Arizona State University)
IT contact email and backup email
Email extension(s) for the organization (i.e. @asu.edu, @student.asu.edu)
Subsequently, we will furnish an access key. This key empowers the Site Admin IT contact to access the 'Site Admin' page. On this page, they can undertake tasks like setting up invoices/licenses and following proliferation instructions.
The aim is to facilitate the granting of student or pro licenses to site users. These licenses can be utilized via online access or on-site lab/cloud computers equipped with the desktop application.
➕ 12. How can I link my existing account to a site license my organization purchased?
Users are required to complete online registration first. Afterward, they can proceed to their profile page and initiate the process of 'Claiming a Site License'. This entails entering a designated special key, which is exclusively provided by their organization's IT Administrator.
Notably, this unique site license key is intended solely for use by individuals affiliated with the organization.
Here are the steps for users who are members of the site:
Open the profile page (click 'My Profile' on the left menubar panel), on the bottom licenses section check the 'Claim Site License' option box
Enter the site specific key that was provided by the Site IT Admin.
Save the Profile.
Logout, and then log back in.
You should be able to see the license type on the title bar of the Solver page. The linked site name will be shown on the status bar panel.
➕ 13. Desktop application fails with WebView2 controllers compatibility
You may need to upgrade to the latest Microsoft Edge Web browser on your computer.
PolymathPlus embeds web content via the Microsoft Edge WebView2 Runtime. Hence, the Windows desktop application requires the WebView2 Runtime in case Microsoft Edge is not already installed on the computer. You can download the WebView2 Runtime from Microsoft Evergreen Bootstrapper.
If the application errors with 'The system cannot find the file specified (0x80070002)' you may need to manually download and install 'WebView2 Runtime' from this Microsoft web link: WebView2 Evergreen Bootstrapper
➕ 14. Troubleshooting: Too many steps in routine or step size underflow
This error occurs when the numerical solver algorithm uses an adaptive step size to maintain error control and reduces the step size excessively, hindering progress in solving the equation set. This is leading to too many steps for getting the solution.
To address this error you may follow these steps:
First ensure the equations are entered correctly as intended. For example: unintentionally using multiplier instead of division: a/b*c vs. a/(b*c)
Verify that all variables are scaled appropriately, ensuring uniformity in magnitude.
Verify unit conversions
Consider reducing the integration range between t(0) and t(f)
You may consider switching to another solving algorithm. You can do these steps by using program hints.
ODE solution method algorithm indexes are: 0=RKF45, 1=RKF56, 2=BS, 3=Stiff, 4=StiffBS. The default solution is 1=RKF56. Here's an example for hint to change to Stiff.
#@DEQ_SOLUTION_METHOD_INDEX = 3
Finally, in rare cases, you may consider adjusting the step size parameters for better efficiency. You can do these steps by using program hints.
Sample hints to control the step size and the error tolerance:
➕ 15. Troubleshooting: LNSRCH: Roundoff problem in lnsrch
The program's arithmetic operations result in invalid numbers (i.e. infinite).
The arithmetic operations generate numbers that are too large or too small leading to significant accuracy errors.
Consider changing initial/final values or explicit variables values. Pay special attention to power operations which may result in huge numbers.
➕ 16. How can I support PolymathPlus?
By purchasing the software, you are supporting its sustainability and ongoing development.
Additionally, we are actively seeking sponsors to support our work. We firmly believe that PolymathPlus has the potential to bring substantial benefits to universities, organizations, and their respective communities.
By becoming a sponsor, your institution can play a pivotal role in advancing mathematical modeling and calculations while also receiving recognition for supporting this widely-used tool.
Organizations interested in sponsoring our activities can ✉ contact us directly.
PolymathPlus began as a Windows desktop application and expanded its offerings to include an online web application. Our passion and dedication drive us to continually innovate and refine our solutions. We are committed to providing a top-notch numerical solver package to tackle mathematical challenges with ease and confidence.
We have recently initiated a new operation in the picturesque region of Georgia. With high hopes and aspirations, we aim to expand our reach and make a more significant and positive impact on the academic and scientific communities.
PLMT Plus LLC
Otar Kinkladze Street, N39 Chughureti District Tbilisi 0101 Georgia
+1 530 405 9303 Pre-scheduled calls: 08:00-10:00 AM ET
Deliver the world's premier, user-friendly, yet advanced math solver, accessible and affordable for users worldwide, empowering learners, professionals, and enthusiasts to confidently conquer mathematical challenges.
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.
Please carefully read the terms of service indicated in the link below.